Automated wire tension measurement system for LHCb muon chambers

Texte intégral

extracted text

Automated Wire Tension Measurement System
for LHCb Muon Chambers

P. Ciambronea , E. Danéb , R. Dumpsc , M. Dwuznikc,1 , G. Felicia , C. Fortia , A. Frenkelb ,
J.-S. Graulichc , A. Kachtchoukc , V.V. Kulikovd , G. Martellottib , A. Medvedkovb ,
A.A. Nedosekind , G. Pensob , D. Pincib , G. Pirozzib , B. Schmidtc , V. Shubine,2
a Laboratori Nazionali di Frascati, Frascati, Italy
b Università “La Sapienza” and INFN, Roma, Italy
c CERN, Genève, Switzerland
d Institute for Theoretical and Experimental Physics, Moscow, Russia
e Joint Institute for Nuclear Research, Dubna, Russia

Abstract
A wire tension meter has been developed for the multiwire proportional chambers of the
LHCb muon detector. The wire tension is deduced from its mechanical resonance frequency.
In the LHCb muon chambers, the wires are 2 mm apart and electrically connected in groups
of 3−32, so that the wire excitation system must be precisely positioned with respect to the
wire to be tested. This wire is forced to oscillate by a periodic high voltage applied between
that wire and a non-oscillating “sense wire” placed parallel and close to it. This oscillation
produces a variation of the capacitance between these two wires which is measured by a high
precision digital electronic circuit. At the resonance frequency this capacitance variation is
maximum. The system has been systematically investigated and its parameters optimized.
In the range 0.4 − 1 N a good agreement is found between the mechanical tension measured
by this system and by a dynamometer.

PACS: 29.40.Cs; 29.40.Gx; 29.90.+r
Keywords: Multiwire proportional chambers; Tracking and position-sensitive detectors; Elementaryparticle and nuclear physics experimental methods and instrumentation.

1 Now at AGH University of Science and Technology, Cracow, Poland.
2 Now at CERN, Genève, Switzerland.

1

Introduction

The LHCb experiment, one of the four experiments that will operate at the Large
Hadron Collider (LHC) at CERN, is dedicated to the study of rare phenomena, and in
particular the CP-violating decays of beauty hadrons. In many of these decays, muons
are present in the final state so that muon triggering and offline muon identification are
fundamental requirements of the experimental set-up. The muon detector [1] consists
of five muon tracking stations placed along the beam axis. The first station (M1)
is placed in front of the electromagnetic and hadronic calorimeters. The remaining
four stations (M2–M5) are interleaved with three iron filters and placed downstream
of the calorimeters. The five stations comprise more than 1300 multiwire proportional
chambers. The chambers contain two wire planes in M1 station and four wire planes
in M2–M5 stations. Altogether the number of wire planes is ∼ 5000. A wire plane
comprises about 150–740 wires, depending on its location in the five stations. The
distance between two neighbouring wire is 2 mm. The total number of wires whose
mechanical tension must be checked is ∼ 3.2 millions. In order to detect any possible
failure occuring during the wiring process, the wire tension check must be performed
online during the chamber production, so that a fast, automated and reliable system
is needed. In the present paper we present a systematic study of the performance of
the wire tension meter we have designed and realized for the multiwire proportional
chambers of the LHCb muon detector.

2

Principle of operation

The mechanical tension τ of a wire is deduced from the measurement of its fundamental
mechanical resonance frequency ν0 , these two quantities are related by the formula:
τ = λ(2`ν0 )2

(1)

where λ and ` are respectively the mass per unit length and the length of the wire.
In the LHCb chambers, wires are made1 of gold-plated tungsten, 30 µm diameter,
∼ 20−32 cm long with a linear density λ ' 13.6 mg/m. Their tension should be in
the range2 0.55−0.75 N which corresponds to a resonance frequency of ∼ 340−470 Hz,
depending on the wire length.
Different methods have been adopted [2–9] to induce mechanical oscillations of the
wire under test and to measure its resonance frequency. The wire tension measurement
(WTM) system used for the LHCb muon chambers is based on the digital electrostatic
method [5]. This method greatly improves the performances of a similar approach
already proposed [9] with a limited success.
Mechanical oscillations of a chamber wire are induced by applying a periodic high
voltage (HV) between a reference electrode (hereafter named “sense wire”, close to
the wire under test, and the chamber wire plane which is grounded. The resulting
electrostatic force induces the chamber wire to oscillate. The resonance frequency ν 0 ,
is found as the value of the HV frequency (ν) which maximizes the wire oscillation
amplitude.
The oscillations of a chamber wire result in a periodical variation of the capacitance
∗
(C ) between the chamber wire and the sense wire. The amplitude of this variation is
1
2

by LUMA-METALL AB, Kalmar, Sweden; http://luma-metall.se/.
The wire tension is often improperly measured in grams, a gram being “equivalent” to 9.81 mN.

1

measured by a digital system, as a function of ν. The measurement of C ∗ is realized by
coupling the capacitance C ∗ to the LC circuit of a high-frequency (≈ 20 MHz) oscillator
(Fig. 1). Considering that C ∗  C the oscillator frequency is:
f=

1
1
C∗
p
)
' √
(1 −
2C
2π LC
2π L[C + C ∗ ]

(2)

When the wire is oscillating at a frequency ν, the capacitance C ∗ and therefore the
high-frequency f vary periodically in time with a period T = 1/ν. The amplitude ∆f
of the high-frequency variation is maximum at the resonance frequency ν0 . To evaluate
this amplitude, two values of f are measured at different phases with respect to the
HV oscillation: fA (ν, φA ) at a phase φA = 2πt/T = 2πνt (Fig. 2) and fB (ν, φB ) at a
phase3 φB = φA + π. By varying ν and t (i.e. φA ) we search for the maximum value of
∆f (ν, φA ) = fA (ν, φA ) − fB (ν, φB ). This maximum occurs for ν = ν0 and at a particular
value of φA which is fixed once the HV waveform is settled.
The frequencies fA (ν, φA ) and fB (ν, φB ) are measured by counting the discriminated
high-frequency oscillations during two identical phase intervals ∆φ (corresponding to a
time interval ∆t = T ∆φ/2π) determined by the gates GA and GB (Fig. 1 and Fig. 2).
The obtained countings are respectively NA = fA ∆t, NB = fB ∆t. Their difference
∆N = NA − NB = ∆f ∆t is large only around the resonance frequency ν0 . This results
in a very good signal-to-noise ratio in the measurement of ∆N (ν). Moreover NA and
NB are measured at a relative time distance (equal to T /2) of the order of a millisecond,
so that their difference ∆N is insensitive to an eventual long-term frequency instability
of the high-frequency oscillator. To achieve a better precision, the countings can be
repeated during many consecutive periods T , and then averaged.

3

The automated setup

The setup for wire tension measurements consists (Fig. 3) of a steady table of about
0.6 × 2 m2 , on which the chamber wire plane to be tested is fixed. To speed up the
wire tension tests, 12 sense wires, parallel to the chamber wires, measure as many wires
of a wire plane at the same time. The 12 sense wires are fixed to a carriage (Fig. 3)
which can be moved perpendicularly to the chamber wires. The distance between two
neighbouring sense wires is 12 mm, which is sufficiently large to avoid any interference
between them. The sense wires are centred longitudinally on the chamber wires to be
tested and their length is about 1/2 of the chamber wire length, so that the chamber
wire vibrates essentially at its fundamental frequency. The sense wires are 100µm in
diameter. Their mass per unit length and their tension are chosen in such a way that
their resonance frequency is far (higher by a factor & 2) from that of the chamber
wires. Therefore the sense wires can be considered as stationary in the explored range
of frequency ν.
The carriage which support the sense wires can be moved horizontally by means of a
precision worm screw (Fig. 3), driven by a stepper motor, type Phytron4 ZSH 87/2.200.6.
The movement is controlled by a stepper motion controller from National Instruments
3

The choice of φB = φA + π is justified by the observation (see next section) that f (t) is, with
very good approximation, a sinusoidal function, so that the phase difference between its maximum and
minimum values is π radians.
4
Phytron-Elektronic GmbH, D-82194 Gröbenzell, Germany; http://www.phytron.de/.

2

(NI)5 , type NI PCI-7334. This system allows the positioning of the carriage with a
precision of about ± 100 µm. The motion controller card is inserted in a computer operating under Windows XP. Two NI PCI-6602 cards are also inserted in that computer.
All the NI cards are controlled by the NI LabVIEW software. The two NI PCI-6602
cards comprise 16 counter/timer modules: 12 of them are used as scalers to count the
∆N values (Fig. 1) relative to the 12 sense wires. The other modules generate the gate
signals (Fig. 2), and a square wave signal having the wire excitation frequency ν. This
square wave signal drives a HV transistor, type TIPL 760A, mounted on the carriage
and connected to the 12 sense wires. The amplitude (V0 , Fig. 2) of the signal delivered by the HV transistor is ∼ 600−1000 V and its frequency (ν) is varied in steps of
0.3−1 Hz in an interval of about ± 30 Hz around the frequency corresponding to the
wire nominal tension.
The 12 HF oscillators (Fig. 1) are mounted on the carriage, close to their respective
sense wires. The distance between the sense wires and the chamber wire plane can be
regulated by acting on special screw placed on the carriage. The adjustment of this
distance is important because the chamber wires are electrically connected in group of
∼ 3−32 (depending on the chamber location in the LHCb experiment). Therefore the
HV applied to a sense wire excite mechanically not only the chamber wire in front of
it but also the neighbouring chamber wires belonging to the same group. To avoid any
interference from these neighbouring wires, the distance between the sense wires and
the chamber wire plane must be lower than ∼ 1.2 mm.

4

Results

In Fig. 4 we report the measured values of ∆N (ν, φA ) performed on a single wire of
a chamber wire plane. In these measurements ∆t is equal to T /20 (corresponding to
∆φ = π/10), and φA is varied in step of π/8, so that the eight series of measurements
reported in Fig. 4 refers to non-overlapping ∆φ intervals. This phase scanning allows
to fix the best phase value for systematic measurements. In our case the maximum
value (∆Nmax ) of ∆N (ν, φA ) is obtained at a phase φA = φ0 ' π/4 (Fig. 4c) and at the
frequency ν = ν0 ' 377 Hz (∆Nmax = ∆N (ν0 , φ0 )). For φA = φ0 the resonance curve
is symmetrical around the resonance frequency ν0 , with a FWHM equal to ∼ 1.2 Hz.
Mechanical and electronic noise may result in fluctuations on the measured ∆N
values. In the data reported in Fig. 4 these fluctuations have been reduced by averaging
100 repeated measurements. This allows to obtain clean resonance peaks on a smooth
baseline, but increases the time needed to determine the tension of a wire. For a faster
measurement the number of averaged data can be reduced provided that the fluctuations
remain small compared to ∆Nmax , so to avoid misidentification of the resonance peak.
Alternatively the measurements can also be sped up by increasing the gate length ∆t
up to a value in the interval T /4 ≤ ∆t ≤ T /2, while keeping the gate centre at the
same phase as in Fig. 4c: φcentre = φ0 + ∆φ/2 = 3π/10.
The behaviour of ∆N (ν, φA ) observed in Fig. 4 can be well described assuming that
the chamber wire oscillates harmonically:


d(t) = d0 + D(ν)cos 2πνt − φ(ν)
(3)
5

National Instruments Corp., Austin, TX 78759-3504, USA; http//www.ni.com/.

3

where d(t) is the effective time-dependent distance6 between the sense wire and the
oscillating chamber wire and d0 is the central value of d(t). D(ν) and φ(ν) are respectively the oscillation amplitude and its phase with respect to the HV excitation. In the
approximation of parallel sense and chamber wires, the capacitance between these two
wires is given, with a good approximation, by the formula:
C ∗ (t) =

π0 l
√

ln d(t)/ ab

(4)

where a and b are the two wire radii and l is the sense-wire length. By combining
Eqs. (2), (3) and (4) we obtain:

∆N = NA (ν, φA ) − NB (ν, φA )

(5)

q
√




NA (ν, φA ) ∝ 1/ 1 + α1 /ln α2 + D(ν)/ ab cos φA − φ(ν)

(6)

q
√




NB (ν, φA ) ∝ 1/ 1 + α1 /ln α2 − D(ν)/ ab cos φA − φ(ν)

(7)

q
√
D(ν)/ ab = α3 α4 ν0 / (ν 2 − ν02 )2 + (α4 ν)2

(8)

φ(ν) = tan−1 α4 ν/(ν02 − ν 2 )

(9)

where:




and where α1 , α2 , α3 , α4 and ν0 are the parameters of a fit to the experimental points
of Fig.4, obtained with eqs (5), (6), (7), (8) and (9). The agreement is quite good. It
turns out from the fit that α3 /α2 = D(ν0 )/d0  1 which is equivalent to the smalloscillation approximation. In that case the Eqs. (6) and (7) simplify and Eq. (5) becomes
∆N (ν, φA ) = β(ν) cos(φA − φ) where β(ν) is a function of ν. The dependence of
∆N (ν, φA ) on φA has been measured at the resonance frequency ν0 . The results are
reported in Fig. 5 together with a sinusoidal fit to the experimental points. The nearly
sinusoidal behaviour of ∆N (ν0 , φA ) validate our assumption that the chamber-wire
oscillates harmonically also for a non-sinusoidal HV excitation and indicates that the
amplitude of the chamber-wire oscillations is small compared to the distance d0 between
the chamber-wire and the sense wire.
The dependence of ∆Nmax on the high-voltage amplitude V0 (Fig. 2) has been measured and the results are reported in Fig. 6. The experimental data follow with a good
precison the expected7 law ∆Nmax ∝ V02 .
6

During the oscillations the chamber wire is no longer parallel to the sense wire. However this
effect has been neglected and an effective distance between the two wires is defined as their distance
averaged on their length.
7
For small oscillations ∆Nmax is proportional to the amplitude of the driving force which in turn
is proportional to V02 .

4

In order to determine the precision required in the positioning of the sense wire
with respect to the chamber wire to be tested, ∆Nmax has been measured at different
positions (x and δ, Fig. 7a) of the sense wire with respect to the chamber wires. In
Fig. 7b we show the dependence of ∆Nmax on the distance δ while keeping the sense
wire “in front” (x = 0) of a chamber wire. A fit to the data with an empirical power
law leads to ∆Nmax ∝ δ −3.2 . At large distance ∆Nmax may become comparable with
the noise, therefore a distance δ lower than ∼ 1.2 mm is recommended. A distance
δ ' 0.9 mm has been chosen for the systematic wire tension check of the produced
chambers.
A second set of measurements of ∆Nmax have been performed by fixing δ ' 0.9 mm
and by varying the position of the sense wire between two neighbouring chamber wires
(0 < x < 2 mm, Fig. 7a). In this geometrical situation the two chamber wires closer to
the sense wire can be simultaneously excited, so both their oscillations can contribute
to ∆Nmax . In order to disentangle these two contributions, the sense wire was moved
between two chamber wires having slightly different resonance frequencies ν1 and ν2 .
This results, for 0 < x < 2 mm, in a double-peaked excitation curve as shown in Fig. 8a.
In Fig. 8b the amplitudes of these two peaks are reported as a function of x. A fit to
−5.1
the experimental points is obtained with an empirical power law ∆Nmax ∝ y1,2
, where
y1,2 (x) are the distances between the sense wire and the two neighbouring chamber wire
(Fig. 7a). The results reported in Fig. 8b show that a precision of about ± 200−300 µm
in sense wire carriage positionning is sufficient to avoid an interference of the two
neighbouring chamber wires.
In order to check the correct operation of the whole system, the tension of a wire was
measured with a dynamometer and with the described set-up. The results, reported
in Fig. 9, show that in the explored range 0.4−1.0 N, the automated wire tension
measurement system has a linear response and provides, within few percent, the correct
tension values.
The position of the peaks i.e. the renonance frequency ν0 of the wires under test is
determined by a program8 based on NI LabVIEW which runs on the same computer
where NI cards are inserted. The full system with 12 sense wires allows to measure
the tension of about 1300 wires per hour a rate sufficiently high to follow the chamber
production rate. In Fig. 10 the result of an automated wire tension measurement
performed on a 200 wires plane is shown. The tensions are distributed around 0.65 N
with a spread of ∼ ±6% in agreement with the design requirements.

5

Conclusions

An automated digital system for measuring the wire tension of the LHCb muon chambers has been developed and tested. The tension of a wire is deduced from the measurement of its mechanical resonance frequency. The forced wire oscillations are induced by
a periodic high voltage applied between the wire under test and a sense wire parallel
and close to it. The particular structure of the LHCb muon chamber wire planes (group
of wires electrically connected with a distance of 2 mm between two neighbouring wires)
makes a precise positionning (of few hundreds of microns) of the sense wire with respect to the chamber wire necessary. This is achieved by a servomechanism driven by
8

For more details on resonance peak detection program see the LHCb-Muon-2004 Internal Notes:
“WTM Program manual and description” and “Background detection and compensation in WTM
peaks detection” by V. Shubin.

5

a computer which also controls the digital electronics and carry out the data taking
and analysis. The wire tension is determined with a precision of the order of 1 %. The
full system comprises 12 sense wires which measure at the same time 12 wires of a wire
plane. This allows to measure the tension of about 1300 wires per hour. This rate is
sufficient to check the wire tension of the muon chambers as they are produced.

References
[1] LHCb Collaboration, LHCb Muon System Technical Design Report, CERN/LHCC
2001-010 (2001); Addendum to the Muon System Technical Design Report,
CERN/LHCC 2003-002 (2003).
[2] R. Stephenson, J.E. Bateman, Nucl. Instr. and Meth. 171 (1980) 338.
[3] M. Calvetti et al., Nucl. Instr. and Meth. 174 (1980) 285.
[4] B. Brinkley et al., Nucl. Instr. and Meth. A 373 (1996) 23.
[5] A. Andryakov et al., Nucl. Instr. and Meth. A 409 (1998) 63.
[6] T. Ohama et al., Nucl. Instr. and Meth. A 410 (1998) 175.
[7] A. Balla et al., CERN/ATL-MUON-2000-002
[8] B. Maréchal et al., CERN/LHCb-MUON 2002-023
[9] L.S. Durkin, et al., IEEE Trans. Nucl. Sc. NS-42 (1995) 1419.

6

variable delay

syncronization

HV oscillator

gates generator
HF oscillator
C∗

SW

C

L

discriminator

GA

GB

scaler

scaler

NA

NB

CW

-

∆N = (NA NB)

Figure 1: Electronic scheme for measuring the variation of the capacitance (C ∗ ) between
the chamber wire (CW) and the sense wire (SW).

V0 = 600-1000 V
HV
GA

0V

GB

∆t

∆t

t

1 ms

T/2

T

Figure 2: Waveforms and timing of the high-voltage oscillator and of the gates GA and
GB .

7

chamber frame

carriage

chamber wires

stepper
motor

12 sense wires
table

worm screw
carriage
threaded hole
sense wires
chamber wires
chamber frame

Figure 3: Schematic view (not in scale) of the setup. The chamber wire plane under
test is fixed on the table. The 12 sense wires are fastened to the carriage which can
be moved by means of a worm screw and a stepper motor. The position during the
measurements of the sense wires with respect to the the chamber wires is shown in the
insert.

(a)

∆N × 10- 3

2

(b)

2

(c)

2

1

1

1

1

0

0

0

0
1

2

(e)

(f)

1

1
0

1
0

0

-1

-1

-1

0
-1

(d)

2

360

380

400

360

380

400

(g)
360

380

400

(h)
-2

360

380

400

ν (Hz)

Figure 4: Difference of the scalers’ counting NA and NB (see Fig. 1) as a
function of the wire excitation frequency ν, for eight different values of φA :
(a) φA = 0; (b) φA = π/8; (c) φA = π/4; (d) φA = 3π/8; (e) φA = π/2; (f) φA = 5π/8;
(g) φA = 3π/4; (h) φA = 7π/8. All the measurements refer to a phase interval ∆φ =
π/10 (see text). The lines are fits to the experimental points, with the Eqs. (5). The
same values of ∆N (ν), but with an opposite sign, are obtained for φA → φA + π.

8

∆N × 10 - 3

3

2

1

0

-1

-2

-3
0

π

2π

3π

φA (rad)

4π

∆N max × 10-3

Figure 5: ∆N measured at the resonance frequency ν0 , as a function of the phase φA .
The curve is a sinusoidal fit to the experimental points.

3

2

1

0

0

200

400

600
800
V0 (V)

Figure 6: ∆Nmax measured as a function of the excitation high-voltage amplitude V0 .
The line is a fit to the experimental data with the expected law ∆Nmax ∝ V02 .

9

x
-2

0

-1

δ
cw

(a)

sw
1

y1

cw

2

4 mm

3

y2

cw

cw

∆N max × 10-3

(b)
x=0

2

1

0
0.8

1.2

2.0

1.6

δ (mm)

Figure 7: (a) Position of the sense wire (SW) with respect to the chamber wires (CW)
during the positionning tests. The origin of the x axis is placed “in front” of an arbitrary
chamber wire. During normal measurements δ ' 0.9 mm and the sense wire is “in
front” (x = 0) of the chamber wire to be measured. (b) ∆Nmax measured at x = 0, as
a function of the distance δ between the sense wire and the chamber wire plane. The
line is a fit to experimental points with a power law ∆Nmax ∝ δ −3.2 .

10

x=0.6 mm

x=1.4 mm

x=2 mm

ν2

ν2

ν (Hz)
2

390

ν1

370

ν2

370

370

ν1
390

ν1

390

0

390

1

370

∆N × 10-3

x=0

2

(a)
(b)

∆Nmax × 10-3

δ = 0.9 mm

1

ν1

0
-0.5

0

ν2

0.5

1

1.5

2
2.5
x (mm)

Figure 8: (a) Excitation curves obtained for four different x-positions of the sense wire.
The distance δ was equal to 0.9 mm. The two peaks occur at the resonance frequencies
of the two neighbouring chamber wires, ν1 ' 374 Hz and ν2 ' 386 Hz. (b) Amplitude of
the resonance peaks occurring at the frequencies ν1 (full points) and ν2 (open points),
as a function of the x-position of the sense wire. The lines are a fit to the experimental
points (see text).

11

WTM tension (N)

1.1

0.9

0.7

0.5

0.3
0.3

0.5

0.7

0.9
1.1
Dynamometer tension (N)

Figure 9: Comparison of the tension of a wire measured by the present wire tension
measurement (WTM) system and with a dynamometer. The line is a linear fit to the
experimantal points.

wire tension (N)

0.8

0.6

0.4
0

50

100

150

200
wire number

Figure 10: Typical results of an automated wire tension measurement performed on a
wire plane comprising 200 wires.

12