Measurement of Wire Sag in a Vibrating Wire Setup* Animesh Jain, Ping He, George Ganetis Superconducting Magnet Division Brookhaven National Laboratory, Upton, NY 11973 and Alexander Temnykh Cornell University 15 th International Magnet Measurement Workshop, Fermilab, August 21-24, 2007 * Work supported by the U.S. Department of Energy under contract DE-AC02-98CH10886.
Introduction • NSLS-II requires a very tight tolerance on the relative alignment of quadrupoles and sextupoles on a girder, which is ~ 6 m long. • Although individual magnets could be fiducialized using a variety of techniques, one is ultimately limited by the survey accuracy (50-100 µ m) for the final installation. • Based on the accuracy required, and the overall length of the girders, the vibrating wire technique developed at Cornell was chosen for aligning magnets to each other. • Cu-Be wire sags 500-600 µ m for ~6 m length. So, accurate calculation of the sag correction is essential. • How well does the sag formula work? BNL Overview: Animesh Jain 1 IMMW-15: August 21-24, 2007
Wire Sag: Symmetric Case T y 0 s y 0 y min y ( z ) L z = 0 z z = L z min = 2 m g 1 T L l = − + = = y ( z ) z ( z L ) y f z 0 1 min 2 T 2 L m 2 l 2 m gL g ( ) l = = − = = Sag s y y 0 min 2 8 T 32 f 1 BNL Overview: Animesh Jain 2 IMMW-15: August 21-24, 2007
Asymmetric Case: How to Define Sag? T y 0 ( z ) s = y ( z ) 0 y 2 − y y y 1 y ( z ) 2 1 + z y y min 1 L z min z = 0 z L z = L z = 2 ( ) 2 − − m g y y L 8 y y f 2 1 2 1 1 = l − + + = − y ( z ) z ( z L ) z y z 1 1 min 2 T L 2 g If we define “sag” as departure from Note that z min may be outside the wire! straight line at z = z min , then it is given by: For y 2 – y 1 = 0.25 mm, L = 6 m, f 1 = 22 Hz: ( ) 2 2 − g 2 f y y z min differs from L /2 by ~ 30 cm 1 2 1 − = − y ( z ) y 0 min min 2 g 32 f Correction term in “sag” is ~ 6 µ m 1 BNL Overview: Animesh Jain 3 IMMW-15: August 21-24, 2007
Definition of Sag: Asymmetric Case T y 0 ( z ) s = y ( z ) 0 y 2 − y y y 1 y ( z ) 2 1 + z y y min 1 L z min z = 0 z L z = L z = 2 m g Deviation from straight line at any position. − = l − y ( z ) y ( z ) z ( z L ) 0 2 T This has the same form as the symmetric case. If we define “sag” as the maximum departure from a straight line then: Same as the symmetric case 2 m gL g [ ] Maximum departure from l = = − = = Sag s y ( z ) y ( z ) 0 max 2 8 T straight line always occurs 32 f 1 at the midpoint. BNL Overview: Animesh Jain 4 IMMW-15: August 21-24, 2007
Measurement of Sag: Concept T Dial indicator 0 0 0 Wire edge detector y 2 y 1 Translation Stage z = 0 L z = L z = 2 • Set up a wire position detector mounted on a translation stage at the mid point. • For a given tension, adjust position of detector until null output is obtained. • Change the tension, and adjust detector again. Measure the amount moved using digital dial indicators. • Study as a function of tension (or resonant frequency) and compare to theory. BNL Overview: Animesh Jain 5 IMMW-15: August 21-24, 2007
Measurement of Sag: Analysis Concept • Vary tension and measure the resonant frequency and s 1 s 2 s 3 s 4 s 5 the change in wire height. Dial Indicator Reading • Plot dial indicator reading vs. 1/ f 2 , which should give a straight line. • Extrapolate to infinite tension. The difference between the intercept and any given dial reading gives the absolute value of sag for 1 1 1 1 1 1 that tension (or frequency). 2 2 2 f 2 f 2 f 2 f 1 f f 2 3 4 5 • Compare to formula. Data points with different values of tension BNL Overview: Animesh Jain 6 IMMW-15: August 21-24, 2007
Wire Sag: Simulation with Random Errors g 0 y = 306180.2x - 1198.5 Horizontal y = 306083.4x - 1198.3 Vertical Wire Height in Center ( µ m) -200 Expected value of slope is -400 306562.5 (error ~ 0.14%) Expected value of offset is 1200 µ m (error ~ 1.5 µ m) -600 -800 Using wire positions computed from measured frequency, with up -1000 to ±3 µ m random errors and an arbitrary offset of 1200 µ m. -1200 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 1/ f 2 (s 2 ) BNL Overview: Animesh Jain 7 IMMW-15: August 21-24, 2007
Experimental Setup for Sag Measurements Dial indicator Sensor Wire A vertical wire sensor is mounted on a vertical stage and is placed at axial center of the wire. For a given weight, the sensor is adjusted until zero signal is obtained, and the resonance frequency is measured. A dial indicator is used to monitor change in detector position (or sag) with weight. BNL Overview: Animesh Jain 8 IMMW-15: August 21-24, 2007
Accuracy of Resonant Frequency A_x Ax_Calc A_y Ay_Calc 4 f_x = 23.362 Hz Correction for large SLS Magnet QA42 3 wire sag (500 to 600 Powered at 10A f_y = 23.361 Hz microns for ~6.2 m 2 <A_x*I> or <A_y*I> length) is very important, which in 1 turn requires a very precise knowlege of 0 resonant frequency. -1 -2 g Sag = 2 -3 32 f -4 20 20.5 21 21.5 22 22.5 23 23.5 24 24.5 25 25.5 26 Frequency (Hz) BNL Overview: Animesh Jain 9 IMMW-15: August 21-24, 2007
Sag: Measured Vs. Calculated 150 Change in Wire Height (micron) Horizontal Sensor #7 #6 100 Vertical Sensor Calculated #5 50 #8 Due to noise in the data, intercept of fitted straight line #4 #1,2 may be in large error, unless 0 the slope is constrained. #9 Dial indicator accuracy #3 is ±3 µ m -50 #11 Wire position appears to have -100 changed systematically by ~19 µ m #10 for data points #10-11. -150 0.0017 0.0019 0.0021 0.0023 0.0025 0.0027 1/ f 2 (s 2 ) BNL Overview: Animesh Jain 10 IMMW-15: August 21-24, 2007
Error in Change of Sag Vs. Weight Used 25 #11 Error in Change in Sag ( µ m) 20 June 5, 2007 ~ 6.2 m long Cu-Be Wire #10 In Background Field 15 10 #9 5 #2 #3 0 #1 #4 Note: Data points #10-11 #5 -5 seem to have shifted by #8 ~19 µ m relative to #1-9. #6 #7 -10 700 750 800 850 900 950 1000 1050 1100 Weight in gms BNL Overview: Animesh Jain 11 IMMW-15: August 21-24, 2007
Summary • Accurate estimation of sag is critical for precise alignment of multipoles on a girder for NSLS-II. • A simple set up was used to measure changes in sag as a function of applied tension. • Noise in the data due to dial indicator resolution, detector noise, wire vibrations, etc. was up to ±5 µ m in wire height. • An unconstrained fit to the data gives large uncertainty in the intercept, or the absolute value of the sag. The change from one tension to another, however, generally agreed with theory. • The set up was not very robust mechanically and unexpected changes in wire position were sometimes seen. • The experiment will be repeated with a better set up when the R&D vibrating wire system at BNL will be operational. BNL Overview: Animesh Jain 12 IMMW-15: August 21-24, 2007
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