Hydraulic fluid power — Determination of the fluid-borne noise characteristics of components and systems — Part 2: Measurement of the speed of sound in a fluid in a pipe

Transmissions hydrauliques — Évaluation des caractéristiques du bruit liquidien des composants et systèmes — Partie 2: Mesurage de la vitesse du son émis dans un fluide dans une tuyauterie

La présente partie de l'ISO 15086 décrit la procédure d'évaluation de la vitesse du son émis par un fluide contenu dans un tube, par la réalisation de mesurages à partir de capteurs de pression montés sur ledit tube. La présente partie de l'ISO 15086 s'applique à tous les types de circuits hydrauliques fonctionnant dans des conditions de régime établi, indépendamment de leur dimension, pour des impulsions de pression dans une gamme de fréquences comprise entre 25 Hz et 2 500 Hz.

Fluidna tehnika - Hidravlika - Ugotavljanje značilnic tekočinskega hrupa v sestavinah in sistemih - 2. del: Merjenje hitrosti zvoka po tekočini v cevi

General Information

Status
Published
Publication Date
09-Feb-2000
Current Stage
9060 - Close of review
Start Date
17-Dec-2010

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INTERNATIONAL ISO
STANDARD 15086-2
First edition
2000-02-01
Hydraulic fluid power — Determination of
fluid-borne noise characteristics of
components and systems —
Part 2:
Measurement of speed of sound in a fluid in
apipe
Transmissions hydrauliques — Évaluation des caractéristiques du bruit
liquidien des composants et systèmes —
Partie 2: Mesurage de la vitesse du son émis dans un fluide dans une
tuyauterie
Reference number
ISO 15086-2:2000(E)
ISO 2000
---------------------- Page: 1 ----------------------
ISO 15086-2:2000(E)
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be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In downloading

this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat accepts no liability in

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Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation

parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In the

unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.

© ISO 2000

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic

or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or ISO's member body

in the country of the requester.
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Printed in Switzerland
ii © ISO 2000 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 15086-2:2000(E)
Contents Page

Foreword.....................................................................................................................................................................iv

Introduction.................................................................................................................................................................v

1 Scope ..............................................................................................................................................................1

2 Normative references ....................................................................................................................................1

3 Terms and definitions ...................................................................................................................................1

4 Symbols and subscripts ...............................................................................................................................2

5 Instrumentation..............................................................................................................................................3

6 Hydraulic noise generator.............................................................................................................................4

7 Test conditions ..............................................................................................................................................5

8 Test rig............................................................................................................................................................5

9 Test procedure for Method 1 ........................................................................................................................9

10 Test procedure for Method 2 ......................................................................................................................10

11 Test report ....................................................................................................................................................11

12 Identification statement (Reference to this part of ISO 15086) ..................................................................12

Annex A (normative) Errors and classes of measurement of mean value ..........................................................13

Annex B (normative) Errors and classes of dynamic measurement....................................................................14

Annex C (normative) Data reduction algorithms....................................................................................................15

Annex D (informative) Example of speed of sound calculation in MATLAB® language using three

pressure transducers in a pipe (Method 1) ...............................................................................................21

Annex E (informative) Example of speed of sound calculation in MATLAB® language using two

pressure transducers in a closed-end pipe (Method 2) ...........................................................................25

Bibliography ..............................................................................................................................................................27

© ISO 2000 – All rights reserved iii
---------------------- Page: 3 ----------------------
ISO 15086-2:2000(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO

member bodies). The work of preparing International Standards is normally carried out through ISO technical

committees. Each member body interested in a subject for which a technical committee has been established has

the right to be represented on that committee. International organizations, governmental and non-governmental, in

liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical

Commission (IEC) on all matters of electrotechnical standardization.

International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 3.

Draft International Standards adopted by the technical committees are circulated to the member bodies for voting.

Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote.

Attention is drawn to the possibility that some of the elements of this part of ISO 15086 may be the subject of patent

rights. ISO shall not be held responsible for identifying any or all such patent rights.

International Standard ISO 15086-2 was prepared by Technical Committee ISO/TC 131, Fluid power systems,

Subcommittee SC 8, Product testing.

ISO 15086 consists of the following parts, under the general title Hydraulic fluid power — Determination of fluid

borne noise characteristics of components and systems:
� Part 1: Introduction
� Part 2: Measurement of the speed of sound in a fluid in a pipe

Annexes A, B and C form a normative part of this part of ISO 15086. Annexes D and E are for information only

iv © ISO 2000 – All rights reserved
---------------------- Page: 4 ----------------------
ISO 15086-2:2000(E)
Introduction

In hydraulic fluid power systems, power is transmitted and controlled through a liquid under pressure within an

enclosed circuit. During the process of converting mechanical power into hydraulic fluid power, flow and pressure

fluctuations and structure-borne vibrations are generated.

Hydro-acoustical characteristics of hydraulic components can be measured with acceptable accuracy if the speed of

sound in the fluid is precisely known.

The measurement technique for determining the speed of sound in a pipe, as described in this part of ISO 15086, is

based upon the application of plane wave transmission line theory to the analysis of pressure fluctuations in rigid

pipes [1].
Two different measurement approaches are presented, namely the use of:
� three pressure transducers in a pipe,
� acoustic antiresonance in a closed-end pipe system.

The three-pressure-transducer method should be used at any time when the speed of sound is to be measured

under the effective working conditions in a system.

The antiresonance method should be used to produce a table of speed-of-sound data as a function of mean

pressure and temperature for a particular fluid.
© ISO 2000 – All rights reserved v
---------------------- Page: 5 ----------------------
INTERNATIONAL STANDARD ISO 15086-2:2000(E)
Hydraulic fluid power — Determination of fluid borne noise
characteristics of components and systems —
Part 2:
Measurement of the speed of sound in a fluid in a pipe
1 Scope

This part of ISO 15086 describes the procedure for the determination of the speed of sound in a fluid enclosed in a

pipe, by measurements from pressure transducers mounted in the pipe.

This part of ISO 15086 is applicable to all types of hydraulic circuit operating under steady state conditions,

irrespective of size, for pressure pulsations over a frequency range from 25 Hz to 2 500 Hz.

2 Normative references

The following normative documents contain provisions which, through reference in this text, constitute provisions of

this part of ISO 15086. For dated references, subsequent amendments to, or revisions of, any of these publications

do not apply. However, parties to agreements based on this part of ISO 15086 are encouraged to investigate the

possibility of applying the most recent editions of the normative documents indicated below. For undated

references, the latest edition of the normative document referred to applies. Members of ISO and IEC maintain

registers of currently valid International Standards.

ISO 1000:1992, SI units and recommendations for the use of their multiples and of certain other units.

ISO 1219-1:1991, Fluid power systems and components — Graphic symbols and circuit diagrams — Part 1:

Graphic symbols.
ISO 5598:1985, Fluid power systems and components — Vocabulary.
3 Terms and definitions

For the purposes of this part of ISO 15086, the terms and definitions given in ISO 5598 and the following apply.

3.1
flow ripple

fluctuating component of flowrate in a hydraulic fluid, caused by interaction with a flow ripple source within the

system
3.2
pressure ripple

fluctuating component of pressure in a hydraulic fluid, caused by interaction with a flow ripple source within the

system
3.3
fundamental frequency

lowest frequency of pressure ripple measured by the frequency-analysis instrument

© ISO 2000 – All rights reserved 1
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ISO 15086-2:2000(E)
3.4
harmonic

sinusoidal component of the pressure ripple or flow ripple occurring at an integer multiple of the fundamental

frequency

NOTE A harmonic may be represented by its amplitude and phase, or alternatively by its real and imaginary parts.

3.5
hydraulic noise generator

hydraulic component generating flow ripple and consequently pressure ripple in the circuit

3.6
measurement pipe
pipe in which the pressure transducers are mounted
3.7
impedance

complex ratio of the pressure ripple to the flow ripple occurring at a given point in a hydraulic system and at a given

frequency
3.8
entry impedance.
impedance at the entry of a pipe or piping system
3.9
first acoustic antiresonance frequency

lowest frequency at which the magnitude of the entry impedance of the measurement pipe is at a minimum

4 Symbols and subscripts
4.1 Symbols

A, A', a, B, B',b Frequency-dependent wave propagation coefficients (complex numbers)

c Acoustic velocity in the fluid
d Internal diameter of pipe
f Frequency of the wave pulsation harmonic
f Vector of frequencies at which measurements are conducted
f First acoustic antiresonance frequency (in hertz)

H Transfer function (complex number) between two pressure transducer signals after calibration

correction

H' Transfer function (complex number) between two pressure transducer signals under calibration

H* Transfer function (complex number) between two pressure transducer signals
j �1
L Distance between transducers 1 and 2 (Method 1)
L' Distance between transducers 2 and 3 (Method 1)
2 © ISO 2000 – All rights reserved
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ISO 15086-2:2000(E)
l Distance between pressure transducers (Method 2)
P Pressure ripple of transducer PT1 (complex number)
P Pressure ripple of transducer PT2 (complex number)
P Pressure ripple of transducer PT3 (complex number)
Q Flow ripple at location 1, from 1 to 2 (complex number)
1� 2
Q Flow ripple at location 2, from 2 to 1 (complex number)
2� 1
Q Flow ripple at location 3, from 2 to 3 (complex number)
2� 3
S Coherence function corresponding to measurement frequencies, f
i i
� Error (complex number)
� Conjugate of complex number � (complex number)
� Real part of �
� Imaginary part of �
� Density of fluid
� Kinematic viscosity of fluid
� 2�f

NOTE H, H', H*, P , P , P , Q , Q , Q are all frequency-dependent terms and hence are designated by upper-

1 2 3 1� 2 2� 1 2� 3
case letters.
Units used in this part of ISO 15086 are in accordance with ISO 1000.
Graphical symbols are in accordance with ISO 1219-1 unless otherwise stated.
4.2 Subscripts
O Index for old value
N Index for new value
5 Instrumentation
5.1 Static measurements
The instruments used to measure
a) mean flow (Method 1 only);
b) mean fluid pressure;
c) fluid temperature;

shall meet the requirements for "industrial class" accuracy of measurement, i.e. class C as given in annex B.

© ISO 2000 – All rights reserved 3
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ISO 15086-2:2000(E)
5.2 Dynamic measurements

The instruments used to measure pressure ripple shall have the following characteristics:

a) resonant frequencyW 30 kHz;
b) linearityW� 1%;
c) preferably include acceleration compensation.

The instruments need not respond to steady-state pressure. It may be advantageous to filter out any steady-state

signal component using a high-pass filter. This filter shall not introduce an additional amplitude or phase error

exceeding 0,5 % or 0,5 respectively of the current measurement.
5.3 Frequency analysis of pressure ripple

A suitable instrument shall be used to measure the amplitude and phase of the pressure ripple.

The instrument shall be capable of measuring the pressure ripple from the pressure transducers such that, for a

particular harmonic, the measurements from each transducer are performed simultaneously and synchronised in

time with respect to each other.

The instrument shall have an accuracy and resolution for harmonic measurements of

a) amplitude within � 0,5 %;
b) phase within � 0,5 ;
c) frequency within � 0,5 %;
over the frequency range from 25 Hz to 2 500 Hz.
5.4 Uncertainty

Compliance with the above specification will result in an uncertainty in measurement of speed of sound of less than

� 3%.
6 Hydraulic noise generator
6.1 General

Any type of hydraulic noise generator may be used, provided that sufficient pressure ripple is created at the

pressure transducers to allow accurate measurements to be taken.

EXAMPLE Pumps and motors create a pressure ripple consisting essentially of many harmonics of the fundamental

frequency. In these cases, the fundamental frequency is equal to the product of the shaft rotational frequency and the number

of gear teeth, vanes or pistons, etc. (as appropriate to the machine employed).
Suitable alternatives include:

� an auxiliary valve with a rotating spool allowing flow to pass to the return line over part of its rotation;

� an electrohydraulic servo-valve driven by a frequency generator.

� The servo-valve may be operated with a white noise signal in order to obtain significant pressure ripple

measurements at each frequency of interest.
4 © ISO 2000 – All rights reserved
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ISO 15086-2:2000(E)
6.2 Generator vibration

If necessary, the measurement pipe should be structurally isolated from the generator to minimize vibration.

7 Test conditions
7.1 General

The required operating conditions shall be maintained throughout each test within the limits specified in Table 1.

7.2 Fluid temperature

The temperature of the fluid shall be that measured at the entry to the measurement pipe.

7.3 Fluid density and viscosity

The density and viscosity of the fluid shall be known to an accuracy within the limits specified in Table 2.

7.4 Mean fluid pressure

The mean fluid pressure of the fluid shall be that measured at the entry to the measurement pipe.

7.5 Mean flow measurement

The mean flow shall be measured down-stream of the measurement pipe (Method 1 only).

Table 1 — Permissible variations in tests conditions
Test parameter Permissible variation
Mean flow �2%
Mean pressure �2%
Temperature
�2°C
Table 2 — Required accuracy of fluid property data
Property Required accuracy
Density
�2%
Viscosity
�5%
8 Test rig
8.1 General

If, at any test condition, the pressure ripple amplitudes are too small for satisfactory frequency-spectrum analysis to

be performed, an alternative noise generator shall be selected.

The pressure transducers shall be mounted such that their diaphragms are flush, within � 0,5 mm, with the inner

wall of the pipe.

Two alternative specifications for the measurement pipe and transducer position are given, in accordance with the

method employed.
© ISO 2000 – All rights reserved 5
---------------------- Page: 10 ----------------------
ISO 15086-2:2000(E)
8.2 Thermal insulation

Temperature shall be measured at both ends of the measurement pipe. The difference in temperature between the

two ends of the measurement pipe shall not exceed 2 °C at any test condition. If necessary, sufficient thermal

lagging shall be applied to the measurement pipe to enable this requirement to be met.

8.3 Method 1: Three-transducer method

8.3.1 This method is suitable when the velocity of sound is to be measured at the same time as other hydro-

acoustical characteristics of hydraulic components, such as impedance, source flow ripple or transfer matrix

coefficients. The measurement pipe shall be installed at the place in the test system where measurement of the

speed of sound is needed. Several measurement pipes may be used simultaneously, if required.

The measurement pipe shall be uniform and straight. Its internal diameter shall be between 80 % and 120 % of the

diameter of the pipes, or component ports, to which it is connected. The pipe should be supported in such a manner

that vibration is minimized.

For cases where other hydro-acoustic properties are not being measured simultaneously, a pump (and if necessary,

a hydraulic noise generator) shall be mounted at one end of the measurement pipe. The other end shall be

terminated by a loading valve without free-moving internal parts, such as a needle valve.

Mean pressure shall be measured at the upstream end of the measurement pipe.

8.3.2 Three pressure transducers are required for Method 1, configured as shown in Figure 1. The transducer

spacing shall be selected according to the standard specifications of hydro-acoustical measurements to be carried

out simultaneously. Otherwise, the distances L and L' between the pressure transducers shall be as specified in

Table 3.
Table 3 — Spacing of transducers: Method 1
L 330 mm �2mm
470 mm �2mm

The distance between each end of the measurement pipe and the nearest pressure transducer shall be at least

10 d, where d is the internal diameter of the pipe. The distances L and L' between the transducers, as shown in

Figure 1, shall be measured to an accuracy of � 0,5 mm.

No other components shall be connected between the inlet port and outlet port of the measurement pipe.

Pressure transducers.
Distances to end of measurement pipe, x W 10d and x W 10d.
1 2
Figure 1 — Arrangement of three pressure transducers in measurement pipe
6 © ISO 2000 – All rights reserved
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ISO 15086-2:2000(E)
8.4 Method 2: Antiresonance method

8.4.1 This method can be used to produce a data chart of the speed of sound for a particular fluid. Due to the

pressure resonances that are created in the system, this method is not appropriate when other hydro-acoustical

measurements are to be undertaken.

8.4.2 An appropriate test rig is presented schematically in Figure 2 a). The loading valve shall not contain free-

moving parts. A needle valve is an example of a suitable loading valve. The measurement pipe takes the form of a

closed-end side-branch line connected to the pump/pipe/loading-valve circuit as shown. It is important that the fluid

in the measurement pipe is at as uniform a temperature as possible, and does not contain gas bubbles. To achieve

these objectives, the measurement pipe is terminated by a bleed valve. A needle valve is an example of a suitable

bleed valve. Prior to measurements being taken, the bleed valve is opened for a period of time sufficient to flush the

pipe of gas bubbles and to stabilize temperature. The measurement pipe shall be orientated downwards with the

bleed valve below the level of the through-flow pipe to prevent the trapping of air in the measurement pipe during

testing. It is important that the bleed valve does not introduce significant extra volume at the end of the line when

the valve is in the closed position.

The pressure transducers, PT and PT in Figure 2 a), are located at each end of the measurement pipe. It is

1 2

essential that transducer PT is mounted as closely as possible to the end of the pipe. Moreover, the location of

transducer PT should be as close as possible to the point where the measurement pipe is connected to the main

circuit. Figure 2 b) provides an example of how these requirements may be achieved. In this example, the

measurement pipe is terminated by a purpose-built housing which contains the needle valve assembly.

The hydraulic components necessary to obtain the appropriate test conditions may, inherently, generate sufficient

pressure pulsation levels to allow satisfactory frequency-spectrum analysis to be performed. Should this not be the

case, a separate hydraulic noise generator shall be connected to the circuit, as shown in Figure 2 a).

In order to maximize the pressure pulsation levels, the distance between the pump (or the noise generator if in use)

and the loading valve should not be greater than one-tenth of the measurement pipe length.

8.4.3 The measurement pipe shall be a uniform, rigid, straight metal pipe. The internal diameter of the pipe shall

be between 50 % and 100 % of the diameter of the line where it is connected. This pipe shall be supported in such

a manner that pipe vibration is minimized.

The distance, l, between the pressure transducers shall be defined according to the first acoustic antiresonance

frequency f by equation (1).
1 B� 10
l � (1)
4 f �

The effective bulk modulus B can be estimated using manufacturer’s data for the fluid consistent with the operating

condition of the tests. An accurate value is not required.
The frequency f should be chosen in the range 100 Hz to 200 Hz.

The distance between the pressure transducers shall be measured to an accuracy of � 0,5 mm.

© ISO 2000 – All rights reserved 7
---------------------- Page: 12 ----------------------
ISO 15086-2:2000(E)
Key
1Pump 6 Loading valve
2 Electric motor 7 Bleed valve
3 Hydraulic noise generator (if used) 8 Measurement pipe
4 Through-flow pipe 9 Temperature transducers
5 Pressure gauge 10 Pressure transducers
a) Circuit layout
Key
1 Through-flow pipe 4 Needle valve adjustment
2 Temperature transducer 5 To reservoir
3 Pressure transducer PT 6 Pressure transducer PT
1 2
b) Example of transducer locations and bleed valve mounting

NOTE Graphical symbols are for illustration purposes and do not conform to ISO 1219-1.

Figure 2 —Typical antiresonance test arrangement
8 © ISO 2000 – All rights reserved
---------------------- Page: 13 ----------------------
ISO 15086-2:2000(E)
8.5 Calibration of pressure transducers

Calibration of pressure transducers and signal conditioning is necessary. Perform relative calibration by mounting

the pressure transducers in a common block such that they measure the same pressure ripple. Construct this

common block such that the pressure transducers are at the same axial position and no more than one internal

diameter of the measurement pipe apart.

Measure the amplitude and phase relationship between the pressure transducers for a range of frequencies

spanning the complete range of interest with one transducer used as a reference. For piezoresistive transducers,

the reference transducer can be calibrated statically using, for example, a deadweight testing machine.

If piezoelectric transducers and charge amplifiers are employed, a calibrated piezoresistive transducer may be used

as a reference for dynamic calibration purposes.

If the amplitude or phase difference between the transducers exceeds 1 % or 0,5° respectively, correct for the

differences in the analysis of the test data (see 9.3 and 10.3). Record the transfer functions.

H� �
and
H� �
obtained during calibration.
9 Test procedure for Method 1

9.1 Prior to the commencement of tests, operate the hydraulic system for a sufficient period of time to purge air

from the system and to stabilize all variables, including fluid condition, to within the limits given in Table 1. If a speed

of sound test is to be performed at the same time as other hydro-acoustical measurements, conditions to the

standard relevant to those measurements can be used.

9.2 Take the ensemble average of at least 16 time-series pressure transfer functions

P P
H**��and H
12 32
P P
2 2

and calculate the coherence function S at each frequency f over the frequency range. Typical examples of the

i i

transfer functions H * and H * are given, for the case of broad-band excitation, in Figure 3.

12 32

9.3 Perform the correction of the ensemble-averaged transfer functions H and H using the transfer functions

12 32

obtained from the calibration procedure H' and H' (see 8.5) using equations (2) and (3).

12 32
H *
H � (2)
H *
H � (3)
If correction is not necessary (see 8.5), then H = H* and H = H* .
12 12 32 32
© ISO 2000 – All rights reserved 9
---------------------- Page: 14 ----------------------
ISO 15086-2:2000(E)
Key
1 Modulus of transfer functions H* and H* 3 Degree
12 32
4 Phase of transfer functions H* and H*
2 Frequency (Hz) 12 32
Figure 3 — Typical example of transfer functions H* and H*
12 32

9.4 Calculate the speed of sound for each frequency having an associated coherence function S greater than

0,95 as described in C.1. The S function is always a positive number less than or equal to 1. The least-squares

error procedure given in C.1 allows the speed of sound, averaged over the frequency range investigated, to be

calculated.

9.5 Calculate the mean fluid velocity by dividing the mean flow by the internal cross-sectional area of the

measurement pipe. If the mean fluid velocity is greater than 5 % of any speed of sound measurement, then the

method is invalid and results shall not be reported.
10 Test procedure for Method 2

10.1 Prior to the commencement of a series of tests, operate the hydraulic system and noise generator (if

included) for a sufficient period of time to purge air from the system and to stabilize all variables, including fluid

condition, to within the limits given in Table 1. Particular attention should be given to obtaining a representative fluid

characteristic, especially the bulk modulus.

The bleed valve should be fully open to allow flow through the measurement pipe during this stabilization period.

The restrictor valve downstream of the bleed valve should be adjusted to create a mean pressure approximately

0,5 MPa below the desired test pressure during this phase. Immediately before pressure transducer measurements

are taken, the bleed valve should be closed and, if necessary, the mean pressure re-established through

adjustment of the loading valve.

Warning — No safety valves are included in the system. Personnel performing tests should exercise great

care to ensure that excessive and dangerous pressures are not created when adjusting restrictor valves.

10 © ISO 2000 – All rights reserved
---------------------- Page: 15 ----------------------
ISO 15086-2:2000(E)

10.2 Take the ensemble average of at least 16 time-series pressure transfer functions.

H *�

10.3 Perform the correction of the measured transfer function H* using the transfer function obtained from the

calibration procedure of transducers PT and PT , H' = P /P (see 8.5) using equation (4).

1 2 21 2 1
H *
H � (4)
If correction is not necessary (see 8.5), then H = H*
21 21.

10.4 Identify and record the frequencies for which the transfer function H is a maximum. Calculate the speed of

sound as described in C.3.
11 Test report
11.1 General information
The test report shall contain the following general information.
a) Name and address of organization performing the test;
b) name of persons performing the test;
c) reference specifications of fluid tested;
d) date and place of tests;
e) conformance statement (see clause 12).
11.2 Test data
The test report shall contain the following test data.
a) Mounting and installation conditions of the measurement pipe:

1) description of measurement pipe (length; internal diameter; wall thickness; material);

2) description of test rig (only for Method 2);

3) nature and characteristics of hydraulic circuit and details of any vibration and thermal insulation treatment;

b) test method adopted (Method 1 or Method 2);
c) instrumentation:
1) class of measurement;

2) details of equipment used for pressure ripple measurements, including type, serial number and

manufacturer;
3) bandwidth of frequency analyser;
4) overall frequency response of instrumentation system and date and met
...

SLOVENSKI STANDARD
SIST ISO 15086-2:2001
01-december-2001
)OXLGQDWHKQLND+LGUDYOLND8JRWDYOMDQMH]QDþLOQLFWHNRþLQVNHJDKUXSDY
VHVWDYLQDKLQVLVWHPLKGHO0HUMHQMHKLWURVWL]YRNDSRWHNRþLQLYFHYL

Hydraulic fluid power -- Determination of the fluid-borne noise characteristics of

components and systems -- Part 2: Measurement of the speed of sound in a fluid in a

pipe

Transmissions hydrauliques -- Évaluation des caractéristiques du bruit liquidien des

composants et systèmes -- Partie 2: Mesurage de la vitesse du son émis dans un fluide

dans une tuyauterie
Ta slovenski standard je istoveten z: ISO 15086-2:2000
ICS:
17.140.20 Emisija hrupa naprav in Noise emitted by machines
opreme and equipment
23.100.01 +LGUDYOLþQLVLVWHPLQDVSORãQR Fluid power systems in
general
SIST ISO 15086-2:2001 en

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------
SIST ISO 15086-2:2001
---------------------- Page: 2 ----------------------
SIST ISO 15086-2:2001
INTERNATIONAL ISO
STANDARD 15086-2
First edition
2000-02-01
Hydraulic fluid power — Determination of
fluid-borne noise characteristics of
components and systems —
Part 2:
Measurement of speed of sound in a fluid in
apipe
Transmissions hydrauliques — Évaluation des caractéristiques du bruit
liquidien des composants et systèmes —
Partie 2: Mesurage de la vitesse du son émis dans un fluide dans une
tuyauterie
Reference number
ISO 15086-2:2000(E)
ISO 2000
---------------------- Page: 3 ----------------------
SIST ISO 15086-2:2001
ISO 15086-2:2000(E)
PDF disclaimer

This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but shall not

be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In downloading

this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat accepts no liability in

this area.
Adobe is a trademark of Adobe Systems Incorporated.

Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation

parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In the

unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.

© ISO 2000

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic

or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or ISO's member body

in the country of the requester.
ISO copyright office
Case postale 56 � CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 734 10 79
E-mail copyright@iso.ch
Web www.iso.ch
Printed in Switzerland
ii © ISO 2000 – All rights reserved
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SIST ISO 15086-2:2001
ISO 15086-2:2000(E)
Contents Page

Foreword.....................................................................................................................................................................iv

Introduction.................................................................................................................................................................v

1 Scope ..............................................................................................................................................................1

2 Normative references ....................................................................................................................................1

3 Terms and definitions ...................................................................................................................................1

4 Symbols and subscripts ...............................................................................................................................2

5 Instrumentation..............................................................................................................................................3

6 Hydraulic noise generator.............................................................................................................................4

7 Test conditions ..............................................................................................................................................5

8 Test rig............................................................................................................................................................5

9 Test procedure for Method 1 ........................................................................................................................9

10 Test procedure for Method 2 ......................................................................................................................10

11 Test report ....................................................................................................................................................11

12 Identification statement (Reference to this part of ISO 15086) ..................................................................12

Annex A (normative) Errors and classes of measurement of mean value ..........................................................13

Annex B (normative) Errors and classes of dynamic measurement....................................................................14

Annex C (normative) Data reduction algorithms....................................................................................................15

Annex D (informative) Example of speed of sound calculation in MATLAB® language using three

pressure transducers in a pipe (Method 1) ...............................................................................................21

Annex E (informative) Example of speed of sound calculation in MATLAB® language using two

pressure transducers in a closed-end pipe (Method 2) ...........................................................................25

Bibliography ..............................................................................................................................................................27

© ISO 2000 – All rights reserved iii
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SIST ISO 15086-2:2001
ISO 15086-2:2000(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO

member bodies). The work of preparing International Standards is normally carried out through ISO technical

committees. Each member body interested in a subject for which a technical committee has been established has

the right to be represented on that committee. International organizations, governmental and non-governmental, in

liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical

Commission (IEC) on all matters of electrotechnical standardization.

International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 3.

Draft International Standards adopted by the technical committees are circulated to the member bodies for voting.

Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote.

Attention is drawn to the possibility that some of the elements of this part of ISO 15086 may be the subject of patent

rights. ISO shall not be held responsible for identifying any or all such patent rights.

International Standard ISO 15086-2 was prepared by Technical Committee ISO/TC 131, Fluid power systems,

Subcommittee SC 8, Product testing.

ISO 15086 consists of the following parts, under the general title Hydraulic fluid power — Determination of fluid

borne noise characteristics of components and systems:
� Part 1: Introduction
� Part 2: Measurement of the speed of sound in a fluid in a pipe

Annexes A, B and C form a normative part of this part of ISO 15086. Annexes D and E are for information only

iv © ISO 2000 – All rights reserved
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SIST ISO 15086-2:2001
ISO 15086-2:2000(E)
Introduction

In hydraulic fluid power systems, power is transmitted and controlled through a liquid under pressure within an

enclosed circuit. During the process of converting mechanical power into hydraulic fluid power, flow and pressure

fluctuations and structure-borne vibrations are generated.

Hydro-acoustical characteristics of hydraulic components can be measured with acceptable accuracy if the speed of

sound in the fluid is precisely known.

The measurement technique for determining the speed of sound in a pipe, as described in this part of ISO 15086, is

based upon the application of plane wave transmission line theory to the analysis of pressure fluctuations in rigid

pipes [1].
Two different measurement approaches are presented, namely the use of:
� three pressure transducers in a pipe,
� acoustic antiresonance in a closed-end pipe system.

The three-pressure-transducer method should be used at any time when the speed of sound is to be measured

under the effective working conditions in a system.

The antiresonance method should be used to produce a table of speed-of-sound data as a function of mean

pressure and temperature for a particular fluid.
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SIST ISO 15086-2:2001
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SIST ISO 15086-2:2001
INTERNATIONAL STANDARD ISO 15086-2:2000(E)
Hydraulic fluid power — Determination of fluid borne noise
characteristics of components and systems —
Part 2:
Measurement of the speed of sound in a fluid in a pipe
1 Scope

This part of ISO 15086 describes the procedure for the determination of the speed of sound in a fluid enclosed in a

pipe, by measurements from pressure transducers mounted in the pipe.

This part of ISO 15086 is applicable to all types of hydraulic circuit operating under steady state conditions,

irrespective of size, for pressure pulsations over a frequency range from 25 Hz to 2 500 Hz.

2 Normative references

The following normative documents contain provisions which, through reference in this text, constitute provisions of

this part of ISO 15086. For dated references, subsequent amendments to, or revisions of, any of these publications

do not apply. However, parties to agreements based on this part of ISO 15086 are encouraged to investigate the

possibility of applying the most recent editions of the normative documents indicated below. For undated

references, the latest edition of the normative document referred to applies. Members of ISO and IEC maintain

registers of currently valid International Standards.

ISO 1000:1992, SI units and recommendations for the use of their multiples and of certain other units.

ISO 1219-1:1991, Fluid power systems and components — Graphic symbols and circuit diagrams — Part 1:

Graphic symbols.
ISO 5598:1985, Fluid power systems and components — Vocabulary.
3 Terms and definitions

For the purposes of this part of ISO 15086, the terms and definitions given in ISO 5598 and the following apply.

3.1
flow ripple

fluctuating component of flowrate in a hydraulic fluid, caused by interaction with a flow ripple source within the

system
3.2
pressure ripple

fluctuating component of pressure in a hydraulic fluid, caused by interaction with a flow ripple source within the

system
3.3
fundamental frequency

lowest frequency of pressure ripple measured by the frequency-analysis instrument

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SIST ISO 15086-2:2001
ISO 15086-2:2000(E)
3.4
harmonic

sinusoidal component of the pressure ripple or flow ripple occurring at an integer multiple of the fundamental

frequency

NOTE A harmonic may be represented by its amplitude and phase, or alternatively by its real and imaginary parts.

3.5
hydraulic noise generator

hydraulic component generating flow ripple and consequently pressure ripple in the circuit

3.6
measurement pipe
pipe in which the pressure transducers are mounted
3.7
impedance

complex ratio of the pressure ripple to the flow ripple occurring at a given point in a hydraulic system and at a given

frequency
3.8
entry impedance.
impedance at the entry of a pipe or piping system
3.9
first acoustic antiresonance frequency

lowest frequency at which the magnitude of the entry impedance of the measurement pipe is at a minimum

4 Symbols and subscripts
4.1 Symbols

A, A', a, B, B',b Frequency-dependent wave propagation coefficients (complex numbers)

c Acoustic velocity in the fluid
d Internal diameter of pipe
f Frequency of the wave pulsation harmonic
f Vector of frequencies at which measurements are conducted
f First acoustic antiresonance frequency (in hertz)

H Transfer function (complex number) between two pressure transducer signals after calibration

correction

H' Transfer function (complex number) between two pressure transducer signals under calibration

H* Transfer function (complex number) between two pressure transducer signals
j �1
L Distance between transducers 1 and 2 (Method 1)
L' Distance between transducers 2 and 3 (Method 1)
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SIST ISO 15086-2:2001
ISO 15086-2:2000(E)
l Distance between pressure transducers (Method 2)
P Pressure ripple of transducer PT1 (complex number)
P Pressure ripple of transducer PT2 (complex number)
P Pressure ripple of transducer PT3 (complex number)
Q Flow ripple at location 1, from 1 to 2 (complex number)
1� 2
Q Flow ripple at location 2, from 2 to 1 (complex number)
2� 1
Q Flow ripple at location 3, from 2 to 3 (complex number)
2� 3
S Coherence function corresponding to measurement frequencies, f
i i
� Error (complex number)
� Conjugate of complex number � (complex number)
� Real part of �
� Imaginary part of �
� Density of fluid
� Kinematic viscosity of fluid
� 2�f

NOTE H, H', H*, P , P , P , Q , Q , Q are all frequency-dependent terms and hence are designated by upper-

1 2 3 1� 2 2� 1 2� 3
case letters.
Units used in this part of ISO 15086 are in accordance with ISO 1000.
Graphical symbols are in accordance with ISO 1219-1 unless otherwise stated.
4.2 Subscripts
O Index for old value
N Index for new value
5 Instrumentation
5.1 Static measurements
The instruments used to measure
a) mean flow (Method 1 only);
b) mean fluid pressure;
c) fluid temperature;

shall meet the requirements for "industrial class" accuracy of measurement, i.e. class C as given in annex B.

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SIST ISO 15086-2:2001
ISO 15086-2:2000(E)
5.2 Dynamic measurements

The instruments used to measure pressure ripple shall have the following characteristics:

a) resonant frequencyW 30 kHz;
b) linearityW� 1%;
c) preferably include acceleration compensation.

The instruments need not respond to steady-state pressure. It may be advantageous to filter out any steady-state

signal component using a high-pass filter. This filter shall not introduce an additional amplitude or phase error

exceeding 0,5 % or 0,5 respectively of the current measurement.
5.3 Frequency analysis of pressure ripple

A suitable instrument shall be used to measure the amplitude and phase of the pressure ripple.

The instrument shall be capable of measuring the pressure ripple from the pressure transducers such that, for a

particular harmonic, the measurements from each transducer are performed simultaneously and synchronised in

time with respect to each other.

The instrument shall have an accuracy and resolution for harmonic measurements of

a) amplitude within � 0,5 %;
b) phase within � 0,5 ;
c) frequency within � 0,5 %;
over the frequency range from 25 Hz to 2 500 Hz.
5.4 Uncertainty

Compliance with the above specification will result in an uncertainty in measurement of speed of sound of less than

� 3%.
6 Hydraulic noise generator
6.1 General

Any type of hydraulic noise generator may be used, provided that sufficient pressure ripple is created at the

pressure transducers to allow accurate measurements to be taken.

EXAMPLE Pumps and motors create a pressure ripple consisting essentially of many harmonics of the fundamental

frequency. In these cases, the fundamental frequency is equal to the product of the shaft rotational frequency and the number

of gear teeth, vanes or pistons, etc. (as appropriate to the machine employed).
Suitable alternatives include:

� an auxiliary valve with a rotating spool allowing flow to pass to the return line over part of its rotation;

� an electrohydraulic servo-valve driven by a frequency generator.

� The servo-valve may be operated with a white noise signal in order to obtain significant pressure ripple

measurements at each frequency of interest.
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SIST ISO 15086-2:2001
ISO 15086-2:2000(E)
6.2 Generator vibration

If necessary, the measurement pipe should be structurally isolated from the generator to minimize vibration.

7 Test conditions
7.1 General

The required operating conditions shall be maintained throughout each test within the limits specified in Table 1.

7.2 Fluid temperature

The temperature of the fluid shall be that measured at the entry to the measurement pipe.

7.3 Fluid density and viscosity

The density and viscosity of the fluid shall be known to an accuracy within the limits specified in Table 2.

7.4 Mean fluid pressure

The mean fluid pressure of the fluid shall be that measured at the entry to the measurement pipe.

7.5 Mean flow measurement

The mean flow shall be measured down-stream of the measurement pipe (Method 1 only).

Table 1 — Permissible variations in tests conditions
Test parameter Permissible variation
Mean flow �2%
Mean pressure �2%
Temperature
�2°C
Table 2 — Required accuracy of fluid property data
Property Required accuracy
Density
�2%
Viscosity
�5%
8 Test rig
8.1 General

If, at any test condition, the pressure ripple amplitudes are too small for satisfactory frequency-spectrum analysis to

be performed, an alternative noise generator shall be selected.

The pressure transducers shall be mounted such that their diaphragms are flush, within � 0,5 mm, with the inner

wall of the pipe.

Two alternative specifications for the measurement pipe and transducer position are given, in accordance with the

method employed.
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SIST ISO 15086-2:2001
ISO 15086-2:2000(E)
8.2 Thermal insulation

Temperature shall be measured at both ends of the measurement pipe. The difference in temperature between the

two ends of the measurement pipe shall not exceed 2 °C at any test condition. If necessary, sufficient thermal

lagging shall be applied to the measurement pipe to enable this requirement to be met.

8.3 Method 1: Three-transducer method

8.3.1 This method is suitable when the velocity of sound is to be measured at the same time as other hydro-

acoustical characteristics of hydraulic components, such as impedance, source flow ripple or transfer matrix

coefficients. The measurement pipe shall be installed at the place in the test system where measurement of the

speed of sound is needed. Several measurement pipes may be used simultaneously, if required.

The measurement pipe shall be uniform and straight. Its internal diameter shall be between 80 % and 120 % of the

diameter of the pipes, or component ports, to which it is connected. The pipe should be supported in such a manner

that vibration is minimized.

For cases where other hydro-acoustic properties are not being measured simultaneously, a pump (and if necessary,

a hydraulic noise generator) shall be mounted at one end of the measurement pipe. The other end shall be

terminated by a loading valve without free-moving internal parts, such as a needle valve.

Mean pressure shall be measured at the upstream end of the measurement pipe.

8.3.2 Three pressure transducers are required for Method 1, configured as shown in Figure 1. The transducer

spacing shall be selected according to the standard specifications of hydro-acoustical measurements to be carried

out simultaneously. Otherwise, the distances L and L' between the pressure transducers shall be as specified in

Table 3.
Table 3 — Spacing of transducers: Method 1
L 330 mm �2mm
470 mm �2mm

The distance between each end of the measurement pipe and the nearest pressure transducer shall be at least

10 d, where d is the internal diameter of the pipe. The distances L and L' between the transducers, as shown in

Figure 1, shall be measured to an accuracy of � 0,5 mm.

No other components shall be connected between the inlet port and outlet port of the measurement pipe.

Pressure transducers.
Distances to end of measurement pipe, x W 10d and x W 10d.
1 2
Figure 1 — Arrangement of three pressure transducers in measurement pipe
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SIST ISO 15086-2:2001
ISO 15086-2:2000(E)
8.4 Method 2: Antiresonance method

8.4.1 This method can be used to produce a data chart of the speed of sound for a particular fluid. Due to the

pressure resonances that are created in the system, this method is not appropriate when other hydro-acoustical

measurements are to be undertaken.

8.4.2 An appropriate test rig is presented schematically in Figure 2 a). The loading valve shall not contain free-

moving parts. A needle valve is an example of a suitable loading valve. The measurement pipe takes the form of a

closed-end side-branch line connected to the pump/pipe/loading-valve circuit as shown. It is important that the fluid

in the measurement pipe is at as uniform a temperature as possible, and does not contain gas bubbles. To achieve

these objectives, the measurement pipe is terminated by a bleed valve. A needle valve is an example of a suitable

bleed valve. Prior to measurements being taken, the bleed valve is opened for a period of time sufficient to flush the

pipe of gas bubbles and to stabilize temperature. The measurement pipe shall be orientated downwards with the

bleed valve below the level of the through-flow pipe to prevent the trapping of air in the measurement pipe during

testing. It is important that the bleed valve does not introduce significant extra volume at the end of the line when

the valve is in the closed position.

The pressure transducers, PT and PT in Figure 2 a), are located at each end of the measurement pipe. It is

1 2

essential that transducer PT is mounted as closely as possible to the end of the pipe. Moreover, the location of

transducer PT should be as close as possible to the point where the measurement pipe is connected to the main

circuit. Figure 2 b) provides an example of how these requirements may be achieved. In this example, the

measurement pipe is terminated by a purpose-built housing which contains the needle valve assembly.

The hydraulic components necessary to obtain the appropriate test conditions may, inherently, generate sufficient

pressure pulsation levels to allow satisfactory frequency-spectrum analysis to be performed. Should this not be the

case, a separate hydraulic noise generator shall be connected to the circuit, as shown in Figure 2 a).

In order to maximize the pressure pulsation levels, the distance between the pump (or the noise generator if in use)

and the loading valve should not be greater than one-tenth of the measurement pipe length.

8.4.3 The measurement pipe shall be a uniform, rigid, straight metal pipe. The internal diameter of the pipe shall

be between 50 % and 100 % of the diameter of the line where it is connected. This pipe shall be supported in such

a manner that pipe vibration is minimized.

The distance, l, between the pressure transducers shall be defined according to the first acoustic antiresonance

frequency f by equation (1).
1 B� 10
l � (1)
4 f �

The effective bulk modulus B can be estimated using manufacturer’s data for the fluid consistent with the operating

condition of the tests. An accurate value is not required.
The frequency f should be chosen in the range 100 Hz to 200 Hz.

The distance between the pressure transducers shall be measured to an accuracy of � 0,5 mm.

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SIST ISO 15086-2:2001
ISO 15086-2:2000(E)
Key
1Pump 6 Loading valve
2 Electric motor 7 Bleed valve
3 Hydraulic noise generator (if used) 8 Measurement pipe
4 Through-flow pipe 9 Temperature transducers
5 Pressure gauge 10 Pressure transducers
a) Circuit layout
Key
1 Through-flow pipe 4 Needle valve adjustment
2 Temperature transducer 5 To reservoir
3 Pressure transducer PT 6 Pressure transducer PT
1 2
b) Example of transducer locations and bleed valve mounting

NOTE Graphical symbols are for illustration purposes and do not conform to ISO 1219-1.

Figure 2 —Typical antiresonance test arrangement
8 © ISO 2000 – All rights reserved
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SIST ISO 15086-2:2001
ISO 15086-2:2000(E)
8.5 Calibration of pressure transducers

Calibration of pressure transducers and signal conditioning is necessary. Perform relative calibration by mounting

the pressure transducers in a common block such that they measure the same pressure ripple. Construct this

common block such that the pressure transducers are at the same axial position and no more than one internal

diameter of the measurement pipe apart.

Measure the amplitude and phase relationship between the pressure transducers for a range of frequencies

spanning the complete range of interest with one transducer used as a reference. For piezoresistive transducers,

the reference transducer can be calibrated statically using, for example, a deadweight testing machine.

If piezoelectric transducers and charge amplifiers are employed, a calibrated piezoresistive transducer may be used

as a reference for dynamic calibration purposes.

If the amplitude or phase difference between the transducers exceeds 1 % or 0,5° respectively, correct for the

differences in the analysis of the test data (see 9.3 and 10.3). Record the transfer functions.

H� �
and
H� �
obtained during calibration.
9 Test procedure for Method 1

9.1 Prior to the commencement of tests, operate the hydraulic system for a sufficient period of time to purge air

from the system and to stabilize all variables, including fluid condition, to within the limits given in Table 1. If a speed

of sound test is to be performed at the same time as other hydro-acoustical measurements, conditions to the

standard relevant to those measurements can be used.

9.2 Take the ensemble average of at least 16 time-series pressure transfer functions

P P
H**��and H
12 32
P P
2 2

and calculate the coherence function S at each frequency f over the frequency range. Typical examples of the

i i

transfer functions H * and H * are given, for the case of broad-band excitation, in Figure 3.

12 32

9.3 Perform the correction of the ensemble-averaged transfer functions H and H using the transfer functions

12 32

obtained from the calibration procedure H' and H' (see 8.5) using equations (2) and (3).

12 32
H *
H � (2)
H *
H � (3)
If correction is not necessary (see 8.5), then H = H* and H = H* .
12 12 32 32
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SIST ISO 15086-2:2001
ISO 15086-2:2000(E)
Key
1 Modulus of transfer functions H* and H* 3 Degree
12 32
4 Phase of transfer functions H* and H*
2 Frequency (Hz) 12 32
Figure 3 — Typical example of transfer functions H* and H*
12 32

9.4 Calculate the speed of sound for each frequency having an associated coherence function S greater than

0,95 as described in C.1. The S function is always a positive number less than or equal to 1. The least-squares

error procedure given in C.1 allows the speed of sound, averaged over the frequency range investigated, to be

calculated.

9.5 Calculate the mean fluid velocity by dividing the mean flow by the internal cross-sectional area of the

measurement pipe. If the mean fluid velocity is greater than 5 % of any speed of sound measurement, then the

method is invalid and results shall not be reported.
10 Test procedure for Method 2

10.1 Prior to the commencement of a series of tests, operate the hydraulic system and noise generator (if

included) for a sufficient period of time to purge air from the system and to stabilize all variables, including fluid

condition, to within the limits given in Table 1. Particular attention should be given to obtaining a representative fluid

characteristic, especially the bulk modulus.

The bleed valve should be fully open to allow flow through the measurement pipe during this stabilization period.

The restrictor valve downstream of the bleed valve should be adjusted to create a mean pressure approximately

0,5 MPa below the desired test pressure during this phase. Immediately before pressure transducer measurements

are taken, the bleed valve should be closed and, if necessary, the mean pressure re-established through

adjustment of the loading valve.

Warning — No safety valves are included in the system. Personnel performing tests should exercise great

care to ensure that excessive and dangerous pressures are not created when adjusting restrictor valves.

10 © ISO 2000 – All rights reserved
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SIST ISO 15086-2:2001
ISO 15086-2:2000(E)
10.2 Take the ensemble ave
...

NORME ISO
INTERNATIONALE 15086-2
Première édition
2000-02-01
Transmissions hydrauliques — Évaluation
des caractéristiques du bruit liquidien des
composants et systèmes —
Partie 2:
Mesurage de la vitesse du son émis dans
un fluide dans une tuyauterie
Hydraulic fluid power — Determination of fluid-borne noise characteristics
of components and systems —
Part 2: Measurement of speed of sound in a fluid in a pipe
Numéro de référence
ISO 15086-2:2000(F)
ISO 2000
---------------------- Page: 1 ----------------------
ISO 15086-2:2000(F)
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ISO 15086-2:2000(F)
Sommaire Page

Avant-propos..............................................................................................................................................................iv

Introduction.................................................................................................................................................................v

1 Domaine d’application ..................................................................................................................................1

2 Références normatives .................................................................................................................................1

3 Termes et définitions.....................................................................................................................................1

4 Symboles et souscrits...................................................................................................................................2

5 Instruments ....................................................................................................................................................3

6 Générateur de bruit hydraulique..................................................................................................................4

7 Conditions d'essai .........................................................................................................................................5

8 Banc d'essai ...................................................................................................................................................6

9 Mode opératoire d'essai de la méthode 1 .................................................................................................10

10 Mode opératoire d'essai de la méthode 2 .................................................................................................11

11 Rapport d'essai ............................................................................................................................................12

12 Phrase d'identification (Référence à la présente partie de l'ISO 15086) ...................................................13

Annexe A (normative) Erreurs et classes de mesure de la valeur moyenne......................................................14

Annexe B (normative) Erreurs et classes de mesure dynamique........................................................................15

Annexe C (normative) Algorithmes de compression des données .....................................................................16

Annexe D (informative) Exemple de calcul de la vitesse du son en langage MATLAB en utilisant trois

capteurs de pression montés sur le tube (Méthode 1) ............................................................................22

Annexe E (informative) Exemple de calcul de la vitesse du son en langage MATLAB en utilisant deux

capteurs de pression montés sur un tube à extrémité fermée (Méthode 2)..........................................26

Bibliographie .............................................................................................................................................................27

© ISO 2000 – Tous droits réservés iii
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ISO 15086-2:2000(F)
Avant-propos

L'ISO (Organisation internationale de normalisation) est une fédération mondiale d'organismes nationaux de

normalisation (comités membres de l'ISO). L'élaboration des Normes internationales est en général confiée aux

comités techniques de l'ISO. Chaque comité membre intéressé par une étude a le droit de faire partie du comité

technique créé à cet effet. Les organisations internationales, gouvernementales et non gouvernementales, en

liaison avec l'ISO participent également aux travaux. L'ISO collabore étroitement avec la Commission

électrotechnique internationale (CEI) en ce qui concerne la normalisation électrotechnique.

Les Normes internationales sont rédigées conformément aux règles données dans les Directives ISO/CEI, Partie 3.

Les projets de Normes internationales adoptés par les comités techniques sont soumis aux comités membres pour

vote. Leur publication comme Normes internationales requiert l'approbation de 75 % au moins des comités

membres votants.

L’attention est appelée sur le fait que certains des éléments de la présente partie de l’ISO 15086 peuvent faire

l’objet de droits de propriété intellectuelle ou de droits analogues. L’ISO ne saurait être tenue pour responsable de

ne pas avoir identifié de tels droits de propriété et averti de leur existence.

La Norme internationale ISO 15086-2 a été élaborée par le comité technique ISO/TC 131, Transmissions

hydrauliques et pneumatiques, sous-comité SC 8, Essais des produits.

L'ISO 15086 comprend les parties suivantes, présentées sous le titre général Transmissions hydrauliques —

Évaluation des caractéristiques du bruit liquidien des composants et systèmes:
� Partie 1: Introduction

� Partie 2: Mesurage de la vitesse du son émis dans un fluide dans une tuyauterie

Les annexes A, B et C constituent des éléments normatifs de la présente partie de l’ISO 15086. Les annexes D et

E sont données uniquement à titre d’information.
iv © ISO 2000 – Tous droits réservés
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ISO 15086-2:2000(F)
Introduction

Dans les systèmes de transmissions hydrauliques, l'énergie est transmise et commandée par l'intermédiaire d'un

fluide sous pression circulant en circuit fermé. Le processus de transformation de l'énergie mécanique en énergie

hydraulique génère des fluctuations de l'écoulement et de la pression ainsi que des vibrations de la structure.

Les caractéristiques hydro-acoustiques des composants hydrauliques peuvent être mesurées avec une précision

acceptable lorsque la vitesse du son émis par le fluide est connue de façon précise.

La méthode de mesurage pour l'évaluation de la vitesse du son dans un tube, comme décrit dans la présente

partie de l’ISO 15086, est fondée sur l'application de la théorie de la ligne de transmission à onde plane à l'analyse

des fluctuations de pression dans des tubes rigides [1].
Deux méthodes différentes sont présentées, à savoir:
� trois capteurs de pression dans un tube;
� l’antirésonance acoustique dans un système de tubes à extrémité fermée.

Il convient d’utiliser la méthode des trois capteurs de pression chaque fois que la vitesse du son est à mesurer

dans les conditions de service efficaces d'un système.

Il convient d’utiliser la méthode antirésonance pour produire un tableau de vitesse des données acoustiques en

fonction de la pression et de la température moyennes d'un fluide particulier.
© ISO 2000 – Tous droits réservés v
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NORME INTERNATIONALE ISO 15086-2:2000(F)
Transmissions hydrauliques — Évaluation des caractéristiques du
bruit liquidien des composants et systèmes —
Partie 2:
Mesurage de la vitesse du son émis dans un fluide dans une
tuyauterie
1 Domaine d’application

La présente partie de l'ISO 15086 décrit la procédure d'évaluation de la vitesse du son émis par un fluide contenu

dans un tube, par la réalisation de mesurages à partir de capteurs de pression montés sur ledit tube.

La présente partie de l'ISO 15086 s'applique à tous les types de circuits hydrauliques fonctionnant dans des

conditions de régime établi, indépendamment de leur dimension, pour des impulsions de pression dans une

gamme de fréquences comprise entre 25 Hz et 2 500 Hz.
2 Références normatives

Les normes suivantes contiennent des dispositions qui, par suite de la référence qui en est faite, constituent des

dispositions valables pour la présente partie de l'ISO 15086. Au moment de la publication, les éditions indiquées

étaient en vigueur. Toute norme est sujette à révision et les parties prenantes des accords fondés sur la présente

partie de l'ISO 15086 sont invitées à rechercher la possibilité d'appliquer les éditions les plus récentes des normes

indiquées ci-après. Les membres de la CEI et de l'ISO possèdent le registre des Normes internationales en vigueur

à un moment donné.

ISO 1000:1992, Unités SI et recommandations pour l'emploi de leurs multiples et de certaines autres unités.

ISO 1219-1:1991, Transmissions hydrauliques et pneumatiques — Symboles graphiques et schémas de circuit —

Partie 1: Symboles graphiques.
ISO 5598:1985, Transmissions hydrauliques et pneumatiques — Vocabulaire.
3 Termes et définitions

Pour les besoins de la présente partie de l'ISO 15086, les termes et définitions donnés dans l’ISO 5598 et les

suivants s'appliquent.
3.1
onde d'écoulement

composant fluctuant de débit dans le fluide hydraulique, provoqué par l'interaction entre l'onde d'écoulement de la

source et le système
3.2
onde de pression

composant fluctuant de pression dans le fluide hydraulique, provoqué par l'interaction entre l'onde d'écoulement de

la source et le système
© ISO 2000 – Tous droits réservés 1
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ISO 15086-2:2000(F)
3.3
fréquence fondamentale

fréquence la plus basse d'onde de pression mesurée à l'aide de l'instrument d'analyse de fréquence

3.4
harmonique

composant sinusoïdal de l'onde de pression ou de l'onde d'écoulement se produisant à un multiple entier de la

fréquence fondamentale

NOTE Une harmonique peut être représentée par son amplitude et sa phase, ou bien par ses parties réelle et imaginaire.

3.5
générateur de bruit hydraulique

composant hydraulique générant une onde d'écoulement puis une onde de pression dans le circuit

3.6
tube de mesure
tube dans lequel sont montés les capteurs de pression
3.7
impédance

rapport complexe de l'onde de pression avec l'onde d'écoulement se produisant à un point donné dans un système

hydraulique et à une fréquence donnée
3.8
impédance d'entrée
impédance à l'entrée d'un tube ou d'une tuyauterie
3.9
première fréquence antirésonance acoustique

fréquence la plus basse à laquelle l'amplitude de l'impédance d'entrée du tube de mesurage est minimale.

4 Symboles et souscrits
4.1 Symboles

A, A',a,B,B', b Coefficients de propagation des ondes dépendant de la fréquence (nombres complexes)

c Vitesse acoustique du fluide
d Diamètre intérieur du tube
f Fréquence de l'harmonique d'onde de pulsation
f Vecteur de fréquences auxquelles sont effectués les mesurages
f Première fréquence antirésonance acoustique (en hertz)

H Fonction transfert (nombre complexe) entre deux signaux de capteurs de pression après

correction de l’étalonnage

H' Fonction transfert (nombre complexe) entre deux signaux de capteurs de pression soumis à

étalonnage

H* Fonction transfert (nombre complexe) entre deux signaux de capteurs de pression après

correction d'étalonnage
j �1
L Distance entre les capteurs 1 et 2 (Méthode 1)
2 © ISO 2000 – Tous droits réservés
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ISO 15086-2:2000(F)
L' Distance entre les capteurs 2 et 3 (Méthode 1)
l Distance entre les capteurs de pression (Méthode 2)
P Onde de pression du capteur PT1 (nombre complexe)
P Onde de pression du capteur PT2 (nombre complexe)
P Onde de pression du capteur PT3 (nombre complexe)
Q Onde d'écoulement à l'emplacement 1, de 1 à 2 (nombre complexe)
1� 2
Q Onde d'écoulement à l'emplacement 2, de 2 à 1 (nombre complexe)
2� 1
Q Onde d'écoulement à l'emplacement 3, de 2 à 3 (nombre complexe)
2� 3
S Fonction de cohérence correspondant aux fréquences de mesure, f
i i
�� Erreur (nombre complexe)
� Conjugué du nombre complexe ��(nombre complexe)
� Partie réelle de �
� Partie imaginaire de �
� Masse volumique du fluide
� Viscosité cinématique du fluide
� 2�f

NOTE H, H', H*, P , P , P , Q , Q , Q sont tous dépendants, de la fréquence et sont donc représentés par des

1 2 3 1� 2 2� 1 2� 3
lettres majuscules.

Les unités utilisées dans la présente partie de l'ISO 15086 sont conformes à l'ISO 1000.

Les symboles graphiques sont conformes à l'ISO 1219-1, sauf indication contraire.

4.2 Souscrits
O Indice de l'ancienne valeur
N Indice de la nouvelle valeur
5 Instruments
5.1 Mesures statiques
Les instruments utilisés pour mesurer
a) l'écoulement moyen (Méthode 1 uniquement);
b) la pression moyenne du fluide;
c) la température du fluide;

doivent satisfaire l'exigence relative à l’exactitude de mesurage de «classe industrielle», c'est-à-dire la classe C

donnée dans l'annexe B.
© ISO 2000 – Tous droits réservés 3
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ISO 15086-2:2000(F)
5.2 Mesures dynamiques

Les instruments utilisés pour mesurer l'onde de pression doivent avoir les caractéristiques suivantes:

a) fréquence de résonanceW 30 kHz;
b) linéaritéW� 1%;
c) compensation d'accélération souhaitable.

Il n'est pas nécessaire que les instruments correspondent à une pression en régime établi, et il peut être

avantageux de filtrer toute composante de signal en régime établi à l'aide d'un filtre passe-haut. Ce filtre ne doit

pas générer d'erreur d'amplitude ou de phase supplémentaire supérieure à 0,5 % ou 0,5° respectivement, de la

mesure courante.
5.3 Analyse de fréquence de l'onde de pression

Un instrument approprié doit être utilisé pour mesurer l'amplitude et la phase de l'onde de pression.

L'instrument doit pouvoir mesurer l'onde de pression à partir des capteurs de pression de telle sorte que, pour un

harmonique particulier, les mesures réalisées à partir de chaque capteur soient effectuées simultanément et de

manière synchronisée les unes par rapport aux autres.

La précision et la résolution de l'instrument pour les mesures d'harmonique doivent être les suivantes:

a) amplitude:� 0,5 %;
b) phase:� 0,5°;
c) fréquence:� 0,5 %;
sur une gamme de fréquences comprise entre 25 Hz et 2 500 Hz.
5.4 Incertitude

La conformité à la spécification ci-dessus donnera une incertitude de la vitesse du son inférieure à� 3%.

6 Générateur de bruit hydraulique
6.1 Généralités

Tout type de générateur de bruit hydraulique peut être utilisé à condition qu'il crée une onde de pression suffisante

au niveau des capteurs de pression permettant ainsi la réalisation de mesures exactes.

EXEMPLE Les pompes et les moteurs créent une onde de pression composée principalement de nombreux harmoniques

de la fréquence fondamentale. Dans ces cas, la fréquence fondamentale est égale au produit de la fréquence de rotation de

l’axe et du nombre de dents de l'engrenage, de palettes ou de pistons, etc. (selon la machine utilisée).

Des méthodes alternatives appropriées comprennent:

� un distributeur auxiliaire équipé d'un tiroir tournant permettant au flux de se diriger vers la canalisation de

retour grâce à sa rotation partielle;

� un servodistributeur électro-hydraulique entraîné par un générateur de fréquence. Le servo-distributeur peut

être déclenché par un signal de bruit blanc afin d'obtenir des mesures d'onde de pression significatives à

chaque fréquence intéressante.
4 © ISO 2000 – Tous droits réservés
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ISO 15086-2:2000(F)
6.2 Vibration du générateur

Si nécessaire, il convient que le tube de mesure soit structurellement isolé du générateur afin de minimiser les

vibrations.
7 Conditions d'essai
7.1 Généralités

Les conditions de service requises doivent être maintenues pour chaque essai dans les limites spécifiées dans le

Tableau 1.
7.2 Température du fluide

La température du fluide doit être la température mesurée à l'entrée du tube de mesure.

7.3 Masse volumique et viscosité du fluide

La masse volumique et la viscosité du fluide doivent être connues avec une exactitude définie dans les limites

spécifiées dans le Tableau 2.
7.4 Pression moyenne du fluide

La pression moyenne du fluide doit être celle mesurée à l'entrée du tube de mesure.

7.5 Mesure de l'écoulement moyen

La mesure de l'écoulement moyen doit être effectuée en aval du tube de mesure (Méthode 1 uniquement).

Tableau 1 — Variations admissibles des conditions d'essai
Paramètre d'essai Variation admissible
Écoulement moyen �2%
Pression moyenne
�2%
Température �2°C
Tableau 2 — Exactitude requise des données de propriétés du fluide
Propriété Exactitude requise
Masse volumique �2%
Viscosité
�5%
© ISO 2000 – Tous droits réservés 5
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ISO 15086-2:2000(F)
8 Banc d'essai
8.1 Généralités

Si, à toute condition d'essai, les amplitudes d'ondes de pression sont trop faibles pour pouvoir réaliser une analyse

satisfaisante du spectre de fréquences, un autre générateur de bruit doit être choisi.

Les capteurs de pression doivent être montés de telle sorte que leurs diaphragmes soient au même niveau que la

paroi intérieure du tube à � 0,5 mm.

Deux spécifications alternatives relatives au tube de mesure et à la position du capteur sont données

conformément à la méthode utilisée.
8.2 Isolation thermique

La température doit être mesurée aux deux extrémités du tube de mesure. La différence de température entre les

deux extrémités du tube de mesure ne doit en aucun cas dépasser 2 °C quelle que soit la condition d'essai. Si

nécessaire, un calorifugeage thermique suffisant doit être appliqué au tube de mesure pour pouvoir satisfaire cette

exigence.
8.3 Méthode 1: Méthode des trois capteurs

8.3.1 Cette méthode peut être utilisée lorsque la vitesse du son doit être mesurée en même temps que les

autres caractéristiques hydro-acoustiques des composants hydrauliques telles que l'impédance, l'onde

d'écoulement de la source ou les coefficients de la matrice-transfert. Le tube de mesure doit être installé dans le

système d'essai à l'endroit où la vitesse du son doit être mesurée. Si nécessaire, plusieurs tubes de mesure

peuvent être utilisés simultanément.

Le tube de mesure doit être uniforme et droit. Son diamètre intérieur doit être compris entre 80 % et 120 % du

diamètre des tubes, ou des orifices de composants, auxquels il est raccordé. Il convient que le tube soit soutenu de

manière à réduire toute vibration.

Dans les cas où les autres propriétés hydro-acoustiques ne sont pas mesurées simultanément, une pompe (et, si

nécessaire, un générateur de bruit hydraulique) doit être montée à une extrémité du tube de mesure. L'autre

extrémité doit avoir la forme d'une soupape de charge ne comportant aucun élément interne libre, telle qu'une

soupape à pointeau.
La pression moyenne doit être mesurée à l'extrémité amont du tube de mesure.

8.3.2 Cette méthode requiert l'utilisation de trois capteurs de pression, configurés comme représenté à la

Figure 1. L'espace entre les capteurs doit être choisi selon les spécifications normalisées des mesures hydro-

acoustiques à effectuer simultanément. Sinon, la distance entre les capteurs de pression L, L' est celle spécifiée

dans le Tableau 3.

La distance entre chaque extrémité du tube de mesure et le capteur de pression le plus proche doit être au moins

égale à 10d,où d est le diamètre intérieur du tube. Les distances L et L' entre les capteurs, comme représenté à la

Figure 1, doivent être mesurées avec une exactitude de � 0,5 mm.

Aucun autre composant ne doit être raccordé entre les orifices d'entrée et de sortie du tube de mesure.

Tableau 3 — Espace entre les capteurs: Méthode 1
330 mm �2mm
470 mm �2mm
6 © ISO 2000 – Tous droits réservés
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ISO 15086-2:2000(F)
Capteurs de pression
Distances par rapport à l'extrémité du tube de mesure, x W 10d et x W 10d
1 2
Figure 1 — Disposition du tube de mesure à trois capteurs de pression
8.4 Méthode 2: Méthode antirésonance

8.4.1 Cette méthode peut être utilisée pour réaliser un organigramme de la vitesse du son d'un fluide particulier.

En raison des résonances de pression créées dans le système, cette méthode ne convient pas lorsque d'autres

mesures hydro-acoustiques doivent être réalisées.

8.4.2 Un banc d'essai approprié est représenté schématiquement à la Figure 2 a). La soupape de charge ne doit

comporter aucun élément libre. Une soupape à pointeau est un exemple de soupape de charge appropriée. Le

tube de mesure prend la forme d'un branchement latéral à extrémité fermée raccordé au circuit

pompe/tube/soupape de charge comme présenté. Il est important que le fluide dans le tube de mesure ait une

température la plus uniforme possible, et qu'il ne contienne pas de bulles de gaz. Pour réaliser ces objectifs,

l'extrémité du tube de mesure est constituée d'un robinet de purge. Une soupape à pointeau est un exemple de

robinet de purge approprié. Avant d'effectuer les mesures, le robinet de purge est ouvert pendant une durée

suffisante pour évacuer les bulles de gaz dans le tube et pour stabiliser la température. Le tube de mesure doit être

orienté vers le bas avec le robinet de purge situé en dessous du niveau du tube d'écoulement de façon à éviter que

de l’air reste piégé dans le tube de mesure durant l’essai. Il est important que le robinet de purge n'achemine pas

un volume supplémentaire significatif à l'extrémité de la conduite lorsque le robinet est fermé.

Les capteurs de pression, PT et PT , représentés à la Figure 2 a), sont situés à chaque extrémité du tube de

1 2

mesure. Il est essentiel que le capteur PT soit monté le plus près possible de l'extrémité du tube. Il convient

également que l'emplacement du capteur PT soit le plus proche possible du point de raccordement du tube de

mesure au circuit principal. La Figure 2 b) donne un exemple de satisfaction de ces exigences. Dans cet exemple,

l'extrémité du tube de mesure est un logement prévu à cet effet comportant la soupape à pointeau.

© ISO 2000 – Tous droits réservés 7
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ISO 15086-2:2000(F)
Légende
1 Pompe 6 Soupape de charge
2 Moteur électrique 7 Robinet de purge
3 Générateur de bruit hydraulique (lorsqu'il est utilisé) 8 Tube de mesure
4 Tube d'écoulement 9 Capteurs de température
5 Manomètre 10 Capteurs de pression
a) Disposition du circuit
8 © ISO 2000 – Tous droits réservés
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ISO 15086-2:2000(F)
Légende
1 À travers la conduite d’écoulement 4 Réglage de la soupape à pointeau
2 Capteur de température 5 Vers le réservoir
3 Capteur de pression PT 6 Capteur de pression PT
1 2
b) Exemple d'emplacements de capteur et de montage du robinet de purge

NOTE Les symboles graphiques sont donnés pour illustration et ne sont pas conformes à l'ISO 1219-1.

Figure 2 — Dispositif type de l'essai antirésonance

Les composants hydrauliques nécessaires pour obtenir les conditions d'essai appropriées peuvent,

intrinsèquement, générer des niveaux d'impulsion de pression suffisants pour pouvoir effectuer l'analyse du spectre

de fréquences de façon satisfaisante. Dans le cas contraire, un générateur de bruit hydraulique séparé doit être

raccordé au circuit, comme représenté à la Figure 2 a).

Afin de maximiser les niveaux d'impulsion de pression, il convient que la distance entre la pompe (ou le générateur

de bruit lorsqu'il fonctionne) et la soupape de charge ne soit pas supérieure à un dixième de la longueur du tube de

mesure.

8.4.3 Le tube de mesure doit être un tube métallique uniforme, rigide et droit. Son diamètre intérieur doit être

compris entre 50 % et 100 % du diamètre de la conduite à laquelle il est raccordé. Ce tube doit être soutenu de

telle sorte que les vibrations soient réduites.

La distance entre les capteurs de pression, l, doit être définie selon la première fréquence antirésonance

acoustique f àl'aidedel'équationsuivante:
1 B�10
l � (1)
4 f �

Le coefficient de charge effectif B peut être évalué en utilisant les données du fabricant relatives au fluide adapté

aux conditions de service des essais. Une valeur précise n'est pas requise.
La fréquence f peut être choisie dans la gamme comprise entre 100 Hz et 200 Hz.

La distance entre les capteurs de pression doit être mesurée avec une précision de � 0,5 mm.

8.5 Étalonnage des capteurs de pression

L'étalonnage des capteurs de pression et la mise en forme de signaux sont des opérations nécessaires.

L'étalonnage relatif doit être effectué en montant les capteurs de pression sur un bloc commun de telle sorte qu'ils

mesurent la même onde de pression. Ce bloc commun doit être construit de sorte que les capteurs de pression

aient la même position axiale et ne soient pas éloignés du tube de mesure de plus d'un diamètre intérieur.

Mesurer la relation amplitude-phase entre les capteurs de pression pour une gamme de fréquences couvrant la

gamme complète concernée avec un capteur utilisé comme élément de référence. Pour les capteurs piézorésistifs,

le capteur de référence peut être étalonné de manière statique en utilisant, par exemple, une machine d'essais à

contre-poids.

Lorsque l'on utilise des capteurs piézo-électriques et des amplificateurs de charge, un capteur piézorésistif

étalonné peut être pris comme référence pour un étalonnage dynamique.

Lorsque la différence d'amplitude ou de phase entre les capteurs dépasse 1 % ou 0,5° respectivement, les

différences doivent être corrigées dans l'analyse des données d'essais (voir 9.3 et 10.3). Enregistrer les fonctions

transfert
© ISO 2000 – Tous droits réservés 9
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ISO 15086-2:2000(F)
obtenues au cours de l'étalonnage.
9 Mode opératoire d'essai de la méthode 1

9.1 Avant de commencer les essais, faire fonctionner le système hydraulique pendant une durée suffisante pour

purger l'air contenu dans le système et stabiliser toutes les variables, y compris l'état du fluide, dans les limites

données dans le Tableau 1. Lorsqu'un essai de vitesse du son doit être réalisé en même temps que d'autres

mesures hydro-acoustiques, il est admis d'appliquer les exigences relatives à la norme correspondant à ces

mesures.

9.2 Prendre la moyenne d'ensemble d'au moins 16 séries temporelles de fonctions transfert de pression

et calculer la fonction de cohérence S à chaque fréquence f sur la gamme de fréquences. Des exemples types de

i i

fonctions transfert H* et H* sont donnés à la Figure 3 pour le cas d'une excitation à large bande.

12 32

9.3 Effectuer la correction de l'ensemble moyennée des fonctions transfert H et H en utilisant les fonctions

12 32

transfert obtenues à partir de la procédure d'étalonnage H' et H' (voir 8.5) en utilisant les équations (2) et (3).

12 32
H12
H � (2)
H � (3)
Lorsque la correction n'est pas nécessaire (voir 8.5), H = H'* et H = H* .
12 32 32
10 © ISO 2000 – Tous droits réservés
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ISO 15086-2:2000(F)
Figure 3 — Exemple type des fonctions transfert H* et H*
12 32

9.4 Calculer la vitesse du son pour chaque fréquence ayant une fonction de cohérence associée S supérieure à

0,95 comme décrit à l'article C.1. La fonction S est toujours un nombre positif inférieur ou égal à 1. La méthode du

carré des erreurs donnée dans l'article C.1 permet de calculer la vitesse du son, moyennée sur la gamme de

fréquences analysée.

9.5 Calculer la vitesse moyenne du fluide en divisant l'écoulement moyen par la superficie de la section interne

du tube de mesure. Lorsque la vitesse moyenne du fluide est supérieure à 5 % de toute mesure de la vitesse du

son, la méthode est alors invalide et les résultats ne doivent pas être consignés.

10 Mode opératoire d'essai de la méthode 2

10.1 Avant de commencer la série d'essais, faire fonctionner le système hydraulique et le générateur de bruit

(lorsqu'il est inclus) pendant une durée suffisante pour purger l'air du système et stabiliser toutes les variables, y

compris l'état du fluide, dans les limi
...

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