Advanced LIGO Spring/Flexure Intermediate Design Review

Transcription

1 Advanced LIGO Spring/Flexure Intermediate Design Review January 13, 2004 Ref: A

2 IDR Objectives Assess and confirm the completion of the spring/flexure parametric design (Task 2 of the Project Implementation Plan). Obtain technical concurrence that the spring/flexure parametric design is complete, as evidenced by completion of: an automated design tool (either in Excel or Matlab) which generates the dimensions of the leaf springs and flexure rods, given the mass properties of the two stages; documentation of the analytical basis for the design approach; plan for accommodating uncertainties in the material properties and dimensional accuracy of the springs and rods; plan for any development testing necessary to mitigate risk. 1/13/ A ASI-2

3 Applicable Design Requirements Parameter Requirements Units Design Status Stage Structures Center of Gravity (Stage 1) The CG of stage 1 shall lie at +/- 1.57" vertically with regard to stage 2 CG. inches Comply Center of Gravity (Stage 2) Rigid Body Frequencies The CG of stage 2 shall lie from 0 to 3.15" below the plane of the centers of the actuators at the stage 1-2 interface. The 12 coupled frequencies shall lie between 2 and 10 Hz. Within this range, lower spring stiffness is prefered. Springs inches Hz Comply Comply General The spring and flexure sets (3 each) shall be located within the structure such that the flexures lie at the corners of an equilateral triangle, which is centered in the structure in the X -Y plane. N/A Comply Spring Material 300 Maraging Steel N/A Comply Configuration Trapezoidal pattern cut by EDM methods and shall follow the patterns shown in the Technology Demonstrator drawings p through 037. N/A Exception Spring Stiffness (Max) 4225 (Stage 0/1) 2512 (Stage 1/2) lb(force)/in Comply Spring Stress 35% of Yield Strength (Goal of 30%), when operating at the working load with the flexure laterally offset as much as 1mm from nominal. N/A Exception Spring Length (Max) 19.7" inches Comply Spring Width (Max) 0.5 of the length inches Comply Spring Position The spring must lie flat at the working load of the system. The radial position of the spring tips and flexures shall fall between 70 % to 90% of the maximum structure radius. N/A Exception Flexures General The spring and flexure sets (3 each) shall be located within the structure such that the flexures lie at the corners of an equilateral triangle, which is centered in the structure in the X -Y plane. N/A Comply Flexure Material 300 Maraging Steel N/A Comply Flexure Moment Location Flexures shall be designed so that the "upper" zero moment point (UZMP) of each flexure shall lie on the neutral axis of its spring. N/A Comply Flexure Position The radial position of the spring tips and flexures shall fall between 70 % to 90% of the maximum structure radius. N/A Comply 1/13/ A ASI-3

4 Stress Requirements Material: Maraging 300 Steel (Allvac Vascomax C-300) Density (lb/in³) Modulus of Elasticity (ksi) CTE, linear 20 C (µin/in- F) 5.6 Tensile Strength (ksi),.250" sheet % Yield Strength (ksi) 309 Proportional Limit (ksi) 272 Endurance Limit (ksi) 125 [Source: Allvac technical data sheet NI-253/154/156/173] Treatment of stress concentrations currently under review by LIGO project Tentative restatement of stress requirement: "... springs and flexures to be designed for a maximum stress of 35% of yield strength, with a goal of 30%, when operating at the working load at 1 g and with the flexure laterally offset as much as 1 mm from its nominal location. An exception to this, for stress risers that are localized, allows peak stresses to be as high as 80% of yield strength, with approval from the LIGO Project. ASI s current design approach: Set max fiber stress in outer surface of spring to less than 100 ksi (33% of nominal yield strength meets requirement of <35%) Ensure local stress concentrations are below 80% of yield 1/13/ A ASI-4

5 Description of Spring/Flexure Reference Design Spring blades lie flat and level under dead load Actuator plane located at LZMP, blade neutral axis located at UZMP Moment V(L-2Z) on stage 1 is unavoidable Z chosen to make M=0 Gravity equilibrium Lateral displacement enforced 1/13/ A ASI-5

6 First Order Spring Blade Sizing Spring blades are sized for vertical spring constant and maximum stress 1. Blade thickness t determined by dead load P and stress allowable σ : t = 6P ( w/ L)σ 2. Blade length L chosen to provide desired stiffness K : 3 Et ( w/ L) L = + a 6K 3. Stiffness K may be related to the SDOF frequency f : K = (2πf ) 2 ( P / g) 2 Notes: Based on simple bending of flat plate Load is applied at apex of triangle Ratio (w/l) is fixed at 0.5 per design requirements Blade has constant curvature, so deformed shape will be a circular arc 1/13/ A ASI-6

7 First Order Spring Blade Sizing (2) Sizing diagrams for σ=100ksi, a=1.5in, E=27.5 msi Probable strategy: choose blade stiffness so highest coupled rigid body frequency is near 10 Hz limit (allows shortest spring blade) Corresponding SDOF frequency depends on final system mass properties f = 2 Hz Thickness t (in) Length L (in) f = 3 Hz f = 3.5 Hz f = 4 Hz Static Payload (lb) Static Payload (lb) 1/13/ A ASI-7

8 Stress Concentration in Spring Blade Moderate variation of stress across width of blade (Poisson effect) Very localized line of stress concentration along fillet ETF: R/T=0.16, K=1.56 Fillet in Bending [Based on formulas from Roark, Table 37, Case 5b] 1/13/ A ASI-8

9 First Order Flexure Rod Sizing Flexure rods sized for lateral spring constant and maximum stress Based on ASI technical note C, Analysis of LIGO Flexure Rods Probable strategy: choose rod stiffness so lowest coupled rigid body frequency is near 2 Hz limit (provides best performance with little penalty) Corresponding SDOF frequency depends on final system mass properties Flexure Diameter D (in) f = 4 Hz f = 3 Hz f = 2.5 Hz f = 2 Hz Flexure Length L (in) f = 2 Hz f = 2.5 Hz f = 3 Hz f = 4 Hz Payload (lb) Payload (lb) 1/13/ A ASI-9

10 Stress Concentration in Flexure Rod Very localized stress concentration at one side of fillet ETF: R/T=0.31 Ka=1.43, Kb=1.33 Axial only Axial and Bending [Based on formulas from Roark, Table 37, Cases 17a and 17b] 1/13/ A ASI-10

11 What Can Go Wrong With the Ideal Design? Deviation Impact Rough-Estimate Error Amount Gravity-induced tilting when Unavoidable tilt-horizontal coupling, only Tilt-horizontal coupling = 1 mrad/in actuating stage 2 on stage 2 Actuator misaligned with LZMP Blade misaligned with UZMP Blade not level Tilt-horizontal coupling occurs, even with upstream stage grounded (due to nonzero M, which is reacted by bending the spring blades) Blade experiences bending or flexure; this introduces additional lateral flexibility, which moves the "effective" LZMP Torsion-vertical coupling ("corkscrew"), if blades are not oriented radially Tilt-horizontal coupling = 1 mrad/in per inch of misalignment (0.04 mrad/in per 0.04 inch of misalignment) Tilt-horizontal coupling = 0.01 mrad/in per inch of misalignment (0.004 mrad/in per 0.04 inch of misalignment) Depends on blade orientation and rod radius; for tangentially oriented blades at 25" radius, torsionvertical coupling = 0.01 mrad/in per mrad out of level Blade not flat Can result in torsion-vertical coupling, if end is not flat. Can also result in tilthorizontal coupling, due to misalignment of UZMP with elastic center of bent blade, or resulting movement of LZMP Depends on details of lack of flatness; one scenario gives tilt-horizontal coupling 0.02 mrad/in per inch of deviation from flat (0.008 mrad/in per 0.04 inch deviation from flat) 1/13/ A ASI-11

12 Other Issues With Reference Design Concerns about flattening the blades by adjusting trim mass Requires trim mass equal to total mass times uncertainty of flattening load, making our mass budget harder to meet LZMP changes with load (approximately inches per 1% of load), so it is difficult to simultaneously flatten and level the blade while precisely positioning the LZMP Program risks Must commit to pre-curved blade shape prior to fabrication Fabrication costs/risks; blade fabrication is on critical path Concern with stiffness effects of supposedly rigid structure (e.g., bending stiffness of blade mount, rotational fixity of rod ends) May contribute non-negligible errors Discovered after fabrication of blade shape 1/13/ A ASI-12

13 Recommended Modification to Reference Design Work to fixed load, rather than adding weight to flatten the spring Consequences: The spring will be operated in a non-flat state Add angular and height trim features on sacrificial mating features Uncertainties on LZMP and corkscrew zeroing make it likely that we will want to allow for a one-time fine adjustment based on measured tilthorizontal and torsion-vertical static coupling 1/13/ A ASI-13

14 Digression: Stiffness Matrix Structure Symmetry in a single spring/flexure system: X Y Z RX RY RZ blade clocking angle 1/13/ A ASI-14

15 Digression: Stiffness Matrix Structure (2) Symmetry in 120º-symmetric 3-spring/flexure system (assuming 3 identical spring/rods) X Y Z... RX RY RZ 1/13/ A ASI-15

16 Digression: Stiffness Matrix Structure (3) Only two nonzero off-diagonal terms in system stiffness matrix Corkscrew : (1,4), (2,5), (3,6) positions Proportional to k 13 sinφ Causes roll/horizontal coupling and torsion/vertical coupling To eliminate, need either sinφ =0 (i.e., radially oriented blades) or k 13 =0 To get k 13 =0, we want a flat blade or a properly angled bent blade, so a pure vertical force produces no lateral translation Overturning : (1,5), (2,4) positions Involves k 13 cosφ, k 15, and k 24 Causes tilt/horizontal coupling* To eliminate, either zero these off-diagonal terms at the single flexure/rod level, or arrange for cancellation at the system level We get k 15 = k 24 = 0 by aligning to the zero moment points *in addition to gravity-induced tilt/horizontal coupling 1/13/ A ASI-16

17 Proposed Fine-Balance Adjustment Plan Separately measure the stiffness of each blade in a bench test Build a full SEI assembly, with full payload mass and nominal spring/flexure geometry Measure stage 2 tilt-horizontal and torsion-vertical coupling Lock stage 1 to stage 0 Energize stage 1-2 lateral and vertical actuator(s), measure optical table translation and rotation Measure stage 1 tilt-horizontal and torsion-vertical coupling Unlock stage 1 from stage 0, lock stage 2 to stage 1 Energize stage 0-1 lateral and vertical actuator(s), measure optical table translation and rotation Calculate LZMP misalignment distance & torsion-vertical thread pitch Final-machine adjustable features to zero out the off-diagonal terms Perform final measurements to validate stiffness decoupling 1/13/ A ASI-17

18 Fine-Balance Adjustment Features 1. Stage 1-to-2 or Stage 0-to-1 vertical alignment Simple shim or final-machined flat mating surface 2. Stage 1-to-2 or Stage 0-to-1 LZMP location Effectively requires relocating blade and rod vertically, while leaving stages relative positions unchanged (two counteracting shims or final-machined flat surfaces, one of which already exists for adjustment #1) 3. Stage 1-to-2 or Stage 0-to-1 corkscrew correction Requires angular change to blade orientation (rotate about UZMP) Resulting base height movement requires adjustment in #1 Resulting angular change at flexure rod support must be counteracted by an angular adjustment feature there Note: if we get good repeatability between blades and rods, the same adjustment can be incorporated equally in all 3 spring/flexure systems, and no fine adjustment will be needed for Phase III 1/13/ A ASI-18

19 Observation on Blade Flatness Since we deem it necessary/prudent to allow for fine adjustment of the spring/flexure system, there is very little penalty to entertain the possibility of moderate curvature in the blade under load Even a moderately curved blade exhibits the same two off-diagonal stiffness features which we are already proposing to compensate for The curved blade and rod under load is amenable to analysis to determine the effective UZMP and LZMP of the system A properly balanced curved-blade system should not degrade the performance of the isolation system in any respect Once we allow a curved blade under load, it is natural to propose an initially flat blade, which significantly reduces fabrication costs, risks, and should allow for a more repeatable blade stiffness 1/13/ A ASI-19

20 Fabrication Notes on an Initially Flat Spring Blade Using flat blade stock would significantly change the processes associated with the fabrication of the springs. This would remove the springs from the high complexity category and place them in the moderate to low complexity category. This change would have the following benefits: Risk The flat-blade concept would reduce the manufacturing risks significantly. It removes the potential issues with EDM machining, cutting contours from thick material and should increase the options for material suppliers. Schedule This should remove the probability that the springs would be a schedule driver Cost The cost associated with the springs would be reduced easily by 50% but would likely be much greater; total Phase III dollar savings in production quantities of 15 HAM s and 15 BSC s are estimated to exceed one million dollars 1/13/ A ASI-20

21 Proposed Design LEAF-SPRING AS MACHINED [Locating features TBD] 1/13/ A ASI-21

22 Spring Blade and Flexure Rod Arrangement UPPER CLAMP UPPER FLEXURE ROD SHIM LOWER LEAF SPRING SHIM SUPPORT POST SUSPENDED STAGE INTERFACE AREA 1/13/ A ASI-22

23 Section View of Spring Blade and Flexure Rod in 1 G FLEXURE ROD UPPER SHIM Height Correction UPPER CLAMP FLEXURE ROD ANGLE ADJUSTMENT SHIM Angle Correction LOWER LEAF SPRING SHIM Angle & Height Correction FLEXURE ROD LOWER SHIM Height Correction 1/13/ A ASI-23

24 Spring Loading Fixture for Precise Characterization BEARING PIVOT LOADING TURNBUCKLE LOAD CELL FORCE VECTOR ADJUSTMENT 1/13/ A ASI-24

25 Stress Condition at Corner Finite element model created to gain better insight into the stress concentration at the interface between the flat blade and the mounting blocks. Normal Stress Concentration No simple hand calculation for contact stress in this configuration. Linear finite element model does not effectively predict the contact stress Steel Vascomax C Steel Unit Load, 1 lbf Interface Overlap, L (in.) Active Blade Length = 10 MSC/Nastran Plain Strain Model Element Size = 0.05 CQUAD4 Elements 1/13/ A ASI-25

26 Discussion of Local Stress Riser at Corner In a effort to maintain spring rate repeatability, the corner radius on the mounting block is intentionally small, reducing the active length ambiguity and increasing repeatability. The small radius results in a higher stress concentration. If the radius was increased, machining tolerances could cause undesirable variability. A final manufacturing step will form the interface between the leaf spring flexure and the root mounting block. The flexure will be loaded to 125% or greater of operational load. If contact stress exceeds the yield strength of the material, the operation will plastically deform the contact zone, redistributing the load, to form the final corner interface geometry Once formed, the stresses in the corner contact zone under operational loading will remain below the 80% of Fty requirement Will size interface fasteners to prevent gapping in the interface Will account for preload uncertainty in calculations Will utilize locating pins to ensure repeatability in the event the joint is disassembled 1/13/ A ASI-26

27 Interface Normal Stress Plot Interface Normal Stress (psi / lbf / in.) Interface Overlap vs. Normal Stress, Radius 0.25, Mounting Blocks 1 Thick " 4" 3" 2.5" 2" 1.5" The trade in interface overlap length shows that as the length decreases, the peak normal stress also increases as does the tensile stress directly behind the contact point. Peak contact stress will increase to with increased mesh refinement. As the corner radius is increased, the contact stress decreases. However, the active length of the flexure blade becomes more ambiguous. Joint Overlap, L (in.) Note: Mesh QUAD element size = /13/ A ASI-27

28 Design Example Lb ½ A286 Bolt, Preload 75% F tu Steel Vascomax C-300 Steel 2500 lb Tip Load, 416 lb/in, Assuming 6 Root Width 0.90 Interface Overlap, 2.5 (in.) Active Blade Length = " Root Overlap Sample Joint Maximum VonMises Stress = 31.8 ksi Plot of normal stress indicates that the overlap interface region does not gap under static and operational loading conditions. Max σ c = -45ksi (true contact stress state is higher, low due to coarseness of the mesh at the contact point) Normal Stress, psi Tip Load Only Preload Only Sum, Preload & Tip Load Joint Overlap, L (in) 1/13/ A ASI-28

29 Representative 12-DOF NASTRAN Model Stage 1/2 springs and flexures r = 25 in Stage 0: GROUND Stage 0/1springs and flexures r = 25 in Stage 1: 1914 lb R TOR = 22.3 in, R TILT = 16.4 in Stage 2: 3470 lb R TOR = 19.5 in, R TILT = 18.7 in Model shown stretched ; stages are actually coincident under 1g 1/13/ A ASI-29

30 NASTRAN Modeling Approach Model is constructed as it will be in 1-g gravity field Gravity preloads are applied Ensure that stress state from preload matches the actual state (e.g., no moment between flexure rods and spring blades) Recover differential stiffness (stiffness term due to initial stress state) from NASTRAN buckling solution Small-motion analysis solutions for stiffness, modes are conducted with differential stiffness added This analysis approach works successfully on test cases (e.g., flexure rod alone) and on the simplified model shown. It can be applied effectively to a more detailed model, including the stiffness effects of adjacent fittings, etc. 1/13/ A ASI-30

31 Stage 0/1 and Stage 1/2 Blade/Rod Geometry Balancing (eliminating off-diagonal terms) was performed empirically in NASTRAN, but matches closely the theoretical LZMP calculation Stage 0/1 Stage 1/2 Length L (in) 5 5 Diameter (in) Load (lb) Z (in) tanh(kl/2)/k H (in) Ψ (deg) /13/ A ASI-31

32 First 12 Coupled Modes of Representative Model Modes 1 and 2, 2.1 Hz 1st Lateral (In-Phase) Mode 3, 2.6 Hz 1st Torsion (In-Phase) Modes 4 and 5, 2.9 Hz 1st Pitch/Yaw (In-Phase) Mode 6, 3.0 Hz 1st Vertical (In-Phase) Modes 7 and 8, 6.3 Hz 2nd Lateral (Out-of-Phase) Mode 9, 7.2 Hz 2nd Torsion (Out-of-Phase) Mode 10, 9.2 Hz 2nd Vertical (Out-of-Phase) Modes 11 and 12, 9.8 Hz 2nd Pitch/Yaw (Out-of-Phase) 1/13/ A ASI-32

33 Stiffness Matrix of Representative Model Units are lb/in, in-lb/in, and in-lb/rad Only the stiffness in the XZ-plane is shown; YZ-plane is identical Small off-diagonal terms can be driven to zero by fine-tuning the model parameters Stage 0 Stage 1 Stage 2 Stage 0 Stage 1 Stage 2 X Z RY RZ X Z RY RZ X Z RY RZ X Z RY E+06 SYM RZ E+06 X Z RY E E+06 RZ E E+06 X E Z E E RY E E+06 RZ E E+06 1/13/ A ASI-33

34 Primary Risks and Possible Development Tests Repeatability of blade stiffness and positional accuracy This risk is greatly reduced by using the flat blade approach; no development tests are considered necessary Ability to analyze, measure, and compensate for off-diagonal coupling of bent-blade configuration Possible risk-mitigating development test Construct half-scale suspension system Suspend half-mass from a rigid foundation Characterize dynamically by modal test (infer static stiffness from modes, based on accurate knowledge of test mass properties) Prove adjustment scheme can take out residual errors 1/13/ A ASI-34

35 Summary of IDR Objectives Success criterion 1: an automated design tool (either in Excel or Matlab) which generates the dimensions of the leaf springs and flexure rods, given the mass properties of the two stages COMPLETED. Excel-based tools allow sizing of the springs and flexures, as a function of mass properties and desired SDOF frequency Success criterion 2: documentation of the analytical basis for the design approach COMPLETED. Flexure rod analysis document released; approach to NASTRAN analysis of springs/flexures has been defined and checked out Success criterion 3: plan for accommodating uncertainties in the material properties and dimensional accuracy of the springs and rods COMPLETED. See proposed fine-balance adjustment plan Success criterion 4: plan for any development testing necessary to mitigate risk IN WORK. Waiting for LIGO project feedback on perceived risks 1/13/ A ASI-35

36 Conclusion If ASI s proposed design modifications are acceptable to LIGO project, some design requirement updates are needed: Treatment of stress concentrations Blade flatness requirement Spring configuration requirements (drawings from ETF) 1/13/ A ASI-36

37 Other Discussions (Time Permitting) Need closure ASAP on the following design requirements to allow HAM and BSC configuration work: Payload mass properties Assumed mass distribution on optical table Stiffness or flexibility off-diagonal requirement Clarification of non-collocated phase requirement Actuator CFM cleaning 1/13/ A ASI-37