DEVELOPMENT OF ADVANCED MECHANICAL SYSTEMS FOR STABILIZATION AND NANO-POSITIONING OF CLIC MAIN BEAM QUADRUPOLES M. Esposito, K. Artoos, C. Collette, P. Fernandez Carmona, S. Janssens, R. Leuxe IWAA 2012 10-14 September 2012, Fermilab The research leading to these results has received funding from the European Commission under the FP7 Research Infrastructures project EuCARD
Outline 2 Introduction & Requirements Active Support for Main Beam Quadrupoles Analytical & Finite Element models Experimental set-ups & sensors Future developments Conclusions M. Esposito, IWAA 2012 Fermilab
Luminosity, beam size 3 and alignment A = L σ σ x y ~40 nm 1 nm I.P. M. Esposito, IWAA 2012 Fermilab
Alignment requirements Contact: H. Mainaud Durand 4 Mechanical prealignment ± 0.1 mm Active prealignment of external references of the accelerating structures and quadrupoles within a few microns Sliding window: zero of component shall be included in a cylinder with radius: 17 µm for MB Quad over 200 m 10 µm BDS over 500 m H. Mainaud Durand, “Validation of the CLIC alignment strategy on short range”, IWAA 2012 M. Esposito, IWAA 2012 Fermilab
Stability requirements 5 Stability (magnetic axis): Vertical 1.5 nm at 1 Hz Lateral 5 nm at 1 Hz Integrated r.m.s. displacement ground vibration Cultural noise -Human activity Earth motion -Incoherent - Coherent -Highly variable Depth tunne l Micro seismic peak Reduced by Beam based feedback M. Esposito, IWAA 2012 Fermilab
Other requirements 6 Stiffness-Robustness Applied forces (water cooling, vacuum, power leads, cabling, interconnects, ventilation, acoustic pressure) - Compatibility alignment -Transportability/Installation Available space Integration in two beam module 620 mm beam height Accelerator environment - High radiation - Stray magnetic field M. Esposito, IWAA 2012 Fermilab
Soft or rigid support ? 7 Active stabilization Soft system is not robust against external forces Artoos K. et al., “Status of a Study Stabilisation and Fine Positioning of CLIC Quadrupoles to the Nanometre Level”, IPAC11 • Janssens S. et al., “System Control for the CLIC Main Beam Quadrupole Stabilization and Nano-positioning”, IPAC11 • M. Esposito, IWAA 2012 Fermilab
Nano-positioning 8 Modify position quadrupole in between pulses (~ 5 ms) Range ± 5 μ m, increments 10 to 50 nm, precision ± 1nm • In addition/ alternative dipole correctors • Use to increase time to next realignment with cams M. Esposito, IWAA 2012 Fermilab
Actuator support 9 stabilisation support section made of PI Piezoelectric Actuator Inclined stiff piezo actuator pairs with High stiffness (480N/ µ m) flexural hinges (vertical + lateral motion) Sufficient travel (15 µ m) Good resolution (0.15 n m) (each magnet will have 2 or 3 sections depending on its length) Universal Flexural Joint 2 rotation axes in the same plane rotational stiffness (k e =220Nm/rad) Axial stiffness (k aj =300N/ µ m) M. Esposito, IWAA 2012 Fermilab
X-y guiding mechanism 10 • Blocks longitudinal movements • Increases lateral stiffness by factor 200, no modes < 100 Hz • Introduces a stiff support for nano-metrology • Transportability LASER interferometere Capacitive Optical gauge encoder Flexural pins 1&2 52 kg mass R. Leuxe M. Esposito, IWAA 2012 Fermilab
Analytical model (1) 11 Coordinate systems D v 𝛄 D h R L m Coordinate transformation q 1 = sinβ x + cosβ y + d v sinβ − d h cosβ θ q 2 = −sinβ x + cosβ y + − d v sinβ + d h cosβ θ α 1 = − cosβ x + sinβ cosβ − d h sinβ y + − d v θ r r r r L b α 2 = − cosβ x − sinβ cosβ − d h sinβ y + − d v θ r r r r M. Esposito, IWAA 2012 Fermilab
Analytical model (2) 12 Lagrangian method for Modal Analysis Constraints R + q 1 ∗ Cos ( β− α 1 ) + 𝜖 m ∗ Sin( θ ) + R + q 2 ∗ Cos ( β + α 2 )=0 R + q 1 ∗ Sin ( β− α 1 ) + 𝜖 m ∗ Cos( θ ) + R + q 2 ∗ Sin ( β + α 2 )- 𝜖 b =0 Stiffness calculation d 𝜖𝜖 − 𝜖𝜖 𝜖 = T − V 𝜖s = 0 with dt 𝜖 s ̇ T = 1 2 Mx ̇ 2 + 1 2 My ̇ 2 + 1 2 I θ̇ 2 and V = 1 2 + q 22 ) + 2 k a (q 1 1 2 k e [ α 12 + α 22 +( α 1 − θ ) 2 + ( α 2 −θ ) 2 ] Principle of virtual work F x *dx=M O1 * d α 1 + M O2 *d α 2 + M A * (d β− d α 1 )+ M B * (d β +d α 2 ) s(t) = s 0 e −iωt −ω 2 M + K = 0 Ms ̈ + Ks = 0 F y *dy=(M O1 + M O2 + M A + M B )* d α 1 +F 1 *dq 1 +F 2 *dq 2 f= ω /2 π ω 2 are the eigenvalues of matrix M -1 K M. Esposito, IWAA 2012 Fermilab
Finite Element models 13 ANSYS Classic ANSYS Workbench Concentrated Rigid links mass Rotational joints Beam elements DISPLACEMENT STEP=1 SUB =2 1&2 AUG 18 2011 FREQ=91.1157 15:11:15 R Y DMX =.384E-07 R R R R Z X R R R R R R R R R R R R R R R R R R R R R R R R R R R R R M. Esposito, IWAA 2012 Fermilab
Analytical & FE results 14 4-bar mode θ mode Vertical mode Hz k h Vt k v [N/ μ m] [N/ μ m] f [Hz] shape f [Hz] shape f [Hz] shape 0.21 203 9.2 255 319 Analytical Without Ansys 0.21 204 9.2 255 319 xy guide classic 0.21 203 8.3 245 312 Ansys WB 35 229 153 310 339 Analytical With xy Ansys 44 225 125 275 327 classic guide 38 220 145 303 336 Ansys WB Type 1 MBQ with k h =69 k v =227 119 303 319 xy guide [N/ μ m] [N/ μ m] [Hz] [Hz] [Hz] Longitudinal stiffness Longitudinal mode With xy guide With xy guide Without xy guide With xy guide With xy guide Without xy guide (pins fixed to steel (pins totally fixed on 1 (pins totally fixed on 1 (pins fixed to steel 3.4 Hz 0.03 N/ μ m plates) end) end) plates) 65 Hz 280 Hz 278N/ μ m 48 N/ μ m M. Esposito, IWAA 2012 Fermilab
Simulated Kinematics (1) 15 3 DOF system Only 2 DOFs are controlled Constraints Cvt= R + q 1 ∗ Cos ( β− α 1 ) + 𝜖 m ∗ Sin( θ ) + R + q 2 ∗ Cos ( β + α 2 ) Chz= R + q 1 ∗ Sin ( β− α 1 ) + 𝜖 m ∗ Cos( θ ) + R + q 2 ∗ Sin ( β + α 2 )- 𝜖 b Potential Energy 𝑟 1 = 𝑡𝑡𝑡𝑡 𝑦 + 𝑑𝑑𝑡𝑡 𝑧 + 𝐸 𝑤 𝑡𝑡𝑡𝑡 − 𝐸 ℎ 𝑑𝑑𝑡𝑡 𝜄 V = 1 2 + q 22 ) + 1 2 k e [ α 12 + α 22 +( α 1 − θ ) 2 + ( α 2 −θ ) 2 ] 2 k a (q 1 𝑟 2 = −𝑡𝑡𝑡𝑡 𝑦 + 𝑑𝑑𝑡𝑡 𝑧 + −𝐸 𝑤 𝑡𝑡𝑡𝑡 + 𝐸 ℎ 𝑑𝑑𝑡𝑡 𝜄 2 controlled DOFs 𝛽 1 = − 𝑑𝑑𝑡𝑡 𝑦 + 𝑡𝑡𝑡𝑡 𝑑𝑑𝑡𝑡 − 𝑒 ℎ 𝑡𝑡𝑡𝑡 𝑧 + −𝐸 𝑤 𝜄 𝑆 𝑆 𝑆 𝑆 𝛽 2 = − 𝑑𝑑𝑡𝑡 𝑦 − 𝑡𝑡𝑡𝑡 𝑑𝑑𝑡𝑡 − 𝐸 ℎ 𝑡𝑡𝑡𝑡 𝑧 + −𝐸 𝑤 𝜄 𝑆 𝑆 𝑆 𝑆 NMinimize[ 𝑊 , Cvt == 0, Chz == 0, dq1 == 1, dq2 == − 1 ] 2 equations necessary to fully describe the kinematics (find a minimum of potential energy respecting the constraint equations and fixing the input values of the actuator displacements) The system is not fully determined without taking into account the reaction forces M. Esposito, IWAA 2012 Fermilab
Simulated Kinematics (2) 16 Hz movement Vt movement x/q 1.3 y/q 1.06 Analytical y/x 0 x/y 0 model 8 PINS 5.15 θ /y [µrad/µm] 0 θ /x [µrad/µm] x/q 1.24 y/q 1.03 y/x 0.05 x/y 0 FE model θ /x [µrad/µm] 5.25 θ /y [µrad/µm] 0 x/q 1.4 y/q 1.06 Analytical y/x 0 x/y 0 model NO PINS θ /x [µrad/µm] 4.64 θ /y [µrad/µm] 0 x/q 1.15 y/q 1.06 y/x 0.03 x/y 0 FE model θ /x [µrad/µm] 6.6 θ /y [µrad/µm] 0 • Pins do not change the “shape” of the movement • Less than 1% of coupling between horizontal and vertical • ≈5 μ rad/ μ m of roll per unit lateral displacement • Translation/actuator elongation ratio is ≈1:1 ( Vt) and ≈ 1.4:1 (Hz) M. Esposito, IWAA 2012 Fermilab
3D simulated Kinematics 17 PITCH YAW T1 MBQ T4 MBQ No loss of translation range for T4 • About 25% of loss of vertical translation range for T1 pitch • About 80% of loss of lateral translation range for T1 yaw • M. Esposito, IWAA 2012 Fermilab
X-y prototype and sensors 18 Capacitive sensor 3 beam interferometer Actuators equipped with strain gauges Optical ruler M. Esposito, IWAA 2012 Fermilab
X-y positioning: lateral and vertical 6 nm steps 19 M. Esposito, IWAA 2012 Fermilab
X-y Positioning 20 1&2 Parasitic roll M. Esposito, IWAA 2012 Fermilab
Comparison sensors 21 Sensor Resolution Main + Main - Actuator sensor 0.15 nm No separate assembly Resolution No direct measurement of magnet movement Capacitive gauge 0.10 nm Gauge radiation hard Mounting tolerances Gain change w. α Orthogonal coupling Interferometer 10 pm Accuracy at freq.> 10 Hz Cost Mounting tolerance Sensitive to air flow Orthogonal coupling Optical ruler 0.5*-1 nm Cost Rad hardness sensor 1% orthogonal coupling head not known Mounting tolerance Limited velocity Small temperature drift displacements Possible absolute sensor Seismometer (after integration) < pm at higher frequencies For cross calibration M. Esposito, IWAA 2012 Fermilab
Noise level in frequency domain (PSD) 22 Cross check between different instrumentation + resolution measurements 1&2 14 pm sine wave 14 nm sine wave M. Esposito, IWAA 2012 Fermilab
Stabilization on Type 1 MBQ 23 Water cooling 4 l/min With magnetic field on With hybrid circuit Figure Value R.m.s @ 1Hz magnet 0.5 nm R.m.s @ 1Hz ground 6.3 nm R.m.s. attenuation ratio ~13 R.m.s @ 1Hz objective 1.5 nm M. Esposito, IWAA 2012 Fermilab
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