PETER: a double torsion pendulum to test quasi Free Fall on two Degrees of Freedom

Transcription

1 PETER: a double torsion pendulum to test quasi Free Fall on two Degrees of Freedom Luciano Di Fiore Lorenzo Marconi, Ruggero Stanga, Noemi Finetti, INFN and Università di Firenze Massimo Bassan, Fabrizio De Marchi, Yury Minenkov, Giuseppe Pucacco, Massimo Visco. INFN and Università di Roma Tor Vergata Martina De Laurentis, Rosario De Rosa, Fabio Garufi, Aniello Grado, Leopoldo Milano. INFN, Università di Napoli "Federico II" and INAF A. Cavalleri, R. Dolesi, M. Hueller, D. Vetrugno, S. Vitale, W.J. Weber. Università di Trento and INFN-TIFPA This work is supported by INFN Commission II Moriond 26/3/217 L.Di Fiore 1

2 This work started within the ground testing activities for the characterization, before flight, of the Gravitational Reference Sensor (GRS) of LISA- Pathfinder: in particular the realization of a two stage torsion pendulum facility (nicknamed PETER, PEndulum soft in Translation and Rotation) for the measurement of GRS actuation Cross Talks (CT) In my talk I will discuss: Introduction principle of operation of the double pendulum few words about the LISA-PF GRS goal of the activity description of the PETER apparatus Cross -talk measurement technique and results possible extension to more than 2 DOFs possible application to other experiments Moriond 26/3/217 L.Di Fiore 2

3 x=f or '== (A.U.) "quasi free fall" with a pendulum F F F 1 or 1 Iω 2 mω 2 for frequency above the resonance frequency the mechanical transfer function is equivalent to the one of a body in free fall ~ A 1 ω ω 2 with ω 2 = k I or g l Moriond 26/3/217 L.Di Fiore 3

4 Single stage torsion pendulum configurations Single mass torsion pendulum four mass torsion pendulum TM In this case we can only measure a torque acting on the TM TM In this case we can only measure a force acting on the TM This kind of device have been extensively used for ground testing during the development of LISA Pathfinder GRS Moriond 26/3/217 L.Di Fiore 4

5 Principle of operation of PETER With a two stages torsion pendulum we can get two soft DOFs in this case we can measure both force TM Moriond 26/3/217 L.Di Fiore 5

6 Principle of operation of PETER With a two stages torsion pendulum we can get two soft DOFs in this case we can measure both force and torque TM Moriond 26/3/217 L.Di Fiore 6

7 Principle of operation of PETER With a two stages torsion pendulum we can get two soft DOFs in this case we can measure both force and torque simultaneously TM Moriond 26/3/217 L.Di Fiore 7

8 Few words a bout LISA-Pathfinder (there is a dedicated session on Tuesday) Drag free spacecraft control : the GRS Moriond 26/3/217 L.Di Fiore 8 Courtesy of S. Vitale

9 . GRS in LISA PF: a capacitive sensor surrounding the TM Moriond 26/3/217 9 L.Di Fiore

10 Goal of the activity Our goal has been the development and operation of a torsion pendulum that is "soft" in 2 DOFs so that the TM is in free-fall in 2 DOFs. This permits simultaneous measurement of force and torque acting on the TM allowing: measurement of stray forces and torques on TM measurement of cross-talks between different DOFs both in readout and actuation. measurement of residual stiffness (force acting on the TM due to GRS motion) both in angle and displacement. other measurements that are also permitted by single pendulums (charge, thermal effects,...) In this talk we will in particular report actuation Cross-Talk measurements Moriond 26/3/217 L.Di Fiore 1

11 PETER in the Napoli lab during the assembling phase reinforced concrete basement crossbar rigid leg GRS dummy TMs Moriond 26/3/217 L.Di Fiore 11

12 The experimental apparatus (PETER) PETER (PEndulum free in Translation and Rotation) We tested a copy of the LISA-PF GRS engineering model (4mm gap sensor in Mo and SHAPAL) The GRS electronics (from ETHZ) is similar to the LISA-PF one. The total length is about 1.7 m The double pendulum is enclosed in a vacuum tank (residual pressure about 1-6 mbar). Moriond 26/3/217 L.Di Fiore 12

13 Equation of motion we used a simplified model considering just the two soft DOFs with: the quantities measure by the GRS are: by solving the motion equations using the measurement of x and j, we can obtain force and torque acting on the TM Moriond 26/3/217 L.Di Fiore 13

14 Readout scheme of PETER The facility has a redundant readout system with combination of different sensors Autocollimator at the crossbar level GRS at the TM level optical read-out (ORO) at the TM level ORO at the crossbar level (being implemented) ORO AC ORO GRS Moriond 26/3/217 L.Di Fiore 14

15 Position and angle measurements displacement (X) PSD [Hz] x [m/ p Hz] x readout noise Angular (j) PSD [Hz] ' [rad/ p Hz] ' readout noise Moriond 26/3/217 L.Di Fiore 15

16 Force and torque measurements From TM angle and position we can compute force and torque acting on the TM Force PSD Torque PSD force [N=Hz 1=2 ] readout noise torque [N m =Hz 1=2 ] readout noise [Hz] [Hz] Moriond 26/3/217 L.Di Fiore 16

17 Actuation for C.T. measurement We actuate on pairs of virtual electrodes (X e Phi) Force is proportional to V 2 the applied voltage is proportional to the square root of the required force V=a sqrt(f) we use one pairs of electrodes for the positive force and the other for the negative one 3 2 Vel phi1 Vel phi 2 F = V 2 1 Force actuation time (s) torque actuation Moriond 26/3/217 L.Di Fiore 17

18 Cross-coupling (C.T.) measurement sinusoidal actuation in force (F) (f m =14 mhz) Measurement of torque at f=f m Sinusoidal actuation in torque (t) (f m =18 mhz) Measured force at f m F 1 =F F 1 =F F 2 = (F +DF) b F 2 = -(F +DF) b F = F 1 + F 2 = ~2F τ = F 1 F 2 b = DF b C.T. = F 2F = τ Fb τ = F 1 F 2 b~2f b F = F 1 + F 2 = DF C.T. F 2F = F τ b Moriond 26/3/217 L.Di Fiore 18

19 mean(y) (micron) C.T. measurement The C.T. measurement is performed by moving with motors the electrode housing (EH) around the TM in x and y along a defined pattern, while acting with a sinusoidal force on the TM For each position the data is acquired for some time (2-6 hours), From the TM position it is possible to measure, both force and torque and then obtain the C.T, In this example we move in a spiral from the EH center by steps of.1 mm in x and y The measurement (25 steps) lasts for 5 h (more than two days) giu : mean(x) (micron) Moriond 26/3/217 L.Di Fiore 19

20 Comparison with the model The force exerted by each electrode can be computed as the gradient of the capacity that is in turn a function of electrode geometry and TM position (in 6 DOF). This allows us to compute force and torque as a function of position in x, y and j (we neglect the other 3 DOFs because they are almost constant and close to zero during the measurements. We stop it to the second order. From that we get a simple analytical model of the cross-talk to compare to the experiment with h x = 4 mm the gap between the TM and the GRS along the x-axis, s = 46 mm the side of the TM d x = 21,5 mm distance between the center of two adjacent x electrodes, Moriond 26/3/217 L.Di Fiore 2

21 Measurement runs we performed a few measurement runs with different grid shapes and different force/torque amplitude Run number Run start time Averaging time per step (hours) Force to torque Cross Talk (actuation force at 14 mhz) N. of steps Step size (mm) Actuation amplitude (V 2 ) 1a June 9, x a June 19, (spiral) 1 2 2a June 26, (spiral) 1 2 Torque to force Cross Talk (actuation torque at 18 mhz) 1b May 25, b May 29, x b November 24, (spiral) 2 2 Moriond 26/3/217 L.Di Fiore 21

22 M-C CT % Force to torque Cross-Talk measurement 1 run 3a model mean(y) (mm) mean(x) (mm) Note that the absolute calibration doesn't affect the result Moriond 26/3/217 L.Di Fiore mean(x) (mm)

23 M-fit CT. % Repeatability run 1a run 2a run 3a mean(y) (mm) Moriond 26/3/217 L.Di Fiore mean(x) (mm) mean(x) (mm) we fitted the whole set of data of the 3 runs with a second order surface in x, y and j. this surface was used to compute the residuals (measured - fit). The measurements are quite repeatable: all the data lay on the same curve fitted to data 3

24 M-C % CT % Torque to force Cross-Talk measurement 4 2 measure 2b computed mean(y) (mm) -1-2 In this case, the measured CT value was larger than expected mean(x) (mm) mean(x) (mm) 2 Moriond 26/3/217 L.Di Fiore 24

25 M-F % C.T. % Torque to force Cross-Talk measurement 4 2 run 1b run 2b run 3b mean(y) (mm) mean(x) (mm) mean(x) (mm) 2 Also in this case we fitted the set of data of the 3 runs with a second order surface in x, y and j and used it to compute the residuals (measured - fit). The measurements are quite repeatable. Moriond 26/3/217 L.Di Fiore 25

26 contour plots of fit to data torque force force torque In conclusion, PETER allowed to prove that, if we look at the central region (+ 1 mm) of the GRS, that is the range of interest for the scientific operations of LPF, the measured CT is less than,2 %, in agreement with requirements Moriond 26/3/217 L.Di Fiore 26

27 summing up We have performed several repeatable measurement runs of Force to Torque and Torque to Force cross-talks of the LISA- PF GRS. measured Force to Torque CT is very close to the expectations: measured Torque to Force CC is larger than expected. Further investigations are going-on to check it there are other features introduced by the apparatus itself. In any case the measured C.T. resulted to be not a problem for LISA-Pathfinder operation Moriond 26/3/217 L.Di Fiore 27

28 Can we approach free fall on more than 2 DOFs? A possible straightforward) upgrade: 3 DOF pendulum In this case we can measure two forces and a torque acting on the TM Force along x Force along y Torque around vertical axis TM Moriond 26/3/217 L.Di Fiore 28

29 A (more triky) extension to torque around the two horizontal axis generally, in a torsion pendulum the suspension wire is attached well above the CM. SP CM if we move the attaching point close to the CM the restoring torque, for rotation around CM approaches zero and the resonance goes to low frequency τ r = kθ = mghθ h SP CM In principle, in this way it is possible to get very low frequency on 2 DOFs CM In real life, when you approach the CM, there are severe limitations due to: mechanical tolerances, TM inhomogeneity, lateral accuracy in attaching the suspending wire Moriond 26/3/217 L.Di Fiore 29

30 The difficult task: vertical direction Venkateswara et al., Rev.Sci.Instrum. 85 (214) 15 they realized a beam balance with a flexure joint resonance frequency: 1.8 mhz CM position: -3 mm flexure it is a tiltometer to be used for Newtonian noise cancellation in LIGO In principle, it is possible to get a system approaching free fall, in low frequency, on 6 DOFs Moriond 26/3/217 L.Di Fiore 3

31 What can we do with a 2 (or more) DOF pendulum? beyond technological applications like LISA-PF GRS characterization, is there any advantage for physics experiments? As an example, I would indicate the lateral Casimir effect: Casimir effect has been extensively studied in the usual plate-plate or plate-sphere configurations If we use periodically corrugates surfaces, aside to the normal Casimir pressure, there is a lateral force, depending on the geometry from Emig et al, 213, Phys. Rev. A 67, In this type of experiments, a delicate point is the presence of the (much larger) normal Casimir force F n = ε +2ε cf H ; cure must be taken to distinguish the two A two DOFs system would allow the simultaneous measurement of both F n and F l Moriond 26/3/217 L.Di Fiore 31

32 Conclusion we have developed a two stages torsion pendulum (PETER) that allows the simultaneous measurement, in 2 DOFs, of force and torque acting on a TM, down to a few mhz The instrument was successfully used for laboratory characterization of actuation cross-talks of for the GRS of the LISA-Pathfinder mission We discussed the possible extension to more than 2 DOFs We mentioned as a possible application in fundamental physics the measurement of latera Casimir force Any other suggestion or comment for other physics experiments that can benefit of approaching free fall on multiple DOSs is very welcome Moriond 26/3/217 L.Di Fiore 32

33 Thank you for your attention Moriond 26/3/217 L.Di Fiore 33