1. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 1 Design, Manufacture, Transport and Integration on-site in Chile of ALMA Antennas FEA MODEL DESCRIPTION AND ANALYSIS PM#03- 05-6 April 2006 Dated November 18 h, 2005

2. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 2 GLOBAL MODEL 90° elevation ELEVATION AXIS RECEIVER CABIN - BOTTOM ELEVATION DRIVE ELEVATION AXIS BOX MATH CAD CALCULATIONS FOR THE ERROR BUDGET FEM ANALYSIS WIND ANALYSIS

3. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 3 GLOBAL MODEL 90° elevation GLOBAL FEA MODEL FEA model of azimuth bearing, modelled by vertical springs and radial springs Back-Up Structure - detail GLOBAL MODEL: -161600 NODES - 68600 ELEMENTS - SHELL 99 (CFRP) - SHELL 63 (STEEL PLATES) - BEAM 4 - COMBIN 14 (SPRINGS) - MASS 21

4. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 4 GLOBAL FEA MODEL GLOBAL MODEL – CALL FOR TENDER 45° elevation BACK-UP STRUCTURE 16 SLICES, UPPER AND LOWER SKIN EVERYTHING MODELED WITH MULTILAYER SHELL ELEMENT RECEIVER CABIN

5. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 5 GLOBAL FEA MODEL QUADRUPODE LEGS CONNECTION BETWEEN LEGS AND BACKUP STRUCTURE

6. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 6 GLOBAL FEA MODEL SUBREFLECTOR MECHANISM: HEXAPODE APEX STRUCTURE – CFRP INTERFACE CYLINDER – ALUMINUM SUBREFLECTOR – ALUMINUM PRIMARY FOCUS FIXED TO THE SUBREFLECTOR VERTEX

7. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 7 GLOBAL FEA MODEL GLOBAL MODEL – CALL FOR TENDER 45° elevation CONNECTION BETWEEN RECEIVER CABIN AND BACKUP STRUCTURE 8 INVAR PLATES MODELED WITH SOLID ELEMENTS

8. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 8 GLOBAL FEA MODEL MASSES INSIDE THE RECEIVER CABIN: - FRONT END SUPPORT STRUCTURE - FRONT END ASSEMBLY FIXED TO THE RECEIVER FLANGE - AUXILIARY ELECTRONICS CHASSIS - RACKS - HVAC FIXED TO THE RECEIVER CABIN FLOOR RECEIVER CABIN FLOOR CONNECTED BY COUPLED DoF TO THE CABIN WALLS

9. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 9 GLOBAL FEA MODEL STEEL STRUCTURE DETAIL: ELEVATION DRIVE SADDLE

10. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 10 GLOBAL FEA MODEL STEEL STRUCTURE BASE YOKE STEEL STRUCTURE SECTION

11. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 11 GLOBAL FEA MODEL CONNECTION BETWEEN YOKE AND RECEIVER CABIN LATERAL COSTRAINT GIVED BY THE ELEVATION DRIVE WHEELS CONNECTION BETWEEN YOKE AND RECEIVER CABIN TANGENTIAL COSTRAINT GIVED BY THE ELEVATION DRIVE

12. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 12 GLOBAL FEA MODEL AZIMUTH BEARING INTERFACE WITH BASE AND YOKE AZIMUTH LOCKING PIN

13. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 13 GLOBAL FEA MODEL AZIMUTH BEARING

14. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 14 GLOBAL FEA MODEL ELEVATION AXIS BOX THE MESH OF THE MEMBRANE HAS BEEN IMPROVED THE ELEVATION SHAFT IS CONNECTED TO THE RECEIVER CABIN BY 5 COUPLED DoFs THE ROTATION AROUND X AXIS (ELEVATION AXIS) IS FREE

15. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 15 GLOBAL FEA MODEL INTERFACE WITH THE FOUNDATION PAD BOTTOM VIEW INTERFACE FLANGE WITH THE FOUNDATION PAD ONLY THE CONTACT SURFACE IS CONNECTED TO THE BASE STRUCTURE

16. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 16 GLOBAL FEA MODEL PLATFORMS ALL THE CABINETS ARE MODELED AS STRUCTURAL MASSES FIRST EIGENFREQUENCY: 12.12Hz

17. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 17 DETAILED MODEL OF THE ELEVATION AXIS FEM ANALYSIS FEA model to evaluate the behaviour of the elevation shaft Stress level in the CFRP around the elevation axis Stress level in the elevation shaft

18. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 18 ELEVATION AXIS BOX FEM ANALYSIS FEA model to evaluate the behaviour of the ELEVATION AXIS BOX

19. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 19 GLOBAL MODEL 0° elevation ERROR BUDGET PANELS DEFORMATION – from FEM analysis SURFACE ACCURACY – from MATH CAD routine

20. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 20 VELOCITY VECTORS WIND ANALYSIS Computational domain Static pressure iso-lines Pressure distribution in the FEA model

21. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 21 DISPLACEMENT IN Z DIRECTION (VERTICAL) GRAVITY ANALYSIS

22. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 22 GLOBAL DISPLACEMENT (USUM) THERMAL DISTORSION (uniform temperature 20°C)

23. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 23 DISPLACEMENT IN Z DIRECTION (VERTICAL) GRAVITY LOAD THERMAL LOAD BEHAVIOUR OF ELEVATION MEMBRANE AND ELEVATION AXIS RING

24. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 24 DISPLACEMENT IN Z DIRECTION (VERTICAL) SEMI-ISOTROPIC LAY-UP OPTIMIZED LAY-UP OPTIMIZATION OF THE CABIN WALL LAY-UP TO MINIMIZE THERMAL DISTORSION

25. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 25 Modal Analysis: First Frequency 8,80 Hz

26. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 26 Modal Analysis: Second Frequency 10,06 Hz

27. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 27 FIRST EIGENFREQUENCY: 12.25Hz QUADRIPODE LEGS SECOND EIGENFREQUENCY: 15.70Hz

28. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 28 Case 1 – 0° azimuth 0° elevation – CRS4 – 10.7m/s WIND ANALYSIS Case 1 – 0° azimuth 0° elevation – Alenia – 9.5m/s

29. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 29 Case 7 – 0° azimuth 60° elevation – CRS4 – 10.7m/s WIND ANALYSIS Case 7 – 0° azimuth 60° elevation – Alenia – 9.5m/s

30. Reproduction interdite © ALMA EUROPEAN CONSORTIUM Reproduction forbidden Design, Manufacture, Transport and Integration in Chile of ALMA Antennas Page 30 Case 11 – 0° azimuth 90° elevation – CRS4 – 10.7m/s WIND ANALYSIS Case 11 – 0° azimuth 90° elevation – Alenia – 9.5m/s