Measurement of Wire Sag in a Vibrating Wire Setup* Animesh Jain, - - PowerPoint PPT Presentation

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

15th International Magnet Measurement Workshop, Fermilab, August 21-24, 2007

* Work supported by the U.S. Department of Energy under contract DE-AC02-98CH10886.

IMMW-15: August 21-24, 2007 BNL Overview: Animesh Jain

1

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 µm) 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 µm for ~6 m length. So,

accurate calculation of the sag correction is essential.

• How well does the sag formula work?

IMMW-15: August 21-24, 2007 BNL Overview: Animesh Jain

2

Wire Sag: Symmetric Case

) ( 2 ) ( y L z z T g m z y + −       =

l

2

min

L z =

l

m T L f       = 2 1

1

( )

2 1 2 min

32 8 Sag f g T gL m y y s =         = − = =

l

z = L z

s T y(z)

ymin

y0 y0

z = 0 2 L

zmin =

IMMW-15: August 21-24, 2007 BNL Overview: Animesh Jain

3

Asymmetric Case: How to Define Sag?

1 1 2

) ( 2 ) ( y z L y y L z z T g m z y + − + −       =

l

( )

        − − = g f y y L z

2 1 1 2 min

8 1 2

z = L z

s T y(z) y0(z)

ymin

y1 y2

z = 0

zmin

2 L

z =

1 1 2

) ( y z L y y z y + − =

( )

g y y f f g y z y

2 1 2 2 1 2 1 min min

2 32 ) ( − − = −

Note that zmin may be outside the wire! For y2 – y1 = 0.25 mm, L = 6 m, f1 = 22 Hz: zmin differs from L/2 by ~ 30 cm Correction term in “sag” is ~ 6 µm If we define “sag” as departure from straight line at z = zmin, then it is given by:

IMMW-15: August 21-24, 2007 BNL Overview: Animesh Jain

4

Definition of Sag: Asymmetric Case

) ( 2 ) ( ) ( L z z T g m z y z y −       = −

l

z = L z

s T y(z) y0(z)

ymin

y1 y2

z = 0

zmin

2 L

z =

1 1 2

) ( y z L y y z y + − =

If we define “sag” as the maximum departure from a straight line then:

Deviation from straight line at any position. This has the same form as the symmetric case.

[ ]

2 1 2 max

32 8 ) ( ) ( Sag f g T gL m z y z y s =         = − = =

l

Same as the symmetric case Maximum departure from straight line always occurs at the midpoint.

IMMW-15: August 21-24, 2007 BNL Overview: Animesh Jain

5

Measurement of Sag: Concept

• 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.

z = L

T y1 y2

z = 0 2 L

z =

0 0 0

Translation Stage Wire edge detector Dial indicator

IMMW-15: August 21-24, 2007 BNL Overview: Animesh Jain

6

Measurement of Sag: Analysis Concept

• Vary tension and measure

the resonant frequency and the change in wire height.

• 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 that tension (or frequency).

• Compare to formula.

2

1 f

2 1

1 f

2 2

1 f

2 3

1 f

2 4

1 f

2 5

1 f

Dial Indicator Reading

Data points with different values of tension

s1 s2 s3 s4 s5

IMMW-15: August 21-24, 2007 BNL Overview: Animesh Jain

7

Wire Sag: Simulation with Random Errors

g

y = 306180.2x - 1198.5 y = 306083.4x - 1198.3

• 1200
• 1000
• 800
• 600
• 400
• 200

0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004

1/f 2 (s2) Wire Height in Center (µm)

Horizontal Vertical

Using wire positions computed from measured frequency, with up to ±3 µm random errors and an arbitrary offset of 1200 µm.

Expected value of slope is 306562.5 (error ~ 0.14%) Expected value of offset is 1200 µm (error ~ 1.5 µm)

IMMW-15: August 21-24, 2007 BNL Overview: Animesh Jain

8

Experimental Setup for Sag Measurements

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. Dial indicator Sensor Wire

IMMW-15: August 21-24, 2007 BNL Overview: Animesh Jain

9

Accuracy of Resonant Frequency

• 4
• 3
• 2
• 1

1 2 3 4 20 20.5 21 21.5 22 22.5 23 23.5 24 24.5 25 25.5 26

Frequency (Hz) <A_x*I> or <A_y*I>

A_x Ax_Calc A_y Ay_Calc

f_x = 23.362 Hz f_y = 23.361 Hz

SLS Magnet QA42 Powered at 10A Correction for large wire sag (500 to 600 microns for ~6.2 m length) is very important, which in turn requires a very precise knowlege of resonant frequency.

2

32 f g Sag =

IMMW-15: August 21-24, 2007 BNL Overview: Animesh Jain

10

Sag: Measured Vs. Calculated

• 150
• 100
• 50

50 100 150 0.0017 0.0019 0.0021 0.0023 0.0025 0.0027

1/f 2 (s2) Change in Wire Height (micron)

Horizontal Sensor Vertical Sensor Calculated

Wire position appears to have changed systematically by ~19 µm for data points #10-11.

#1,2 #10 #3 #4 #5 #6 #7 #8 #9 #11 Due to noise in the data, intercept of fitted straight line may be in large error, unless the slope is constrained.

Dial indicator accuracy is ±3 µm

IMMW-15: August 21-24, 2007 BNL Overview: Animesh Jain

11

Error in Change of Sag Vs. Weight Used

• 10
• 5

5 10 15 20 25 700 750 800 850 900 950 1000 1050 1100

Weight in gms Error in Change in Sag (µm)

June 5, 2007 ~ 6.2 m long Cu-Be Wire In Background Field

Note: Data points #10-11 seem to have shifted by ~19 µm relative to #1-9. #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11

IMMW-15: August 21-24, 2007 BNL Overview: Animesh Jain

12

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 µm 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.