October 31, 2006 Global Design Effort 1 IR hall deflection study October 31, 2006 John Amann, Andrei Seryi

October 31, 2006 Global Design Effort 1

IR hall deflection study

October 31, 2006

John Amann, Andrei Seryi

Oct 31, 06 2

Motivation and content

• To understand deformation of the floor in case of push-pull operation of detector– Displacement of the floor during push-pull operation is

an important consideration that may affect design of the detector support and alignment system

– A simplified estimation is discussed below

• Thank Gordon Bowden for a lot of help and comments

• Thanks to all colleagues who were involved in discussion

Oct 31, 06 3

Air-pads at CMS

Photo from the talk by Y.Sugimoto, http://ilcphys.kek.jp/meeting/lcdds/archives/2006-10-03/

Single air-pad capacity ~385tons (for the first end-cap disk which weighs 1400 tons). Each of air-pads equipped with hydraulic jack for fine adjustment in height, also allowing exchange of air pad if needed. Lift is ~8mm for 385t units. Cracks in the floor should be avoided, to prevent damage of the floor by compressed air (up to 50bars) – use steel plates (4cm thick). Inclination of ~1% of LHC hall floor is not a problem. Last 10cm of motion in CMS is performed on grease pads to avoid any vertical movements. [Alain Herve, et al.]

Oct 31, 06 4

Displacement of collider hall

• Disclaimer– The estimations shown below are intended for

very rough estimation of the variation of deformation under the detector, which affects design of its support and alignment system

– Simplified elastic model is assumed, and essential effects such as long term settlement, inelastic motion, non-homogeneity of rock, IR hall shape, etc, were not taken into account

– Early investigations (drilling, etc) of the site in the location of IR hall and careful engineering are crucial, independent of push-pull scheme

Oct 31, 06 5

Displacements of collider hall

• Modeling it now with ANSYS, first results below • Also use approximate analytical model

– displacement of elastic half-space under load of circular load** or radius R and mass M:

– where E-Young’s modulus, -Poisson ratio– and displacement outside falls as 1/r– express via Elliptical integrals– approximate analytically as show on next page

ERπ

)ν(1M2z

2

max

π

2zz maxedge

*) 1) Gordon Bowden, private communication 2) [FORMULAS FOR STRESS AND STRAIN, 5th EDITION, Roark & Young, Table 33, p.519.]

Oct 31, 06 6

Deformation & its approximation

Approximation:Z0= (2*M/(pi * E * r0))*(1-nu^2) * 1000; % in mmee=2; aa=ee*0.25; cc=ee*1; bb=(1+aa)*(pi/2)^2-1-cc; Zapprox= Z0 * (( 1+aa*(x/r0).^2 )./ (1 + bb*(x/r0).^2 + cc*(x/r0).^4)).^0.5;

Theory [1]:Theor_coeff=4*M/(pi^2*r0*E)*(1-nu^2) * 1000; % mmif x(i) <= r0 em=(x(i)/r0)^2; [Kell,Eell]=ellipke(em); Ztheory(i)= Theor_coeff* Eell; else em=(r0/x(i))^2; [Kell,Eell]=ellipke(em); Ztheory(i)= Theor_coeff* x(i)/r0*(Eell-(1-em)*Kell);end[1] Theory of elasticity, Timoshenko & Goodier, 1951

Example of theoretical deformation for infinite half space under circular load and approximation used in the Matlab model

Oct 31, 06 7

Assumptions for strength

• Typical values of Young’s modulus– Granite, Dolomite: 50-70 GPa (Japan & FNAL ILC sites)

– Sandstone: 20 GPa (CERN ILC site)

– Concrete: 30 GPa – Soil (varies a lot): 0.1 GPa

• Will assume 30GPa (3e9 kg/m2) which is conservative for deep site, and assume that sufficient amount of concrete is used for shallow sites to make its strength close to this value

Oct 31, 06 8

Note the comparison

• IR hall 110*25*35m – volume ~100 000 m3

– amount of removed rock: 250 kton– two detectors: ~30 kton

• the structural stability of the hall that need to be provided by careful design, does not depend much on the need to move the detector

• If the IR hall built in water table, will have to solve engineering issues of buoyancy anyway. Detector moving along the longer dimension of the hall (and not along shorter dimension), which helps.

Oct 31, 06 9

Displacement, Matlab model

Parameters: M=14000 tonR=0.75m (radius of air-pad)E=3e9 kg/m^2, n=0.15 (as for concrete)Number of air-pads=36

Oct 31, 06 10

Displacement, Matlab model

Parameters: M=14000 tonR=0.375m (radius of air-pad)E=3e9 kg/m^2, n=0.15 (as for concrete)Number of air-pads=36

Oct 31, 06 11

Displacement . . ANSYS Results

• Same Young’s Modulus and Poisson’s Ratio as MATLAB Model

• Finite Slab - 25m x 25m x 3m

• Air Caster Modeled as Circular Indentation

• Slab Restrained in all DOF at Side and Bottom Areas

• Material Model - Linear Elastic Isotropic

• Mesh Element Type - SOLID92, 10 Node Tetrahedral

• Plotted Nodal Solution for Y Displacement

Oct 31, 06 12

Displacement . . . ANSYS Results

.75m Air Casters x36, 14000 ton Load Evenly Distributed

Y Max. Displacement = .003391” or .086131mm

25m x 25m x3m Slab

Oct 31, 06 13


.375m Air Casters x36, 14000 ton Load Evenly Distributed

Y Max. Displacement = .006956” or .176682mm

25m x 25m x3m Slab

Oct 31, 06 14


Analytical Model Predicts (Formulas for Stress and Strain, Roark, 4th Ed. p.323 eq.13)

Y max = .003823” Y edge = .002438” Y max = .007646” Y edge = .004868”

ANSYS Predicts

Y max = .002789” Y edge = ~.00092” Y max = .005825” Y edge = ~.003233”

5m x 5m x 1m Slab .75m R Air Caster

5m x 5m x 1m Slab .375m R Air Caster

Oct 31, 06 15


Displacement vs. Slab Thickness5m x 5m

Y max displacement = .002879” Y max displacement = .249e-3”

1m Thick Slab .1m Thick Slab

Oct 31, 06 16


• Want to Investigate Y Displacement 1/r Decay

• Model Changes to Cylinder on Block

• Eliminates Indentation

• Coarse Mesh – Fast, Now Can Model Contact

• Cylinder/Slab Surface/Volume Interaction

• No Friction

• Vary Slab Thickness 1m, 5m, 10m

Oct 31, 06 17


5m x 5m x 1m 5m x 5m x 5m

A36 Steel Cylinder .75m R x .75m H

Oct 31, 06 18


Radial Growth of Y Displacement with Increasing Slab Thickness

5m x 5m x 1m Slab 5m x 5m x 5m Slab

Oct 31, 06 19


5m x 5m x 10m Slab

Y max displacement = .002737” ???

Oct 31, 06 20


Restrained Sides and Bottom All DOF Restrained Bottom Only All DOF

Difference in Y Max = .001373”

5m x 5m x 10m Slab

Oct 31, 06 21


Restrained Sides and Bottom All DOF Restrained Bottom Only All DOF

Difference in Y max = .0001”

25m x 25m x 3m Slab

Oct 31, 06 22

Summary

• For typical ILC sites, expected detector displacements are about 0.5mm and local variation under supports around 0.1-0.2mm

• Displacement estimated for elastic half-space may not be a good model for collider hall, so accuracy of estimations may be not more than a factor of two

• Uniform distribution of support point is desirable (need to study its feasibility, assuming the need for maintenance of air-pads). More local distribution of air-pads closer to perimeter would increase variation of local deformations

• Steel plates on the floor may help. They were not yet included in the estimations

Documents

October 31, 2006 Global Design Effort 1 IR hall deflection study October 31, 2006 John Amann, Andrei Seryi