SALT SAC. Nom & Fonction Name & Function. JP MAGNAT Mechanical Engineer P. DAUGY. X. BOZEC IPDE A. FLECHET IQP J. BERNIER R&D Unit Manager

Transcription

1 Page : 1 / 42 Nature : PRELIMINARY MECHANICAL DESIGN REPORT Titre / Title PREMILINARY MECHANICAL DESIGN REPORT Résumé / Summary : Classification This document presents the mechanical concept for the SAC-SALT NC Mots clés : Classement / Record Répertoire : Fichier : Original : Papier Préparé par : Vérifié par : Prepared by : Checked by : Approbation PROJET : PROJECT approval : Approbation Qualité : P. A. Approval : Autorisation de Diffusion externe : Release Approval : Approbation client : Customer Approval : Nom & Fonction Name & Function JP MAGNAT Mechanical Engineer P. DAUGY X. BOZEC IPDE A. FLECHET IQP J. BERNIER R&D Unit Manager Date Signature EVOLUTION DIFFUSION Document complet Full document Edition Date Observation Pages modifiées n 1 15/01/02 First issue E. RUCH L. NEL (SALT) X. BOZEC H. ROCIPON P. DAUGY JP MAGNAT T. BONTOUX X

2 Page : 2 / 42 TABLE OF CONTENTS 1. SUBJECT APPLICABLE AND REFERENCE DOCUMENT APPLICABLE DOCUMENTS REFERENCE DOCUMENTS UNDERSTANDING OF SPECIFICATION STIFFNESS MASS OPTICAL FORMULA PRESERVATION OVERPRESSURIZATION ADJUSTEMENTS INTERFACES CONE SETTING PLANE ADC MOUNTING PLANE FIXING POINTS FOR CALIBRATION SCREEN SAC AXIS DEFINITIONS SELECTED SOLUTION M2 AND M3 MIRRORS M5 MIRRORS MIROIRS M M4 MIRROR ADJUSTMENT MODULE CONE TUBE M4/M TUBE M TUBE M DIAPHRAGMS MASS BUDGET FINITE ELEMENT MODELING... 19

3 Page : 3 / MODEL MASSES ET INERTIA MATERIAL PROPERTIES SAFETY MARGINS STRESS IN ZERODUR STRESS IN INVAR STRESS IN E24 STEEL GLUE TENSILE STRENGTH GLUE SHEARING MODAL ANALYSIS SCOPE OF THE MODAL ANALYSIS RESULTS THERMAL ANALYSIS SURVIVAL ENVIRONNEMENT 20 C THERMAL VARIATION ( T=1 C) RADIAL GRADIENT (1 C) AXIAL GRADIENT (1 C) GRAVITY INFLUENCE GRAVITY OF 1G ALONG Z AXIS (TEST POSITION) GRAVITY OF 1G WITH A 37 INCLINATION VARIATION OF GRAVITY GRAVITY VARIATION 0 / GRAVITY VARIATION 37/ GRAVITY VARIATION 37 / SUMMARY TABLE CONCLUSION... 42

4 Page : 4 / SUBJECT The purpose of this document is to describe and to give the justification for the conception of the opto-mecanical design of the SAC, in compliance with the specification [AD1] and with the optical choose described in the [RD1] et[rd2] documents. 2. APPLICABLE AND REFERENCE DOCUMENT 2.1 APPLICABLE DOCUMENTS AD Title Reference Date AD 1 SAC specification SALT-1523AS0001, Issue 2 AD 2 Optical specification for the SALT Spherical Aberration Corrector, 1523AS0002 version3.1 15/08/ REFERENCE DOCUMENTS RD Title Reference Date RD 1 Preliminary Tolerance Budget for the SAC INGE1285, Issue 1 RD 2 Preliminary optical design report INGE1284, Issue 1 3. UNDERSTANDING OF SPECIFICATION The SAC mechanical structure shall be compliant with several main criteria: To provide the mechanical interface for mirror mounting compliant with optical performance budget. After analysis, the tolerance budget has defined the main parameters of the mirror mounting interface. This fixation device shall introduce to the mirror no deformation of the optical surface. Furthermore, some adjustment devices shall be implemented for mirror alignment in order to reach the global quality image performance. Sensitivity of the adjustment shall in accordance with positioning requirement defined in the tolerance budget. The mirror fixation shall also taking into account the integration strategy constraints. Mounting and dismounting operations shall be easy. To guarantee the optical performances with respect to thermal and mechanical environments. Thermal effects due to the operational temperature range is an important contributor of the tolerance budget. The choice of the material for the structure shall be made according the output of the optical design phase. Of course, adjustment devices shall be designed with taking into account the different position of the SAC with respect to gravity. To reduce gravity effect on the SAC, a minimum stiffness of the structure shall be reached during design phase. We shall keep in mind that the optimisation of the stiffness should be performed with taking into account the severe mass requirement.

5 Page : 5 / 42 To comply with the mechanical interface requirements and allocated volume To allow fixation of specific devices as stray light baffle To provide air interface and connection with the pressurisation system 3.1 STIFFNESS No stiffness criterion has been mentioned in the SALT-SAC specification. Nonetheless, it has been agreed upon that the first structure mode frequency shall be superior to 15 Hz. 3.2 MASS The targeted mass of the SAC itself is 200kg; the cone mass ( see geometry in the plan) must be added (t.b.d.). 3.3 OPTICAL FORMULA PRESERVATION The dimensional stability of the SAC must be to a level allowing the stability of the optical formula with respect with operational thermal variations and angular motion ( ± 8.5 ). Tilting motions and translations of the SAC are allowed in order to correct errors. 3.4 OVERPRESSURIZATION The SAC will form a shape driving the air inwards through a surrounding piping system and outwards through both ends. 3.5 ADJUSTEMENTS The optical performance imposes a precise mirror positioning. This positioning brings about a translation and tilting mirror-setting. This liaison piece shall be designed in order to limit the mirror elastic deformations. 3.6 INTERFACES Cone setting plane The SAC is fixed on a ring shaped mounting plane (inner diameter 1720 mm, outer diameter 1800 mm ). 24 equidistant 13mm diameter holes around a 1760 mm diameter allow mounting with the interface ADC mounting plane A ring shaped mounting plane of 760 mm exterior diameter and 710 mm interior diameter is dedicated to integrate ADC device. 24 equidistant M holes around 740 mm diameter allows its mounting Fixing points for calibration screen Three equidistant M holes around a 740 mm diameter allow calibration screen fixing (not furnished by SAGEM) These holes are located at the inferior extremity of the SAC.

6 Page : 6 / SAC AXIS DEFINITIONS Axis Z is collinear to optical axis ( mirrors revolution axis ) and oriented from down to up Axis Y is horizontal, in order to complete a direct frame Axis X is perpendicular to optical axis Z Y X Figure 1: SAC axis 5. SELECTED SOLUTION The SAC is composed of 4 ZERODUR mirrors, marked M2, M3, M4 and M5, located inside a stiff steel structure thanks to adjustable settings. The steel structure is composed of an interface and of 3 tubular sections, marked tube M3, tube M2, and tube M4/M5. The following diagram presents the mechanical structure of the SAC SAC BAFFLE M3 TUBE M2 TUBE M4/M5 TUBE CONE M3 MIRROR M3 Alignment M2 MIRROR M2 Alignment M4 MIRROR M4 Alignment M5 MIRROR M5 Alignment The relative position between the three sections are done thanks a preliminary adjustment between the mirror M5 and M2, and M2 and M3. The preservation of these adjustment is done by the positioning of 2 centering pins on each interface.

7 Page : 7 / 42 Overpressurization holes Tube M3 Tube M4/M5 Conical interface Tube M2 Figure 2: SAC + conical interface

8 Page : 8 / 42 Figure 3: SAC + conical interface (top view)

9 Page : 9 / 42 Mirror M4 Mirror M5 Diaphragms Mirror M2 Spider Mirror M3 Figure 4: SAC + conical interface

10 Page : 10 / 42 Figure 5: SAC + conical interface (Section) The different parts are detailed in the following chapters 5.1 M2 AND M3 MIRRORS A three-point fixation is enough for the 2 mirrors since deformations under gravity balance each other in the optical path. 3 Invar blocks are glued ( 120 ) on the side of the mirrors. These blocks limit the thermodeformations and define interface with link connection rods. Block position along optical axis Z is calculated to minimize the mirror deformation.

11 Page : 11 / 42 Three 120 rods link the invar blocks to the steel structure (see Figure 6). These rods guarantee the positioning along mirror axis X and Y and block RZ rotation. At each rod extremity, the joints are made by spherical ball joints in order to reduce parasitic efforts. Mirror M2/M3 Tube Link connecting rod Figure 6: M2 M3 mirrors and their fixations Three 120 adjustable screws define the mirror position along Z axis and allow RX and RY tilting adjustments. Each screw is located at the 3 spherical joints exterior cage level (see Figure 8), limiting the stresses due to the friction. Three locking devices opposed to the screw stops allow mirror immobilization during transport. For easy integration, each device previously detailed (connection rods, adjustable stops and lock device) could be adjusted from the outer of the structure.

12 Page : 12 / 42 Tube M2 Link connecting rod Adjustable screw Invar block Tube M3 Figure 7: M3 fixation device (idem for M2) Tube M2 Invar block Spherical joint Adjustable screw Tube M3 Mirror M3 Figure 8: M3 (or M2) mirror adjustment device

13 Page : 13 / 42 Notes: The spherical joints have a positive allowance, but the play is overcome during the 37 inclination of the SAC. When mirrors are integrated, all plays will be overcome in the same direction. Therefore it is necessary to identify the RZ orientation on the SAC. The spherical joints are calculated for a dynamic load of 10g. 5.2 M5 MIRRORS A three-point fixing (see Figure 9) is enough since the deformation under gravity is poor compared to the global WFE. A 6-point fixing (3 locating points and 3 springs) was considered at the beginning, but was soon dropped down due to the poor gain in terms of WFE and the complexity of mounting phases. 3 Invar blocks are glued ( 120 ) on the mirror side. These blocks limit the thermo-deformations and define interface with link connection rods. Block position along optical axis Z is calculated to minimize the mirror deformation. Three 120 rods link the invar blocks to the steel structure. These rods guarantee the positioning along mirror axis X and Y and block RZ rotation. At each rod extremity, the joints are made by spherical ball points in order to reduce parasitic efforts. Three 120 adjustable screws define the mirror position along Z axis and allow RX and RY tilting adjustments. Each screw is located at the 3 spherical joints exterior cage level (see Figure 10), limiting the stresses due to the friction. M5 mirror M2 mirror Link connecting rod Mirror fixation Figure 9: M5 fixation and adjustment Three locking devices (screws) opposed to the screw stops allow mirror immobilization during transport. These devices can be reached from the top of the SAC.

14 Page : 14 / 42 Locking screw Adapter flange Fixation Mirror M5 Invar block Spherical joint fixation Figure 10: M5 mirror fixation Notes : The spherical joints have a positive allowance, but the play is overcome during the 37 inclination of the SAC. When mirrors are integrated, all plays will be overcome in the same direction. Therefore it is necessary to identify the RZ orientation on the SAC. The spherical joints are calculated for a dynamic load of 10g.

15 Page : 15 / MIROIRS M4 Considering its small size, M4 mirror is glued on a single invar piece called tripod. This one limits the thermo-elastic deformation and filters probable mounting plane deformations. This tripod is mounted to an intermediate steel part called star (see Figure 11). Three blades disposed at 120 are clamped by two M5 screws at the star level. A small module located at the blade extremities allows the mirror adjustment in translation along X Y and Z directions and rotations around RX and RY. Tripod Blade Star Mirror M4 Figure 11: M4 mirror and its fixation

16 Page : 16 / M4 MIRROR ADJUSTMENT MODULE To allow the M4 adjustment, modules have been designed, each of them is fixed at the end of the three blades (see Figure 12) and is composed of: - A small block fixed at the end of the blade with a M5 screw. - An U-shaped stirrup fixed on the structure, this one is used to fix the small block by clamping after the block has been adjusted radially and along Z axis. Blade Reosc screw Cone Small block Straining screw U-shaped stirrup Figure 12: M4 mirror adjustment module Note : The blades can be slightly tightened in order to increase the stiffness of the mounting. 5.5 CONE The cone is almost completely defined in the interface plane (TBD) We have decreased the cone thickness from 5 mm (in the interface plane) to 3 mm in order to lighten the SAC. The cone ends have 3 thick flanges (25 mm). Note : As defined, the cone represents the heaviest part of the total mass budget. 5.6 TUBE M4/M5 Tube has a 2 mm thickness skin. Each tube end has one thick flange (8 mm). The tube is fixed to the conical interface with the help of 24 8 mm bolts. The relative positioning is made by 2 centering pins. Note: connecting areas are reinforced (8mm thick)

17 Page : 17 / TUBE M2 Tube has a 2 mm thickness skin. Each tube end has one thick flange (8 mm). The tube is fixed to the previous one (M4/M5) with the help of 24 8mm bolts. The relative positioning is made by 2 centering pins. Six 30 mm diameter tubes on surroundings allow overpressurization. Note: connecting rods, screw stops and handling devices are reinforced (8 mm thick). 5.8 TUBE M3 Tube has a 2 mm thickness skin. Each tube end has one thick flange (8 mm). The tube is fixed to the M2 one with the help of 24 8 mm bolts. The relative positioning is made by 2 centering pins. Note: connecting areas are reinforced (8 mm thick). 5.9 DIAPHRAGMS Two diaphragms are fixed on the SAC (see Figure 4), one in the upper part, between M4 and M5 mirrors, the second one at the bottom, under the M3 mirror. These diaphragms have two functions: 1. To limit apertures in the SAC and then provide a system with few leaks in order to reduce the flowrate required to over-pressurize the SAC. 2. To prevent stray light by closing non useful areas.

18 Page : 18 / MASS BUDGET Parts Material Mass (kg) Conical interface E24 Steel 149,1 SAC Structure without the cone E24 Steel 89,4 M2 Mirror Zerodur 49,8 M3 Mirror Zerodur 53,7 M4 Mirror Zerodur 0,8 M5 Mirror Zerodur 19,9 Articulation connecting Stainless Steel 2,5 Invar blocs Invar 2,7 Tripod Invar 0,2 Star E24 Steel 1 3 M4 blocs E24 Steel 2,1 3 M4 blades E24 Steel 0,4 SAC TOTAL 222,5 TOTAL 371,6 The SAC mass ( 223 kg) is over the specified value (200 kg). This value is obtained on preliminary drawings with common margins. A reduce of 20 kg of the mass is reachable by optimization of the structure (flange shape, reinforced areas ).

19 Page : 19 / FINITE ELEMENT MODELING 7.1 MODEL The SAC is modelized with hexaedric volumic elements (8 Nodes Solid45). The link connection rods are modelized with rod elements (2 nodes Link8). 7.2 MASSES ET INERTIA The following figures give the position of the center of gravity as well as inertia related to the origin and the center of gravity. TOTAL MASS = MOM. OF INERTIA MOM. OF INERTIA CENTROID ABOUT ORIGIN ABOUT CENTROID XC = E-06 IXX = IXX = YC = E-07 IYY = IYY = ZC = IZZ = IZZ = IXY = E-04 IXY = E-04 IYZ = E-05 IYZ = E-06 IZX = E-04 IZX = E MATERIAL PROPERTIES Material Young s Modulus (MPa) Density (kg/m 3 ) Poisson s ratio Coefficient of Thermal Expension ( C -1 ) Zerodur ,24 0 Steel E ,30 13, Stainless Steel ,30 16, Glue DP , Invar ,30 1, SAFETY MARGINS These margins are commonly used in optical sub assemblies defined by SAGEM. A positive margin identified for each loading case will guarantee a good stability and a reliability of the design with respect to the optical performances Stress in ZERODUR MS = σ R p Tresca 1 > 0

20 Page : 20 / 42 R p : Bending strength Tresca : Tresca stress with R p = 10 MPa Stress in INVAR MS = LEP σ *1.5 VMS 1 > 0 LEP : Micro yield stress σ : Von Mises stress VMS The LEP value is equal to 100 MPa Stress in E24 steel MS = LEP σ *1.5 VMS 1 > 0 LEP : Micro yield stress σ : Von Mises stress VMS The LEP value is equal to the quarter of the elastic limit (50 MPa) Glue tensile strength MS = σ R t Tr *3 1 > 0 R t : tensile strength σ : tensile stress Tr with R t = 36 MPa.

21 7.4.5 Glue shearing Page : 21 / 42 MS Rc = τ *3 1 > 0 R c : shearing strength τ : shearing stress with R c = 27 MPa.

22 Page : 22 / MODAL ANALYSIS 8.1 SCOPE OF THE MODAL ANALYSIS The aim of the modal analysis is to estimate the frequencies of the eigen modes of the SAC and check the compliance with the mutually agreed value of 15 Hz. We have performed the calculation of the 20 first eigen modes. For the calculation, the SAC assembly is blocked for the translation motions only with the 48 interfaces locking points (rotation motions are free). 8.2 RESULTS The following table gives the twenty natural frequencies and their modal mass. MODAL MASS (kg) MODE FREQUENCIES X Y Z TOTAL

23 Page : 23 / 42 Figure 13: First mode modal deformation The frequency of the first mode, 35 Hz, is greater than the minimum value of 15 Hz.

24 Page : 24 / THERMAL ANALYSIS 9.1 SURVIVAL ENVIRONNEMENT 20 C For this simulation, the SAC is free along the radial direction at the fixation level. The nominal temperature is 20 C for a lowest temperature of 20 C (survival mode), so the first study consists in studying the SAC behavior under a thermal loading of 40 C. The result of this calculation is given hereunder, Tresca stresses in the mechanical parts and tensile and shear stresses inside the glue: Maximal Tresca stress (MPa) SAC M2 mirror 2,022 M3 mirror 1,967 M4 mirror 1,461 M5 mirror 1,326 M2 fixation 0,021 M3 fixation 0,000 M5 fixation 0,015 Tubes 0,026 Tripod 38,1 Star 15,9 Blades 0,138 Conical interface 0,008 Maxi stress inside the glue (MPa) Tensile 6,649 Shear 3,378 Stresses are mainly located at the interface between the different materials: - Invar/Steel - Invar/Glue - Zerodur/Glue

25 Page : 25 / THERMAL VARIATION ( T=1 C) The locating points translations are blocked (free rotations). The calculation gives the sensitivity of the stresses due to the temperature constraints. The following tables give the maximum Tresca stresses in the different mechanical parts and tensile/shear stresses inside the glue: Maximal Tresca stress (MPa) SAC M2 mirror 0,051 M3 mirror 0,049 M4 mirror 0,037 M5 mirror 0,033 M2 fixation 0,001 M3 fixation 0,000 M5 fixation 0,000 Tubes 0,004 Tripod 6,935 Star 1,053 Blades 0,004 Conical interface 5,379 Maxi stress inside the glue (MPa) Tensile 0,166 Shear 0,084 The following table gives the maximum efforts inside the interface screws: Effort (N) FX 383,1 FY 383,1 FZ 0 FT 383,1 We can see that the shear stress, in the screws of the upper conical interface part, is very important, 383N, this value is due to the model (no deformation of the cone mounting plane with the hexapod).

26 Page : 26 / 42 The following table gives the mirror displacements (translations and rotations): M2 M3 M4 M5 UX (µm) UY (µm) UZ (µm) -5,143-14,27-0,746-4,22 RX (µrad) RY (µrad) The following maps give the mirror deformation along the normal to the mirror surface (this one is approximated with a mean radius). In this study we only take into account the clear aperture of the mirrors, tilt and focus contributions are canceled. The mirror displacements and WFE maps are used to verify the compatibility between the mechanical design and the optical requirements. Especially SAC motion abilities in order to reach the required performances are tested (CODE V calculation).

27 Page : 27 / 42 M2 mirror M3 mirror M4 mirror M5 mirror Conclusion: M4 and M5 deformations are mainly due to the rigid body displacement.

28 Page : 28 / RADIAL GRADIENT (1 C) In this paragraph, we study the sensitivity of the mirror due to a radial gradient of temperature. The radial gradient is 1 C for 1800 mm (0,56 C/m). Tresca s stresses The following table gives the maximum stresses for all the components: Stress inside the glue Efforts in the screws Maximal Tresca stress (MPa) SAC M2 mirror 0,036 M3 mirror 0,035 M4 mirror 0,019 M5 mirror 0,024 M2 fixation 0,003 M3 fixation 0,003 M5 fixation 0,031 Tubes 0,092 Tripod 3,53 Star 0,539 Blades 0,023 Conical interface 5,244 Maxi stress inside the glue (MPa) Tensile 0,111 Shear 0,061 The following table gives the maximum efforts at the interface screw level: Effort (N) FX 518,71 FY 467,64 FZ 20,21 FT 571,91

29 Page : 29 / 42 The following table gives the mirror displacements (translations and rotations): M2 M3 M4 M5 UX (µm) 2,071 14,144-3,201-0,512 UY (µm) 0,185 0, ,225 UZ (µm) -2,577-7,135-0,373-2,111 RX (µrad) -0,001 0,003 0,001 0,037 RY (µrad) -15,055-26,552-9,472-13,946 The following maps give the mirror deformation along the normal to the mirror surface (this one is approximated with a mean radius). In this study we only take into account the clear aperture of the mirrors, tilt and focus contributions are canceled. M2 mirror M3 mirror M4 mirror M5 mirror Conclusion: M5 deformation is mainly due to a rigid body displacement.

30 Page : 30 / AXIAL GRADIENT (1 C) In this paragraph, we study the sensitivity of the mirror due to an axial gradient of temperature. The axial gradient is 1 C for 1580 mm (0,63 C/m). The following table gives the maximum stresses for all the components: Maximal Tresca stress (MPa) SAC M2 mirror 0,027 M3 mirror 0,047 M4 mirror 0,010 M5 mirror 0,016 M2 fixation 0,012 M3 fixation 0,002 M5 fixation 0,012 Tubes 0,585 Tripod 1,011 Star 1,011 Blades 0,441 Conical interface 0,042 Maxi stress inside the glue (MPa) Tensile 0,159 Shear 0,081 The following table gives the maximum efforts at the interface screw level: Effort (N) FX 0,12 FY 0,14 FZ 0,12 FT 0,14

31 Page : 31 / 42 The following table gives the mirror displacements (translations and rotations): M2 M3 M4 M5 UX (µm) UY (µm) UZ (µm) -1,729-8,597-1,792-1,429 RX (µrad) 0-0, RY (µrad) The following maps give the mirror deformation along the normal to the mirror surface (this one is approximated with a mean radius). In this study we only take into account the clear aperture of the mirrors, tilt and focus contributions are canceled. M2 mirror M3 mirror M4 mirror M5 mirror Conclusion: M4 and M5 deformations are mainly due to rigid body displacement.

32 Page : 32 / GRAVITY INFLUENCE 10.1 GRAVITY OF 1G ALONG Z AXIS (TEST POSITION) During the integration and test phases, the SAC is not inclined (vertical position). The following calculation gives the gravity effect under this loading case. It shows the displacements and stresses in the different parts of the SAC for a vertical position. The following table gives the maximum stresses for all the components: Maximal Tresca stress (MPa) SAC M2 mirror 0,208 M3 mirror 0,208 M4 mirror 0,033 M5 mirror 0,181 M2 fixation 6,794 M3 fixation 7,238 M5 fixation 4,329 Tubes 14,114 Tripod 3,251 Star 3,251 Blades 6,171 Conical interface 2,059 Maxi stress inside the glue (MPa) Tensile 0,198 Shear 0,080 The following table gives the maximum efforts at the interface screw level: Effort (N) FX 31,21 FY 38,63 FZ 79,62 FT 38,66

33 Page : 33 / 42 The following table gives the mirror displacements (translations and rotations): M2 M3 M4 M5 UX (µm) 0,009 0,006-0,001-0,036 UY (µm) -0,055-0,207 0,024 0,021 UZ (µm) -43,450-61,618-57,089-44,765 RX (µrad) -0,191-0,279 0,077-0,154 RY (µrad) -0,014-0, , GRAVITY OF 1G WITH A 37 INCLINATION In operational conditions, the SAC is inclined to 37 from the vertical axis. This study evaluates the stresses in the different parts for a 37 inclination. The following table gives the maximum stresses for all the parts: Maximal Tresca stress (MPa) SAC M2 mirror 0,302 M3 mirror 0,311 M4 mirror 0,061 M5 mirror 0,305 M2 fixation 5,46 M3 fixation 5,796 M5 fixation 3,467 Tubes 32,791 Tripod 2,973 Star 2,973 Blades 5,4 Conical interface 4,242 Maxi stress inside the glue (MPa) Tensile 0,435 Shear 0,118

34 Page : 34 / 42 The following table gives the maximum efforts at the interface screw level: Effort (N) FX 132,03 FY 89,56 FZ 143,81 FT 136,61 The following table gives the mirror displacements (translations and rotations): M2 M3 M4 M5 UX (µm) -46, ,583-3,23-32,045 UY (µm) 1,465-1,972 0,244 8,394 UZ (µm) -34, ,209-45,593-35,748 RX (µrad) -6,107-1,696 0,413 6,281 RY (µrad) 107, ,516 87,306 75,723 We have checked that the mirror displacements are compliant with the optical formula using the Warpp maps in the CODE V software.

35 Page : 35 / 42 Figure 14: SAC deformation for a 37 inclination Conclusion: This deformation is close to the first mode modal deformation VARIATION OF GRAVITY This study shows the effect on different parts of the inclination of the SAC from the vertical position (test position) to the 37 inclination. The aim of this paragraph is to show the mirror displacements during this inclination, this study is necessary to verify if the displacements are compensable by a SAC motion or not (translations and rotations). The same study is performed for the displacements around the nominal inclination (37 ) with a functional motion of ±8.5.

36 Page : 36 / Gravity variation 0 /37 The following table gives the mirror displacements (translations and rotations): M2 M3 M4 M5 UX (µm) -47, ,589-3,23-32,009 UY (µm) 1,52-1,764 0,267 8,373 UZ (µm) 8,751 12,408 11,496 9,017 RX (µrad) -5,916-1,416 0,336 6,435 RY (µrad) 107, ,518 87,306 75,719 The following maps give the mirror deformation along the normal to the mirror surface (this one is approximated with a mean radius). In this study we only take into account the clear aperture of the mirrors, tilt and focus contributions are canceled. M2 mirror M3 mirror

37 M4 mirror Page : 37 / 42 M5 mirror Conclusion: - M2 and M3 deformations are very similar. Optical analysis shows that there is a compensation between the two deformations, for this reason it is necessary to position the three M2 mirror fixations facing the M3 ones. - Except rigid body displacement the M4 deformation is completely negligible. - M5 deformation is very low (7 nm RMS), this loading case shows the validity and performance of the three-points fixation concept Gravity Variation 37/45.5 The following table gives the mirror displacements (translations and rotations): M2 M3 M4 M5 UX (µm) -8,704-24,551-0,598-5,9259 UY (µm) 0,285-0,314 0,051 1,549 UZ (µm) 4,246 6,022 5,579 4,375 RX (µrad) -1,084-0,245 0,058 1,201 RY (µrad) 19,845 28,241 16,166 14,02 The following maps give the mirror deformation along the normal to the mirror surface (this one is approximated with a mean radius). In this study we only take into account the clear aperture of the mirrors, tilt and focus contributions are canceled.

38 Page : 38 / 42 M2 mirror M3 mirror M4 mirror M5 mirror Conclusion: Except rigid body displacement the M4 deformation is completely negligible. Optical study shows that a SAC motion is necessary to compensate the SAC structure deflection due to the functional inclination (37 45,5 )

39 Page : 39 / Gravity variation 37 /28.5 The following table gives the mirror displacements (translations and rotations): M2 M3 M4 M5 UX (µm) 9,736 27,464 0,669 6,629 UY (µm) -0,317 0,357-0,056-1,734 UZ (µm) -3,484-4,941-4,578-3,59 RX (µrad) 1,218 0,283-0,067-1,339 RY (µrad) -22,199-31,592-18,084-15,684 The following maps give the mirror deformation along the normal to the mirror surface (this one is approximated with a mean radius). In this study we only take into account the clear aperture of the mirrors, tilt and focus contributions are canceled. M2 mirror M3 mirror M4 mirror M5 mirror

40 Page : 40 / 42 Conclusion: Except rigid body displacement the M4 deformation is completely negligible. Optical study shows that a SAC motion is necessary to compensate the SAC structure deflection due to the functional inclination (37 28,5 )

41 Page : 41 / SYNTHESIS TABLE The following table gives the RMS deformation values for each mirror for the different loading cases (tilt and focus contributions are canceled). M2 Mirror (nm RMS) M3 Mirror (nm RMS) M4 Mirror (nm RMS) M5 Mirror (nm RMS) T 1 C Thermal Radial Gradient Axial Gradient Variation de la 0 to (1) (1) gravité due à l inclinaison 37 to de : 37 to (1) M2 and M3 deformation are compensated (see ) The following table gives a summary of the different loading cases and the computed stresses. The MS margin is calculated for the maximum stress in each SAC parts (the formula are given in 7.4). Stresses (MPa) Survival -20 C T 1 C Thermal radial gradient axial gradient Gravity 1 g Z 1 g à 37 Maxi stress Limit (MPa) Tresca stress M2 mirror M3 mirror M4 mirror M5 mirror Von Mises stress M2 fixation M3 fixation M5 fixation Tube (1) tripod star blades cone Tensile inside the glue Shear inside the glue (1) the MS margin is equal to 0 in the tube. Slight modifications will be necessary to reduce stresses in the tube/cone interface area and then to restore the margin. MS

42 Page : 42 / CONCLUSION In conclusion, we can say that the study, detailed in this report, validates all the chosen design concept. Slight modifications will be necessary in order to enhance and increase the design quality, especially to reduce the stresses between the tube and the conical interface (MS margin increase). The SAC mass is slightly over the 200 kg specified ( 220 kg), this one can be reduced by a structure optimization (flange shape, reinforced areas). The conical interface mass is 150 kg, as explained previously this one is for us not included in the total mass budget. The mirror displacements, for the different loading case, have been introduced in the CODE V modelization. The results of these calculations show that all the displacements are compatible of the optical formula, all aberrations can be compensated by a SAC motion (tilts and focus), no modification of the SAC stiffness is necessary. Transport conditions have not been studied, only locking devices have been design and fixations are calculated for a dynamic load of 10g. This design is compliant with the specifications ( 3), all the required performances are reached (stiffness, compatibility between mirror displacements and optical formula, compatibility between adjustment and fixation devices and the tolerance budget...) even if some modifications will be necessary (preliminary design).