Vibrating Wire Test23 March 2007

A wire of mass per unit length μ under tension T, of length Lheld fixed at each end has a fundamental vibration frequency

f1 = 1/(2L) √(T/μ)

A magnetic field, in combination with an alternating currentthrough the wire will create an oscillating transverse force onthe wire. If the AC frequency matches one of the harmonicfrequencies of th wire, a resonant condition occurs.

Vibrating Wire Test

By sweeping frequency of AC through the wire, the amplitude of vibration and its phase relativeto the driving force trace out resonance response.

With thin, flexible wire the damping is mainly fromfriction of air and the Q is quite high, making methodsensitive to weak fields.

Size and sign of resonance depends upon locationof applied periodic force. Conversely, measuringsize/sign of many harmonics allows the B fielddistribution along the wire to be calculated.

Vibrating Wire Test

Scrounged from Wayne Faszer• 100um Cu-Be wire• plastic V-pulley c/w mount• 96 g weight

Collected and assembled by Peter• H21A1 optical limit switch (detects wire motion), 9V battery and resistors• var. frequency sine-wave generator• amplifier• scope• DVM

Vibrating Wire Test: apparatus

• Wire position sensor (H21A1 optical limit switch) mounted on x-y stage.

Cu-Be wire

Pulley WireFixed end

C-magnet

96g weight

DVM

Scope

Scope readout: 25 Hz driving force

Vibrating wire test

• First test using earth’s mag. field (0.52 Gauss vert.)• Length of wire 2.28 m, tension 96 g-wt

calc. fundamental frequency 27 Hz• Substantial signal seen: Vrms ~ 20 mV for 0.1A current

through wire• See resonance @ 25.4 Hz, FWHM < 1 Hz

• Second test using C-magnet

-- placed 3/5 of distance from sensor end to far end

-- at wire: approx. 2-3 Gauss max. with ~50cm FWHM

f (Hz) Amplitude24 19

24.5 3225 75

25.35 18025.45 -15425.5 -128

26 -41

|<:::::: :::::::: ::::::: L 2.28m ::::::: ::::::::::>Harmonic Amp 10 30 50 70 90 110 130 150 170

1 180 31.3 90 138 169 180 169 138 90 312 -100 -34.2 -86.6 -98 -64 -0 64 98 87 343 -20 -10 -20 -10 10 20 10 -10 -20 -104 50 32.1 43.3 -17 -49 -0 49 17 -43 -325 2 1.53 1 -1.9 -0.3 2 -0.3 -1.9 1 1.56 -12 -10.4 -0 10 -10 -0 10 -10 -0 107 15 14.1 -7.5 -2.6 11 -15 11 -2.6 -8 14

..|..Sum 24.4 20.2 18 66 187 314 229 107 49

Fundamental resonance

-200

-100

0

100

200

23 24 25 26 27

AC frequency (Hz)

Vrm

s(m

V)

Series1

Vibrating Wire Test

• Approx. to Fourier components good enough to

reveal magnet location, approx. length of field• Could easily could have sensed 10x smaller field

say 3 G x 50 cm / 10 = 15 G-cm

(also ~sens’y quoted in Temnikh article)• If this can be achieved in a quad of r=75mm and

pole-tip field 2.4 kG and eff. length 30cm,

find magnet centre to within 15/(32x30) = 16 um

(relative to ??)

• Next: test in a section of DRAGON separator?