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Mechanical calculations of the CDC end-plates

KEK H. Yamaoka

July 8th, '09KEK H. Yamaoka

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Introduction

Mechanical calculations of CDC end-plates was carried out. Load: Wire tension ~4000kg in total. Material: Outer cylinder CFRP End plates Aluminum, CFRP Assumption: All wire tension is supported by the outer cylinder.

CDC

End-plate

Deformation(< 5mm), Stress?Buckling strength?

~R

10

90

~2400

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Wire configuration Given by Taniguchi-san

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Distributions of wire tension in R-direction

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0.3

kg/mm1073.0EEE

:Al

0.3

kg/mm769G

kg/mm101.1E

kg/mm100.2E

kg/mm102.0E

Cyl.r Outer/Inne:CFRP

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0.3

5769kg/mmG

kg/mm100.2E

kg/mm100.2E

kg/mm101.5E

Plates End:CFRP

xy

24zr

xy

2xy

24z

24

24r

xy

2xy

24z

24

24r

xy

rxy

EG

Material propertiesLoad conditions

Constraints

R: Free: FixedZ: fixedRotR: FixedRot: FreeRotZ: fixed

Total: 3725kg

Definitions for FEM

No inner cylinder

6

2.9mm 2.7mm

31MPa

Results - End-plates: 10mm-thick(Al), Outer-cylinder(CFRP): 5mm-thick.

Deformation

Stress

Deformation

Stress

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Calculations of buckling strengthRef: E.H.Baker, et. al. 'STRUCTURAL ANALYSIS OF SHELLS'

The buckling strength of the outer/inner cylinder is calculated.

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Material: CFRP

Dia. 340mm

Length: 1000mm E： 110GPa : 0.3

2322kg

4.54.01702

2

:load Buckling

545.4

170

4.0101.16.035.01

170

4.0

105.1

6.0C

0.35

is , therefore425, 170/0.4R/t

fig.10 from Determined :

buckling elasticfor 1 :

stress Buckling :

2

4

24

c

crcr

ccr

cr

ccr

rtP

MPammkg

R

EtC

mmR

mmt

mmkgE

R

EtC

12474kg

6.148.01702

2

:load Buckling

14614.6

170

8.0101.16.047.01

170

8.0

105.1

6.0C

0.47

is , therefore212.5, 170/0.8R/t

fig.10 from Determined :

buckling elasticfor 1 :

stress Buckling :

2

4

24

c

crcr

ccr

cr

ccr

rtP

MPammkg

R

EtC

mmR

mmt

mmkgE

R

EtC

t=0.4mm t=0.8mmBuckling strength: Inner cylinder

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Assumptions

Material: CFRP

Dia. 2190mm

Length: 2328mm

E： 110GPa

: 0.3

315039kg

9.130.510902

2

:load Buckling

13913.9

1090

4.0101.16.046.01

170

5

101.1

6.0C

0.46

is , therefore218, 1090/5.R/t

fig.10 from Determined :

buckling elasticfor 1 :

stress Buckling :

2

4

24

c

crcr

ccr

cr

ccr

rtP

MPammkg

R

EtC

mmR

mmt

mmkgE

R

EtC

8218kg

2.10.110902

2

:load Buckling

121.2

1090

0.1101.16.02.01

1090

0.1

101.1

6.0C

0.2

is , therefore1090, 1090/1.0R/t

fig.10 from Determined :

buckling elasticfor 1 :

stress Buckling :

2

4

24

c

crcr

ccr

cr

ccr

rtP

MPammkg

R

EtC

mmR

mmt

mmkgE

R

EtCIf t=5.0mm

If t=1.0mm

Wire tension: 3725kg

Buckling strength: Outer cylinder

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Outer Cyl.

CFRP Thikness Deformation Stress Deformation Stres5mm 2mm 17.6mm 312MPa 13.0mm 616MPa5 3 11.6 180 8.3 3275 4 8.6 118 6.0 1935 5 6.8 85 4.7 1235 6 5.5 66 3.7 865 7 4.6 53 3.1 735 8 3.8 44 2.6 635 9 3.3 37 2.2 555 10 2.9 32 1.9 48

1 10 3.5 33 2.5 512 10 3.0 33 2.2 503 10 3.2 33 2.0 504 10 3.0 32 2.0 49

End Plates(Al) End Plates(CFRP)

Tensile(t) N/mm2

Yeild（σy） N/mm2

F -1 Ｆ-1＝σy 205 195 205F-2 F-2=0.7*σt 280 161 364F Smaller value 205 161 205

Allowable stress(MPa)Long Short Long Short Long Short

Tension ft＝Ｆ/1.5 137 205 107 161 137 205

Shearing fs＝Ｆ/(1.5√ 3) 79 118 62 93 79 118

Bending fb＝Ｆ/1.3 158 237 124 186 158 237

Hertz stress fp＝Ｆ/1.1 186 280 146 220 186 280

Bolt(Tension) ft＝Ｆ/2 103 154 81 121 103 154

Bolt(Shear) fs＝Ｆ/(1.5√ 3) 79 118 62 93 79 118

Bolt(Hertz) fp＝1.25Ｆ 256 384 201 302 256 384

Roller fp＝1.9Ｆ 390 584 306 459 390 584

Welding(PT) fs＝Ｆ/(1.5√ 3) 79 118 62 93 79 118

Welding(No PT) fs＝0.45Ｆ/(1.5√ 3) 36 53 28 42 36 53

Long term:

Short term:

400220

230195

520205

StainlessMaterial SS400

SUS304AluminumA5052-H32

Conditions

Static load

Seismic, Thermal load

Long x 1.5

Calculation results in various parameters

Allowable stress （ Japanese: Koukozo sekkei kijun ） This criterion was used for the mechanical design of the Belle.

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- If deformation has to keep less than 5mm,thickness of end-plates should be thicker than 7mm(Al). Calculation at the practical configuration will be necessary.- To know the mechanical properties of CFRP is important, We have contacted to a CFRP fabricator.

Configuration

END

ConclusionMade by Kohriki-san

http://wiki.kek.jp/display/~yamaokah/CDC

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層 R(mm) Z+(mm) Z-(mm) 数　　　角度 1 A 172.0 602.6 -337.9 160 0.0 2 A 182.0 635.3 -355.2 160 0.0 3 A 192.0 668.0 -372.6 160 0.0 4 A 202.0 700.7 -389.9 160 0.0 5 A 212.0 733.4 -407.2 160 0.0 6 A 222.0 766.1 -424.5 160 0.0 7 A 232.0 798.8 -441.8 160 0.0 8 A 242.0 831.5 -459.2 160 0.0 9 U 266.0 910.0 -500.7 160 37.0 10 U 282.0 962.4 -528.4 160 37.1 11 U 298.0 1014.7 -556.2 160 37.3 12 U 314.0 1067.0 -583.9 160 37.4 13 U 330.0 1119.4 -611.6 160 37.4 14 U 346.0 1171.7 -639.3 160 37.5 15 A 368.0 1441.4 -641.4 192 0.0 16 A 384.0 1444.1 -644.1 192 0.0 17 A 400.0 1446.9 -646.9 192 0.0 18 A 416.0 1449.7 -649.7 192 0.0 19 A 432.0 1452.4 -652.4 192 0.0 20 A 448.0 1455.2 -655.2 192 0.0 21 V 464.0 1458.0 -658.0 224 -36.9 22 V 480.0 1460.7 -660.7 224 -38.1 23 V 496.0 1463.5 -663.5 224 -39.3 24 V 512.0 1466.3 -666.3 224 -40.4 25 V 528.0 1469.0 -669.0 224 -41.6 26 V 544.0 1471.8 -671.8 224 -42.7 27 A 562.0 1474.9 -674.9 256 0.0 28 A 580.0 1478.0 -678.0 256 0.0 29 A 598.0 1481.1 -681.1 256 0.0 30 A 616.0 1484.3 -684.3 256 0.031 A 634.0 1487.4 -687.4 256 0.0 32 A 652.0 1490.5 -690.5 256 0.0 33 U 670.0 1493.6 -693.6 288 46.8 34 U 688.0 1496.7 -696.7 288 47.9 35 U 706.0 1499.8 -699.8 288 49.0 36 U 724.0 1502.9 -702.9 288 50.1 37 U 742.0 1506.0 -706.0 288 51.2 38 U 760.0 1509.1 -709.1 288 52.3 39 A 778.0 1512.3 -712.3 320 0.0 40 A 796.0 1515.4 -715.4 320 0.0

層 R(mm) Z+(mm) Z-(mm) 数　　　角度

41 A 814.0 1518.5 -718.5 320 0.0 42 A 832.0 1521.6 -721.6 320 0.0 43 A 850.0 1524.7 -724.7 320 0.0 44 A 868.0 1527.8 -727.8 320 0.0 45 V 886.0 1530.9 -730.9 352 -56.0 46 V 904.0 1534.0 -734.0 352 -56.9 47 V 922.0 1537.2 -737.2 352 -57.9 48 V 940.0 1540.3 -740.3 352 -58.9 49 V 958.0 1543.4 -743.4 352 -59.9 50 V 976.0 1546.5 -746.5 352 -60.8 51 A 994.0 1549.6 -749.6 384 0.0 52 A 1012.0 1552.7 -752.7 384 0.0 53 A 1030.0 1555.8 -755.8 384 0.0 54 A 1048.0 1558.9 -758.9 384 0.0 55 A 1066.0 1562.0 -762.0 384 0.0 56 A 1084.0 1565.2 -765.2 384 0.0 57 A 1102.0 1568.3 -768.3 384 0.0 58 A 1120.0 1571.4 -771.4 384 0.0

張力分布 (リスト )

Z+

1

X

Y

Z

End plates(Al): t10mm, Outer cyl.(CFRP): t5mm

JUN 23 200914:13:28

NODES

内筒なしZ+

R+(X+)