Design Optimization for Shear Key on the TF Coil Structure of the KSTAR Tokamak
The KSTAR tokamak is comprised of a magnet system, vacuum vessel, and cryostat, thereby facilitating vacuum conditions for plasma gas at high temperatures, along with low-temperature helium gas for cooling. The TF coil structure, a part of the magnet system, is constructed and jointed with 16 pieces...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
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irk-123456789-1734152020-12-04T01:26:27Z Design Optimization for Shear Key on the TF Coil Structure of the KSTAR Tokamak Lee, D.S. Kwon, Y.D. Han, J.S. Научно-технический раздел The KSTAR tokamak is comprised of a magnet system, vacuum vessel, and cryostat, thereby facilitating vacuum conditions for plasma gas at high temperatures, along with low-temperature helium gas for cooling. The TF coil structure, a part of the magnet system, is constructed and jointed with 16 pieces at 22.5-degree intervals using a conical bolt and shear key. The main function of the shear key in the inner and outer inter-coil structures is to resist in-plane and out-of-plane forces and to increase the shear stiffness for the inter coil structures. However, since the shape of the shear key is difficult to produce and can incur high costs, the shear key needs to be dimensionally optimized to regularize the stress between the key and the structure. Accordingly, shape optimization of the shear key was carried out using the Taguchi method and the stresses analyzed by ANSYS. 2016 Article Design Optimization for Shear Key on the TF Coil Structure of the KSTAR Tokamak / D.S. Lee, Y.D. Kwon, J. S. Han // Проблемы прочности. — 2016. — № 1. — С. 39-46. — Бібліогр.: 14 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/173415 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Научно-технический раздел Научно-технический раздел |
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Научно-технический раздел Научно-технический раздел Lee, D.S. Kwon, Y.D. Han, J.S. Design Optimization for Shear Key on the TF Coil Structure of the KSTAR Tokamak Проблемы прочности |
| description |
The KSTAR tokamak is comprised of a magnet system, vacuum vessel, and cryostat, thereby facilitating vacuum conditions for plasma gas at high temperatures, along with low-temperature helium gas for cooling. The TF coil structure, a part of the magnet system, is constructed and jointed with 16 pieces at 22.5-degree intervals using a conical bolt and shear key. The main function of the shear key in the inner and outer inter-coil structures is to resist in-plane and out-of-plane forces and to increase the shear stiffness for the inter coil structures. However, since the shape of the shear key is difficult to produce and can incur high costs, the shear key needs to be dimensionally optimized to regularize the stress between the key and the structure. Accordingly, shape optimization of the shear key was carried out using the Taguchi method and the stresses analyzed by ANSYS. |
| format |
Article |
| author |
Lee, D.S. Kwon, Y.D. Han, J.S. |
| author_facet |
Lee, D.S. Kwon, Y.D. Han, J.S. |
| author_sort |
Lee, D.S. |
| title |
Design Optimization for Shear Key on the TF Coil Structure of the KSTAR Tokamak |
| title_short |
Design Optimization for Shear Key on the TF Coil Structure of the KSTAR Tokamak |
| title_full |
Design Optimization for Shear Key on the TF Coil Structure of the KSTAR Tokamak |
| title_fullStr |
Design Optimization for Shear Key on the TF Coil Structure of the KSTAR Tokamak |
| title_full_unstemmed |
Design Optimization for Shear Key on the TF Coil Structure of the KSTAR Tokamak |
| title_sort |
design optimization for shear key on the tf coil structure of the kstar tokamak |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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2016 |
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Научно-технический раздел |
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http://dspace.nbuv.gov.ua/handle/123456789/173415 |
| citation_txt |
Design Optimization for Shear Key on the TF Coil Structure of the KSTAR Tokamak / D.S. Lee, Y.D. Kwon, J. S. Han // Проблемы прочности. — 2016. — № 1. — С. 39-46. — Бібліогр.: 14 назв. — англ. |
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Проблемы прочности |
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2025-07-15T10:04:22Z |
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| fulltext |
UDC 539.4
Design Optimization for Shear Key on the TF Coil Structure of the KSTAR
Tokamak
D. S. Lee,
a,1
Y. D. Kwon,
b
and J. S. Han
c
a Division of Computer Aided Mechanical Engineering, Yeungjin College, Daegu, Republic of Korea
b Department of Mechanical Engineering, Kyungpook National University, Daegu, Republic of Korea
c Graduate School, Kyungpook National University, Daegu, Republic of Korea
1 dslee@yjc.ac.kr
The KSTAR tokamak is comprised of a magnet system, vacuum vessel, and cryostat, thereby
facilitating vacuum conditions for plasma gas at high temperatures, along with low-temperature
helium gas for cooling. The TF coil structure, a part of the magnet system, is constructed and jointed
with 16 pieces at 22.5-degree intervals using a conical bolt and shear key. The main function of the
shear key in the inner and outer inter-coil structures is to resist in-plane and out-of-plane forces and
to increase the shear stiffness for the inter coil structures. However, since the shape of the shear key
is difficult to produce and can incur high costs, the shear key needs to be dimensionally optimized to
regularize the stress between the key and the structure. Accordingly, shape optimization of the shear
key was carried out using the Taguchi method and the stresses analyzed by ANSYS.
Keywords: KSTAR, Taguchi method, optimization, shear key, TF coil structure.
Introduction. The development of nuclear fusion is becoming the main energy of the
future. As part of this process, plasma needs to be sealed at an ultrahigh temperature in a
fixed space for 1 s. The sealed space is called Tokamak that is a device sealing up plasma
as sending an electric current to the plasma existing a powerful magnetic field and at
Tokamak’s center to prevent fusing due to contact with the plasma. Korea is currently
constructing a nuclear fusion power plant on the basis of Korea Superconducting Tokamak
Advanced Research (KSTAR) [1–3]. The toroidal field (TF) coil structure of the KSTAR
tokamak is D-shaped, with a size of 4.2 m�3 m�22.5� (height width angle), and
assembled into a total of 16 fan-shapes. The inner and outer inter-coil are joined at the top
and bottom, and shear key [4, 5] used to support the shear force in terms of gravity and set
assembling datum, as shown in Fig. 1.
Thus, this paper fixes the design factors for optimizing the shape of the shear key and
selects models to perform a finite element analysis [6, 7] with an orthogonal array, plus
CATIA is used for the modeling, ANSYS for the finite element analysis, and the Taguchi
method for the optimization and statistical analysis.
© D. S. LEE, Y. D. KWON, J. S. HAN, 2016
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 1 39
Fig. 1. The shape of TF coil structure for KSTAR.
Optimization of Shear Key.
The Taguchi Method [8, 9]. A table of an orthogonal array has been used for efficient
design in a discrete design space, and it can produce similar results to the trial and error
method (one-factor-at-a-time) with a small size experiment by combining the factors used
to design the experiment. Therefore, this paper used a table of an orthogonal array to
optimize the shape of the shear key, determine the target optimum conditions, and evaluate
the stability of these conditions. Circular and rectangular shapes are known to reduce the
maximum stress of the shear key. Thus, the table initially covered five kinds of the factor,
including the shape of the shear key and two kinds of level. Yet, since it was impossible to
obtain the optimal conditions due to the influence of the same interaction for each different
shape of the shear key, the shear key was optimized for each shape according to the
strength of the shape and convenience of productivity. Thus, final factors and levels are
shown in Table 1. In this paper, each shape has four kinds of the factor and two kinds of
level.
The table of the orthogonal array used was L8 (27). The level of the design factors
was determined based on the initial design factors, then each matrix from the table of the
orthogonal array tested, resulting in a corresponding objective function. Then, a characteristic
value was identified using the characteristic function accorded to the objective function.
After that, the optimum design value was determined through a mean analysis based on the
characteristic function and compared with the value for each matrix tested. To select the
optimum level, the effects of different design factors on the design values were evaluated,
and the statistical analysis used the signal-to-noise ratios. Taguchi defined several signal to
noise ratios, according to the performance characteristics. The signal to noise ratio, a value
induced from a quality loss function assigned with a second-order formula, is a measure
that considers both the mean and the distribution of the performance characteristics. In this
paper, the maximum stress that appears at the shear key is a smaller-the-better characteristic.
Thus, the signal-to-noise was performed according to a smaller-the-better type analysis.
Smaller-then-better type: S N
n
yi
i
n
��
�
�
�
�
�
�
�
�10
1
10
2
0
log ,
where n is the frequency of the repeated measurements under a combination of similar
control factors and yi is the value of each measurement to perform the finite element
analysis. Thus, the design factor conditions that maximized the signal-to-noise ratio were
found by considering the objective function of the characteristic value on the table of the
orthogonal array. As a result, the design factor conditions that produced a small variation in
the performance characteristics under noise and the mean were identified using the
D. S. Lee, Y. D. Kwon, and J. S. Han
40 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 1
T a b l e 1
Factors and Levels
Factor Level
1 (left side) 2 (right side)
A Key hole Exist Nothing
B Material Inconel 718 Brass
C Aspect ratio 1:1 1:0.8
D Fillet of flange Exist Nothing
E, F, G Error effect – –
objective function. This paper also determined the design factor conditions where the
objective function was the maximum stress obtained from the shear key, the characteristic
value on the table of the orthogonal array, and the mean was the minimum. Plus, the
significant design factors were determined based on a 95% confidence interval using
ANOVA (analysis of variation). To validate the optimization conditions, the optimized
final model according to the Taguchi method was performed using a finite element
analysis. Finally, it can be conformed the reappearance for signal-to-noise ratio.
Design Factors. For the TF coil structure, the shear key [10] is the datum for
assembling with inner and outer inter-coil structure and is supported shear force in terms of
gravity. Optimizing its shape is important because the TF coil structure’s shear key has
many spatial limitations. Figure 2 shows a cross-section of the TF coil structure, while
Table 2 shows the grade and properties of the material used in the TF coil structure.
The sample structures made according to the table of the orthogonal array were
subjected to a finite element analysis and analyzed for their maximum stress. The boundary
condition gave a load of 1 MN with the shear force in terms of the gravity of the structure.
The contact condition between the parts was used as the surface-to-surface [10–14]. In the
finite element analysis (FEA), the main assumption was the conical bolt and a lot of the
bolts were tightened in the structure, and in the case of the circular-type shear key, when it
gave the shear force in terms of gravity, the structure was not allowed to open at the circle
line and additional pre-tension occurred at the conical bolt, plus a lot of bolts was not
allowed.
Optimization of Circular-Type Shear Key. Table 3 shows the results of the FEA for
eight models of a circular shear key (see Fig. 2a, b) when using an orthogonal array.
At this table, converted stresses of shear key mean the stress that multiplied the
calculated stress by the ratio of yield stress (
y Inconel y brass, , � 2.3) between brass and
Design Optimization for Shear Key ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 1 41
T a b l e 2
Section Drawing of TF Coil Structure
No. Part name Material Young modulus
(MPa)
Poisson’s
ratio
1 Inner inter-coil structure JJ1 186 105. � 0.280
2 Outer inter-coil structure JJ1 186 105. � 0.295
3 Shear key Inconel 718 211 105. � 0.295
Brass 106 105. � 0.292
a b c d
Fig. 2. Section drawing for design factors of circular type shear key and rectangular type shear key.
Inconel to consider similar stress condition. When comparing the S N ratio for the stress
calculated using the orthogonal array (Table 3), the results are shown in Fig. 3. As a result
of the ANOVA analysis of the interaction for each design factor of a circular shear key, the
percentage contribution left much to be desired and is the design factors were found to be
independent of each other.
Table 4 shows the optimum shape model for the shear key as regards the smaller-the-
better type value based on the effect of the design factors (Fig. 3).
An FEA of the shear key model was also performed, and the model with the minimum
stress for the shear key compared with the samples in the orthogonal array (see Table 5).
The FEA results for the optimized circular shear key are shown in Fig. 4.
42 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 1
T a b l e 3
The Result of FEA by Using Orthogonal Array
No. Key hole Material Aspect ratio Fillet of flange Converted stress (MPa)
# 1 R � 5 mm Inconel 1:1 R � 5 mm 344
# 2 R � 5 mm Inconel 1:1 No 237
# 3 R � 5 mm Brass 1:0.8 R � 5 mm 2699
# 4 R � 5 mm Brass 1:0.8 No 2529
# 5 No Inconel 1:0.8 R � 5 mm 848
# 6 No Inconel 1:0.8 No 497
# 7 No Brass 1:1 R � 5 mm 386
# 8 No Brass 1:1 No 280
T a b l e 4
Optimum Shape of the Rounding Shear Key
Factor Optimized model Level
A Key hole No 2
B Material Inconel 718 1
C Aspect ratio 1:1 1
D Fillet of flange No 2
Fig. 3. Illustration of design factor effect.
T a b l e 5
The Results of FEA
Item Shear key
Model # 8 140 MPa
Optimized model 137 MPa
D. S. Lee, Y. D. Kwon, and J. S. Han
FEA Optimization of Rectangular-Type Shear Key. Table 6 shows the results of the
FEA for eight models with a rectangular shear key (see Fig. 4c, d) when using an
orthogonal array.
As the circular-type shear key, converted stresses of shear key mean the stress that
multiplied the calculated stress by the ratio of yield stress (
y Inconel y brass, , � 2.3)
between brass and Inconel to consider similar stress condition. From Table 6, after
comparing S N ratio for the stress calculated using the orthogonal array, the results are
shown in Fig. 5.
As a result of the ANOVA analysis of the interaction for each design factor of a
rectangular shear key, an effective interaction (42.7%) was found between the key hole and
the aspect ratio. But interactions between the key hole and the material, between the key
and fillet of the flange were ignored due to low percentage contribution. Thus, the key hole
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 1 43
a b
Fig. 4. FEA result of the optimized shear key structure (a); FEA result of the optimized shear key (b).
T a b l e 6
The Result of FEA by Using Orthogonal Array
No. Key hole Material Aspect ratio Fillet of flange Converted stress (MPa)
# 1 R � 5 mm Inconel 1:1 R � 5 mm 372
# 2 R � 5 mm Inconel 1:1 No 751
# 3 R � 5 mm Brass 1:0.8 R � 5 mm 855
# 4 R � 5 mm Brass 1:0.8 No 1586
# 5 No Inconel 1:0.8 R � 5 mm 322
# 6 No Inconel 1:0.8 No 275
# 7 No Brass 1:1 R � 5 mm 777
# 8 No Brass 1:1 No 611
Fig. 5. Illustration of design factor effect (A�B/A�C/A�D: interaction).
Design Optimization for Shear Key ...
and aspect ratio were found to be interdependent, while the other two variables were
independent. Table 7 shows the optimum shape model for the rectangular shear key as
regards the smaller-the-better type value based on the effect of the design factors (Fig. 5).
An FEA of the shear key model was also conducted, as shown in Table 7, and the
model with the minimum stress for the shear key was the same with sample # 6 in
orthogonal array (see Table 8).
The FEA results for the optimized rectangular shear key are shown in Fig. 6.
From the FEA results, the stress of the rectangular shear key was 200.7% higher
compared to the circular shear key (circular/rectangular = 137 MPa/275 MPa). When the
shear force of the circular shear key occurred due to the weight between inter-coil
structures, the shear force was generated in the circumference direction and caused a gap
between the inter-coil structures. Especially, the conical bolt joining the TF coil structure
had the potential to be over-supported by pre-tension. While it is difficult to manufacture a
44 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 1
T a b l e 7
Optimum Shape of the Rectangular Shear Key
Factor Optimized model Level
A Key hole No 2
B Material Inconel 718 1
C Aspect ratio (1:1) � Not use 1
D Fillet of flange No 2
A�B Key hole Neglect due to
low % contribution
–
Material
A�C Key hole No 2
Aspect ratio 1:0.8 2
A�D Key hole Neglect due to
low % contribution
–
Fillet of flange
T a b l e 8
The Results of FEA
Item Shear key
Optimized model (model # 6) 275 MPa
a b
Fig. 6. FEA result of the optimized shear key structure (a); FEA result of the optimized shear key (b).
D. S. Lee, Y. D. Kwon, and J. S. Han
semicircular shaped inter-coil structure, a rectangular shear key can be easily manufactured,
and support the whole shear force. As such, a rectangular shear key was found to be a
suitable alternative to a circular shear key.
Taguchi Optimization of Rectangular-Type Shear Key. The optimized shape for the
rectangular shear key was obtained using the Taguchi method. The assembly of the shear
key and flange was also optimized. First, the effect of the gap between the shear key and
the flange was examined. As shown in Fig. 7, when confirming the stress change of the
shear key for the gap, the least stress was obtained with a fillet (R � 5 mm) for the flange.
Table 9 shows the stress improvement ratio when optimizing the fillet of the shear key
and flange.
The FEA results for optimizing the fillet of the rectangular shear key are shown in
Fig. 8.
Conclusions. This study optimized the shape of the shear key joining the TF coil
structure of the KSTAR tokamak, and the results were as follows:
1. To optimize the shape of the shear key, the present study used an orthogonal array
of an experimental design and the Taguchi method, which is a statistical design and quality
technique.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 1 45
T a b l e 9
Stress as Fillet of the Shear Key
Item Shear key
Optimized model by Taguchi 275.0 MPa
Optimized model (gap = 3.2 mm) 211.6 MPa
Improving ratio 29.8%
Fig. 7. Stress change of the shear key as gap.
a b
Fig. 8. Analysis result of optimized shear key structure (a); analysis result of optimized shear key (b).
Design Optimization for Shear Key ...
2. The design specifications with the least stress were obtained when using optimized
circular and rectangular shear keys based on the Taguchi method.
3. The design variables for the circular shear key were independent, so 4 variables
could be separately applied as design variables, which is advantageous.
4. A rectangular shear key was obtained by simultaneously considering the interaction
between the key hole and aspect ratio.
5. From the FEA results, the stress of the circular shear key was more than twice
lower compared to the rectangular shear key (circular/rectangular = 137 MPa/275 MPa).
Thus, the circular shear key exhibited an advantage as regards shear force.
6. By adjusting the gap and fillet between the rectangular shear key and flange, the
stress of the shear key was reduced by 29.8%.
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Hyundai Heavy Industries Co., Ltd., Korea Basic Science Institute (2001).
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Press (1999).
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bending rigidity: restricted and unrestricted step sizes,” Int. J. Mod. Phys. B, 12, No. 14,
1531–1538 (1998).
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Element Analysis, 3rd edition, John Wiley & Sons, New York (1989).
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elements through modification of Gauss integration,” Int. J. Mod. Phys. B, 17, No. 8-9,
1877–1883 (2003).
14. Y. D. Kwon, N. S. Goo, and T. H. Yun, “Non-conforming solid elements for the
analysis of bending deformation of isotropic/orthotropic materials with the smallest
D.O.F., Int. J. Mod. Phys. B, 17, No. 8-9, 1863–1869 (2003).
Received 03. 08. 2015
46 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2016, ¹ 1
D. S. Lee, Y. D. Kwon, and J. S. Han
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/ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /ConvertToCMYK
/DestinationProfileName ()
/DestinationProfileSelector /DocumentCMYK
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure false
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles false
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /DocumentCMYK
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /UseDocumentProfile
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|