Finite Element Analysis of Dee with fixed reinforcing beam .
description
Transcript of Finite Element Analysis of Dee with fixed reinforcing beam .
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 1
Alexandre Riabov (IHEP, Protvino)
Justin Greenhalgh (RAL)
Finite Element Analysis of Dee with fixed reinforcing beam.
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 2
General IssuesGeneral Issues
• This work is based on the note “Request for calculation of effect of reinforcing beam on Dee backplates” (EE/358/RJSG/2004) by Justin Greenhalgh and preliminary results presented in the note “FE analysis of Dee with reinforcing beam” (EE/445/RJSG+AR/2005)
• Two Extreme variants which can be realized at SC assembly and Dee transportation stages have been considered. Along with the natural gravitation the Dee can be exposed to an additional acceleration of 0.35g in all directions which is equal to the static equivalent seismic load. Maximal braking accelerator allowed is 1g. The worst combined load cases are (X-axis is vertical, Z-axis is perpendicular to Dee plane, Y-axis is in a transportation direction - see pictures for explanation of the global coordinate system of the model) :
E1: Accel=(1.35, 1, +0.35) g
E2: Accel=(1.35, 1, -0.35) g
• At installation stage the worst combination of gravity and seismic loads is described by accelerating load vector (here Y-axis becomes vertical, and X-axis – horizontal):
E3: Accel=(0.35, 1.35, 0.35) g
• Additional load case C7 without seismic loads is also have been considered:
C7: Accel=(0, 1.35, 035) g
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 3
Questions.Questions.
• Displacements and Stresses in the aluminum of the backplate;
• Stresses in the steel of the brackets and reinforcing beam;
• Axial forces in all bolts; Shear forces in all dowels (pins);
• Reaction forces on the reinforcing beam and the brackets bolts from the direction of the OPAL frame;
• Loss of SC clearance. Where does the maximum loss occur?
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 4
The full FE ModelThe full FE Model
Support ring (SR) Brackets (BR)
Reinforcing Beam
Backplate (BP)
Supercrystals (SC)
Global CS (X,Y,Z)
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 5
Backplate detailsBackplate details
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 6
BR details and some definitionsBR details and some definitions
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 7
SC ArrangementsSC Arrangements
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 8
Boundary conditionsBoundary conditions
Beam ends fixed
Brackets fixed
Coupling between the model parts (bolts and pins)
Loading: Acceleration vector A=(αx, αy, αz) g
g
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 9
E1: BP&SC displacementsE1: BP&SC displacements
Result: The maximal displacements of BP are very low ~ 0.9 mm
Assembly/Transp.
A=(1.35, 1, 0.35) g
Beam ends fixed
Last BR removed
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 10
E1: Von Mises Stresses in BPE1: Von Mises Stresses in BP
Assembly/Transp.
A=(1.35, 1, 0.35) g
Beam ends fixed
Last BR removed
Result: The stress concentration is ~ 56 MPa. Overall stress is low
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 11
E1: Brackets displacementsE1: Brackets displacements
Assembly/Transp.
A=(1.35, 1, 0.35) g
Beam ends fixed
Last BR removed
Result: The maximal displacements are low ~ 0.2 mm (reached for -70ºBR)
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 12
E1: Von Mises Stresses in BRsE1: Von Mises Stresses in BRs
Assembly/Transp.
A=(1.35, 1, 0.35) g
Beam ends fixed
Last BR removed
Result: The stress concentration is ~ 40 MPa. It’s very low for steel
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 13
E1: Reinforcing Beam StressesE1: Reinforcing Beam Stresses
L-Beam (LB)
L-Section (LS)
Assembly/Transp.
A=(1.35, 1, 0.35) g
Beam ends fixed
Last BR removed
Result: The stress concentration is ~ 170 MPa. It occurs near LS-LB bolts
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 14
E1: Stresses in Support RingE1: Stresses in Support Ring
Assembly/Transp.
A=(1.35, 1,0.35) g
Beam ends fixed
Last BR removed
Result: The stress concentration is ~ 40 MPa. It occurs at SR-BP bolts
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 15
E2: BP&SC displacementsE2: BP&SC displacements
Result: The maximal displacements of BP and SCs are very low ~ 0.55 mm
Assembly/Transp.
A=(1.35, 1,-0.35) g
Beam ends fixed
Last BR removed
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 16
E2: Von Mises Stresses in BPE2: Von Mises Stresses in BP
Result: The stress concentration is ~ 32 MPa. It occurs near BP-BR bolts
Assembly/Transp.
A=(1.35, 1,-0.35) g
Beam ends fixed
Last BR removed
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 17
E2: Von Mises Stresses in BRsE2: Von Mises Stresses in BRs
Result: The stress concentration is ~ 98 MPa. It is not critical for the steel
Assembly/Transp.
A=(1.35, 1,-0.35) g
Beam ends fixed
Last BR removed
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 18
E2: Reinforcing Beam StressesE2: Reinforcing Beam Stresses
Result: The stress concentration is ~ 56 MPa. It occurs in L-section
Assembly/Transp.
A=(1.35, 1,-0.35) g
Beam ends fixed
Last BR removed
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 19
E3: BP&SC displacementsE3: BP&SC displacements
Installation
A=(0.35,1.35,0.35)g
Beam removed
Last BR removed
Result: The maximal displacements of BP are rather large ~ 8.6 mm
Large displacements are due to Z-direction seismic load. This may be dangerous from the point of view loss of SC clearance.
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 20
E3: Von Mises Stresses in BPE3: Von Mises Stresses in BP
Installation
A=(0.35,1.35,0.35)g
Beam removed
Last BR removed
Result: The stress concentration is ~ 103 MPa. It occurs near BP-BR bolts
For the Aluminium σyield = 270 MPa.
The safety factor is 0.9*(270/103) = 2.4.
Overall stress is small- it is not greater than 40MPa
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 21
E3: Bracket displacementsE3: Bracket displacements
Result: The maximal displacements is ~ 1.4 mm for the lower bracket.
Installation
A=(0.35,1.35,0.35)g
Beam removed
Last BR removed
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 22
E3: Von Mises Stresses in BRsE3: Von Mises Stresses in BRs
Installation
A=(0.35,1.35,0.35)g
Beam removed
Last BR removed
Result: The stress concentration is ~ 330 MPa. The Steel of BRs should be good
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 23
C7: BP displacementsC7: BP displacements
Installation
A=(0,1.35,0)g
Beam removed
Last BR removed
No seismic
Result: Without seismic the displacements are small: ~ 0.7 mm.
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 24
Loss of CS clearance in DeeLoss of CS clearance in Dee
Result: Variant E3 may be problematic
It was suggested (RJSG) to consider the value of 0.18 mm as a worrying limit for loss of clearance between supercrystals in a Dee. From this one can conclude that a worrying limit for loss of clearance between SCs centers of masses is 0.18/(400/300) = 0.135 mm.
Here: 400mm – length of the SCs, 300mm – the distance of the SCs mass centers from the BP
Next table presents maximal loss of clearance, SC pair for which this maximum occurs, and the number of SCs pairs with Loss ≥ 0.135 mm.
For detailed results see files Case_*.doc.
Case : (accel) Maximal Loss of Clearance [mm] /SCs pair for which it’s reached
Number of problematic SC pairs(Loss ≥ 0.135 mm)
E1 : (1.35,1, 0.35) 0.144 / (B2M, C2M) 1
E2 : (1.35,1,-0.35) 0.019 / (B2, B3) 0
E3 : (0.35,1.35,0.35) 0.353 / (C1, C2) 46
C7 : (0,1.35,0) < 0.075 for all SCs 0
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 25
Forces in BP-BR bolts and pinsForces in BP-BR bolts and pinsCase E1: Acce l=(1.35,1,0.35) g
-2
-1
0
1
2
3
4
5
6
7
8
-80 -60 -40 -20 0 20 40 60 80
Bracket pos ition [degree]
Fo
rce
[k
N]
Lef t Bolt
Right Bolt
Pin
Case E2: Acce l=(1.35,1,-0.35) g
-2
0
2
4
6
8
10
-80 -60 -40 -20 0 20 40 60 80
Bracket pos ition [degree]
Fo
rce
[kN
]
Lef t Bolt
Right Bolt
Pin
Case E3: Accel=(0.35,1.35,0.35) g
-25
-20
-15
-10
-5
0
5
10
15
20
-80 -60 -40 -20 0 20 40 60 80
Bracket position [degree]
Fo
rce
[k
N]
Lef t Bolt
Right Bolt
Pin
Case C7: Accel=(0,1.35,0) g
-10-8-6-4-202468
10
-80 -60 -40 -20 0 20 40 60 80Bracket position [degree]
Forc
e [k
N]
Left Bolt
Right Bolt
P in
For bolts: positive value denotes tension, negative – compression. For pins shear forces are given.
Result: For all cases forces are acceptable. Maximal axial force is ~ 9 kN,
maximal shear force is ~ 15 kN
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 26
Forces in LS-BP bolts and pinsForces in LS-BP bolts and pinsCase E2: Acce l=(1.35,1,-0.35)
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
-1600 -1200 -800 -400 0 400 800 1200 1600
Y-pos ition of LS-BP bolts and pins [m m ]
Fo
rce
[kN
]
Bolts
Pins
Case E1: Accel=(1.35,1,0.35)
-20
-15
-10
-5
0
5
10
15
20
-1600 -1200 -800 -400 0 400 800 1200 1600
Y-position of LS-BP bolts and pins [m m ]
Fo
rce
[kN
]
Bolts
Pins
Result: Maximal forces are due to braking and they occur at one of the L-beam ends. Maximal reaction force is about 4.5 tons.
Result: The LS-BP bolts practically do not work. Maximal shear force is about 1.5 tons. It is due to Braking.
Reaction forces [kN] Force Moments [kN∙m]
Case Y-pos RX RY RZ MX MY MZ
E1 1700 -3.81 6.45 -13.98 -15.57 -0.15 7.41
-1700 -19.29 -36.69 -18.69 21.93 -0.31 -29.78
E2 1700 2.53 -9.79 -1.19 -1.47 0.03 -3.15
-1700 -12.95 -20.45 -5.90 7.83 -0.13 -19.21
This table presents reaction forces and moments on the beam ends from OPAL frame
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 27
Case E1: Axial Forces in BR-FR bolts
-5
-4
-3
-2
-1
0
1
2
3
4
-80 -60 -40 -20 0 20 40 60 80
Bracket pos ition [degree]
Fo
rce
[kN
]
LW right
LW lef t
UP right
UP lef t
Case E1: ShearForces in BR-FR bolts
0
1
2
3
4
5
6
-80 -60 -40 -20 0 20 40 60 80
Bracket pos ition [degree]
Fo
rce
[kN
]
LW right
LW lef t
UP right
UP lef t
Case E2: Axial Forces in BR-FR bolts
-15
-10
-5
0
5
10
15
-80 -60 -40 -20 0 20 40 60 80
Bracket pos ition [degree]
Fo
rce
[kN
]
LW right
LW lef t
UP right
UP lef t
Case E2: ShearForces in BR-FR bolts
0
2
4
6
8
10
12
-80 -60 -40 -20 0 20 40 60 80
Bracket pos ition [degree]
Fo
rce
[kN
]
LW right
LW lef t
UP right
UP lef t
E1&E2: BR-OPAL frame boltsE1&E2: BR-OPAL frame bolts
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 28
E3&C7: BR-OPAL frame boltsE3&C7: BR-OPAL frame boltsCase E3: Axial Forces in BR-FR bolts
-40
-30
-20
-10
0
10
20
30
40
50
-80 -60 -40 -20 0 20 40 60 80
Bracket pos ition [degree]
Fo
rce
[kN
]
LW right
LW lef t
UP right
UP lef t
Case E3: Shear Forces in BR-FR bolts
0
5
10
15
20
25
30
35
-80 -60 -40 -20 0 20 40 60 80
Bracket pos ition [degree]
Fo
rce
[kN
]
LW right
LW lef t
UP right
UP lef t
Case C7: Axial Forces in BR-FR bolts
-15
-10
-5
0
5
10
15
-80 -60 -40 -20 0 20 40 60 80
Bracket pos ition [degree]
Fo
rce
[kN
]
LW right
LW lef t
UP right
UP lef t
Case C7: Shear Forces in BR-FR bolts
0
2
4
6
8
10
12
-80 -60 -40 -20 0 20 40 60 80
Bracket pos ition [degree]
Fo
rce
[kN
]
LW right
LW lef t
UP right
UP lef t
ECAL
End Cap
Dee Assembly, Transport, Installation CERN January 2006 AR / RJSG – 29
ConclusionsConclusions• Fixing of the reinforcing beam ends to the OPAL frame fully solves all mechanical problems
which can arise at stages of the Dee assembly and transportations. The deflections and stresses in all parts of the construction are small, the loss of the SC clearance lies within specified limits (0.18 mm).
• At the stage of installation seismic load acting in the direction perpendicular to the backplate plane produces rather large deflections (up to 8.6 mm) and consequently rather large stresses in the backplate (~ 100 MPa) and in the brackets (~ 330 MPa). It should be noted that it is the stress concentration which arises locally. Overall stresses are much less. Nevertheless the mechanical quality of materials of the backplate and the brackets should be good enough. The loss of SC clearance in the Dee can reach 0.47 mm.
• In case of seismic absence (Case C7) the stress concentrations do not exceed 60 MPa in the backplate and 85 MPa in the brackets. The losses of SC clearance in a Dee are negligible - for all SC pairs the losses do not exceed 0.1 mm.
• We can not make true conclusions about the loss of SC clearance between Dees without performing additional calculations. The question is that during the installation of one Dee which is supporting by the brackets the another Dee has already installed in operational position and it is supported by the support flange (on HE). So the Dees are under different boundary conditions and additional calculations should be done for the Dee in the operational mode. We can only present here the maximum displacements of the A-column SCs towards to another Dee: they are ~1.95 mm for the E3 load case and only 0.27 mm for the C7 load case.