1. 10/11/03 TGC1 Design problem Muon Week, 10 th November 2003 R. Vuillermet on behalf of the Muon Design Team : E. Fernandez, D. Mladenov, P. Minginette, G. Spigo, A. Tanklevski

2. 10/11/03 R. Vuillermet TGC1 Main Characteristics  Dimensions : Diameter : 23300 mm Thickness : 250 mm  Weight : Mass of the structure 18T Chambers mass 17.5T Bracket mass 1T PS Packs + services 2.6Tout of mid plane Electronics racks 2 Tout of mid plane Services around the wheel 3.5T _________________________________ TOTAL 44.6T

3. 10/11/03 R. Vuillermet TGC1 Initial design 25 m 23 m

4. 10/11/03 R. Vuillermet TGC1 rim with services Electronic racks Services around the rim PS-packs

5. 10/11/03 R. Vuillermet Edge beam cross section  The top beam initial cross section is composed 2 squares extruded profile (250x250x12) distant of 50 mm.  This section is reinforced on both sides by two 10mm thick plates, 180 mm away from the mid plane.

6. 10/11/03 R. Vuillermet Finite Element model used for the stability calculation Rack masses PS pack masses

7. 10/11/03 R. Vuillermet Finite Element model used for the stability calculation Bracket supporting chambers

8. 10/11/03 R. Vuillermet Finite Element model used for the stability calculation TGC chambers

9. 10/11/03 R. Vuillermet Model with initial reinforcement Initial top edge beams reinforcement Cross section

10. 10/11/03 R. Vuillermet Boundary conditions -Boundary condition are located at the two supporting points. -Since guarantying a perfect fully fix support is not possible (even with one rigid chariot), articulated fixations have been considered in these stability calculations. -These articulated boundary conditions are for a stability point of view a conservative assumption. Ux=Uy=Uz= 0 mm Uz=Uy= 0 mm

11. 10/11/03 R. Vuillermet Non linear buckling calculation -1  Non linear buckling calculation consist of : 1- Appling to the model a perturbation forces image of : - Extrusion tolerances - Manufacturing tolerances - Assembly uncertainties - Modeling imperfection The purpose of this perturbation is to initiate the buckling mode and then increase the convergence of the calculations. Three different values for the perturbation forces have been considered 0 N, 1000 N and 2000 N applied on the top edge beam of the Wheel. These perturbation forces can create up to 35 mm initial out of plane displacement.

12. 10/11/03 R. Vuillermet Non linear buckling calculation -2 2- Calculation procedures Increasing the forces that can create instability of the system while monitoring a deformation. In the TGC1 case the instability foreseen is due to the buckling of the top beam which is under compression. This compression is created by the weight of the structure. The gravity is ramped linearly from 1 g to 3.5 g updating the geometrical non linear deformation of the structure while monitoring the displacement (in Z) of the top edge beam. As no plasticity is met during the calculation process, the wheel is subjected to an elastic buckling phenomenon.

13. 10/11/03 R. Vuillermet Non linear buckling calculation -3 3- Acceptability criteria For column design, most of the national regulations consider a safety factor between 2.5 and 3 as the minimum. As the TGC1 wheel do not have any analogy to other kind of “standard” structures, a safety factor of 3 as driven our studies.

14. 10/11/03 R. Vuillermet Results

15. 10/11/03 R. Vuillermet Solutions  Solution : - Increase the modulus of inertia in Z direction by adding materials out of mid plane. - Two temporary 250x250x12 square profiles will be added and connected to the sector edge beam. - In that way the TGC1 wheel is stable during assembly and up to the connection to MDT. 250x250x12 squared profile

16. 10/11/03 R. Vuillermet Model beams reinforcement 2 Square profiles Edge beam cross section

17. 10/11/03 R. Vuillermet Results

18. 10/11/03 R. Vuillermet Consequences - Modify the edge beam in order to allow fast and easy connection and un-connection of the reinforcement beam. - Design the connection between the reinforcement beams, to guaranty a good force transfer. - Modify the sector assembly procedure to include the reinforcement beams on surface hall. - Modify the movement and the opening scenario in the cavern to assure that the Wheel TGC1 is always in safe situation (either connected to MDT wheel or to HS structure) - Modify the position of temporary supporting points on HM structure. - TGC1 wheel (and probably others too) will need a particular care during opening scenario throughout all life of the Experiment (from commissioning to decommissioning).

19. 10/11/03 R. Vuillermet TGC1 wheel displacement in the cavern after assembly

20. 10/11/03 R. Vuillermet Opening scenario between MDT and TGC1 Previous scenarioNew scenario

21. 10/11/03 R. Vuillermet Stability of TGC1 connected to MDT wheel  The previous assembly scenario is based on the stability of the MDT and TGC1 wheel when connected together.  A dedicated model has been developed integrating :  The stepping connection of TGC1 to MDT. (e.g. no forces passing through the connecting beams during the connection steps).  Characteristics command to perform a non linear buckling calculation.

22. 10/11/03 R. Vuillermet TGC1 connected to MDT model

23. 10/11/03 R. Vuillermet Results

24. 10/11/03 R. Vuillermet Conclusion  TGC1 and MDT wheel connected together are stable.  This stability calculation validate the assembly and moving scenario adopted so far.  Next step : stability calculation of TGC2 and TGC3 individually and connected together.