SIST-TP CEN/TR 16891:2016
(Main)Railway applications - Acoustics - Measurement method for combined roughness, track decay rates and transfer functions
Railway applications - Acoustics - Measurement method for combined roughness, track decay rates and transfer functions
This method is used to determine combined wheel-rail roughness and track decay rates from rail vibration during the pass-by of a train. By combining sound pressure measurement from the same pass-by, a vibro-acoustic transfer function for rolling noise is determined.
The track decay rate is a vibration quantity that characterizes the attenuation of rail vibration along the track for a given wheel/rail contact excitation, and thereby affects the amount of sound radiation from the track.
Combined roughness is a quantity that determines the level of excitation of wheel-rail rolling noise. It can be determined from vertical rail vibration during a train pass-by and the vertical track decay rate. The transfer function can be used to characterize the vibro-acoustic behaviour of the vehicle-track system for a given roughness excitation and in relation to rolling noise. Combined roughness, track decay rates and transfer functions are determined as one-third octave spectra.
The method can be used for the following purposes:
- to measure track decay rates under operational conditions;
- to characterize the effectiveness of noise control measures in terms of combined roughness, transfer function and track decay rate;
- to compare the combined roughness before and after noise control measures are implemented (thereby quantifying the effect of any change in wheel or rail roughness);
- to monitor wheel roughness during a pass-by, either of whole trains or parts of trains;
- to separate rolling noise from other sources;
- to assess a threshold for the rail roughness by measuring multiple pass-bys.
The method is not for approval of sections of reference track in terms of acoustic rail roughness and track decay rates, which are covered by EN 15610 and EN 15461, respectively.
The method is applicable to trains on conventional tracks, i.e. normal ballasted tracks with wooden or concrete sleepers and on ballastless track systems.
The method has not yet been validated for:
- non-standard wheel types such as small wheels, resilient tram wheels;
- non-standard track types such as embedded rail or grooved rail.
Bahnanwendung - Geräuschemission - Messmethode für kombinierte Rauheit, Schienenabklingraten und Übertragungsfunktions
Dieses Verfahren wird angewendet, um die kombinierte Rauheit von Rad und Schiene und die Gleisabkling¬raten bei Vorbeifahrt eines Zuges zu ermitteln. Durch Kombination mit Schalldruckmessung aus derselben Vorbeifahrt wird eine vibroakustische Übertragungsfunktion für das Rollgeräusch bestimmt.
Die Gleisabklingrate ist eine Schwingungsgröße, die die Dämpfung der Schienenschwingung entlang der Strecke bei einer gegebenen Anregung beim Kontakt zwischen Rad und Schiene charakterisiert, und sich dabei auf die Höhe der Schallabstrahlung der Strecke auswirkt.
Die kombinierte Rauheit ist eine Größe, die den Anregungspegel des Rad-Schiene-Rollgeräuschs bestimmt. Sie kann aus vertikalen Schienenschwingungen während der Vorbeifahrt eines Zuges und der vertikalen Gleisabklingrate ermittelt werden. Die Übertragungsfunktion kann angewendet werden, um das vibro-akustische Verhalten des Systems Fahrzeug-Strecke bei einer gegebenen Rauheitsanregung und in Bezug auf das Rollgeräusch zu charakterisieren. Kombinierte Rauheit, Gleisabklingraten und Übertragungsfunktionen werden als Terzspektren bestimmt.
Das Verfahren kann für folgende Zwecke angewendet werden:
um die Gleisabklingraten unter Betriebsbedingungen zu messen;
um die Wirksamkeit von Schallschutzmaßnahmen in Bezug auf kombinierte Rauheit, Übertragungs-funktion und Gleisabklingrate zu charakterisieren;
um die kombinierte Rauheit vor und nach den umgesetzten Schallschutzmaßnahmen zu vergleichen (um damit die Auswirkung jeglicher Änderung der Rad oder Schienenrauheit quantitativ zu bestim-men);
um die Radrauheit während einer Vorbeifahrt zu überwachen, entweder von ganzen Zügen oder Teilen von Zügen;
um das Rollgeräusch von anderen Quellen zu trennen;
um durch die Messung mehrerer Vorbeifahrten einen Schwellenwert für die Schienenrauheit zu ermitteln.
Das Verfahren eignet sich nicht zur Prüfung von Referenzgleisen in Bezug auf akustische Schienenrauheit und Gleisabklingraten, die von EN 15610 bzw. EN 15461 abgedeckt werden.
Das Verfahren ist anwendbar auf Züge, die auf herkömmlichen Gleisen fahren, d. h. mit normalem Schotter-oberbau, mit Holz oder Betonschwellen und auf schotterlosen Gleisanlagen.
Das Verfahren wurde noch nicht validiert für:
nicht übliche Radtypen wie beispielsweise kleine Räder bis zu 600 mm Durchmesser, elastische Straßenbahnräder;
nicht übliche Gleisarten wie eingedeckte Schienen oder Rillenschienen.
Dieses Verfahren ist nicht für Gleise mit Schienenstößen anwendbar.
Applications ferroviaires - Acoustique - Méthode de mesurage pour la rugosité combinée, les taux de décroissance de la voie et les fonctions de transfert
La présente méthode permet de déterminer la rugosité roue-rail et le taux de décroissance des voies à partir des vibrations des rails pendant le passage d’un train. En combinant avec les mesures de la pression acoustique issues du même passage, la fonction de transfert vibro-acoustique du bruit de roulement est déterminée.
Le taux de décroissance de la voie est une quantité vibratoire qui caractérise l’atténuation des vibrations des rails le long de voies pour une excitation donnée du contact roue/rail et affecte par conséquent le rayonnement sonore de la voie.
La rugosité combinée est la quantité qui caractérise le niveau d'excitation du bruit de roulement roue/rail. Elle peut être déterminée à partir de la vibration verticale des rails pendant le passage du train et à partir du taux de décroissance vertical de la voie. La fonction de transfert peut être utilisée pour caractériser le comportement vibro-acoustique du système véhicule-voie pour une excitation de rugosité donnée et en rapport avec le bruit de roulement. La rugosité combinée, les taux de décroissance de la voie, ainsi que les fonctions de transfert sont déterminés sous la forme de spectres par bande de tiers d’octave.
La présente méthode peut être utilisée pour les applications suivantes :
mesurer les taux de décroissance de la voie dans des conditions d’exploitation ;
caractériser l'efficacité des mesures de contrôle du bruit en termes de rugosité combinée, de fonction de transfert et de taux de décroissance de la voie ;
comparer la rugosité combinée avant et après que les mesures de contrôle du bruit ne soient mises en œuvre (quantifier ainsi l'effet de tout changement de la rugosité de la roue ou du rail) ;
contrôler la rugosité des roues pendant le passage, soit de trains complets, soit de parties de trains ;
séparer le bruit de roulement des autres sources de bruit ;
évaluer le seuil de la rugosité du rail en mesurant de multiples passages.
La méthode ne concerne pas l'approbation des sections de la voie de référence en termes de rugosité acoustique du rail et des taux de décroissance de la voie, qui sont couverts respectivement par les normes EN 15610 et EN 15461.
La méthode s'applique aux trains circulant sur les voies conventionnelles, c'est-à-dire sur des voies ballastées normales avec des traverses en bois ou en béton et sur des systèmes de voies sans ballast.
La méthode n'est pas encore validée pour :
des types de roues non standard, tels que des petites roues, des roues de tram à bandage élastique ;
des types de rails non standard, tels que les rails noyés ou les rails à gorge.
La méthode ne s’applique pas aux voies avec des rails joints.
Železniške naprave - Akustika - Metode merjenja kombinirane hrapavosti, stopnje upadanja tirnice in prenosnih funkcij
Ta metoda se uporablja za določevanje kombinirane hrapavosti površine kolesa in tirnice ter stopnje upadanja tirnice zaradi vibracij, ki jih povzroči mimo vozeči vlak. S kombinacijo meritve zvočnega tlaka iz iste mimovožnje se določi vibro-akustična prenosna funkcija za kotalni hrup.
Stopnja upadanja tirnice je količina vibracij, ki označuje slabljenje vibracij vzdolž tirnice za dano vzbujanje stika kolo-tirnica ter posledično vpliva na količino sevanja zvoka s tirnice.
Kombinirana hrapavost je količina, ki določa raven vzbujanja kotalnega hrupa kolesa in tirnice. Določiti jo je mogoče na podlagi navpičnih vibracij tirnice med mimovožnjo vlaka in navpične stopnje upadanja tirnice. Prenosno funkcijo je mogoče uporabiti za opis vibro-akustičnega vedenja sistema vozila in tirnice za dano vzbujanje hrapavosti ter v povezavi s kotalnim hrupom. Kombinirana hrapavost, stopnja upadanja tirnice in prenosne funkcije se določajo kot terčni spekter.
To metodo je mogoče uporabiti za naslednje namene:
– merjenje stopnje upadanja tirnice pod delovnimi pogoji;
– določevanje učinkovitosti ukrepov za nadzor hrupa v smislu kombinirane hrapavosti, prenosne funkcije in stopnje upadanja tirnice;
– primerjava kombinirane hrapavosti pred in po uvedbi ukrepov za nadzor hrupa (ter s tem količinsko ovrednotenje učinka kakršne koli spremembe v hrapavosti kolesa in tirnice);
– spremljanje hrapavosti kolesa med mimovožnjo celotne vlakovne kompozicije ali posameznih vagonov;
– ločitev kotalnega hrupa od drugih virov;
– ocena praga za hrapavost tirnice z merjenjem več mimovoženj.
Ta metoda ni namenjena odobritvi odsekov referenčne tirnice v smislu akustične hrapavosti in stopnje upadanja tirnice, ki sta obravnavani v standardu EN 15610 oz. EN 15461.
Metoda se uporablja za vlake na običajnih tirnicah, tj. tirnicah na gramozni gredi z lesenimi ali betonskimi pragovi, in v sistemih tirnic brez gramozne grede.
Metoda še ni bila potrjena za:
– nestandardne vrste koles, kot so majhna kolesa, odporna kolesa tramvajev;
– nestandardne vrste tirnic, kot je vgrajena tirnica ali žlebasta tirnica.
General Information
Standards Content (Sample)
SLOVENSKI STANDARD
SIST-TP CEN/TR 16891:2016
01-september-2016
Železniške naprave - Akustika - Metode merjenja kombinirane hrapavosti, stopnje
upadanja tirnice in prenosnih funkcij
Railway applications - Acoustics - Measurement method for combined roughness, track
decay rates and transfer functions
Bahnanwendung - Geräuschemission - Messmethode für kombinierte Rauheit,
Schienenabklingraten und Übertragungsfunktions
Ta slovenski standard je istoveten z: CEN/TR 16891:2016
ICS:
17.140.30 Emisija hrupa transportnih Noise emitted by means of
sredstev transport
93.100 Gradnja železnic Construction of railways
SIST-TP CEN/TR 16891:2016 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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CEN/TR 16891
TECHNICAL REPORT
RAPPORT TECHNIQUE
May 2016
TECHNISCHER BERICHT
ICS 17.140.30; 93.100
English Version
Railway applications - Acoustics - Measurement method
for combined roughness, track decay rates and transfer
functions
Bahnanwendungen - Akustik - Messmethode für
kombinierte Rauheit, Gleisabklingraten und
Übertragungsfunktionen
This Technical Report was approved by CEN on 13 May 2016. It has been drawn up by the Technical Committee CEN/TC 256.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2016 CEN All rights of exploitation in any form and by any means reserved Ref. No. CEN/TR 16891:2016 E
worldwide for CEN national Members.
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Contents Page
European foreword . 4
Introduction . 5
1 Scope . 6
2 Normative references . 6
3 Terms and definitions . 7
4 Symbols and abbreviations . 8
5 Instrumentation . 8
6 Installation aspects. 9
7 Measurement positions . 9
8 Measured quantities . 10
9 Test procedure . 10
10 Data processing . 10
11 Method to determine the track decay rate from rail vibration . 11
11.1 General . 11
11.2 Energy iteration method . 11
12 Method to determine the combined roughness from vertical railhead vibration . 18
13 Method to convert roughness from frequency to wavelength domain. 20
14 Method to determine the rolling noise transfer function. 22
14.1 Definition . 22
14.2 Application examples . 23
15 Test report . 23
16 Uncertainty and grade . 23
Annex A (informative) A factor, difference between the combined roughness and the
2
contact point displacement . 25
Annex B (informative) Benchmark examples and background information . 28
B.1 General . 28
B.2 Examples of vertical decay rates determined for several different tracks . 28
B.3 Comparison with direct measurements . 29
B.4 Comparison of TDR methods . 33
B.5 Repeatability . 35
B.6 Reproducibility . 38
B.7 Effect of accelerometer position . 42
B.8 Effect of speed and averaging . 48
B.9 Effect of wheel defects . 52
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B.10 Effect of temperature . 52
B.11 Effect of load . 52
Annex C (informative) Slope methods . 53
C.1 Single accelerometer slope method . 53
C.2 Two accelerometer method . 54
Bibliography . 55
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European foreword
This document (CEN/TR 16891:2016) has been prepared by Technical Committee CEN/TC 256
“Railway applications”, the secretariat of which is held by DIN.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
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Introduction
This Technical Report provides a basis for a standard on measurement of combined wheel-rail
roughness, track decay rates and transfer functions from train pass-bys.
The main items required for a standard are covered but also additional background information and
benchmark results are included.
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1 Scope
This method is used to determine combined wheel-rail roughness and track decay rates from rail
vibration during the pass-by of a train. By combining sound pressure measurement from the same pass-
by, a vibro-acoustic transfer function for rolling noise is determined.
The track decay rate is a vibration quantity that characterizes the attenuation of rail vibration along the
track for a given wheel/rail contact excitation, and thereby affects the amount of sound radiation from
the track.
Combined roughness is a quantity that determines the level of excitation of wheel-rail rolling noise. It
can be determined from vertical rail vibration during a train pass-by and the vertical track decay rate.
The transfer function can be used to characterize the vibro-acoustic behaviour of the vehicle-track
system for a given roughness excitation and in relation to rolling noise. Combined roughness, track
decay rates and transfer functions are determined as one-third octave spectra.
The method can be used for the following purposes:
— to measure track decay rates under operational conditions;
— to characterize the effectiveness of noise control measures in terms of combined roughness,
transfer function and track decay rate;
— to compare the combined roughness before and after noise control measures are implemented
(thereby quantifying the effect of any change in wheel or rail roughness);
— to monitor wheel roughness during a pass-by, either of whole trains or parts of trains;
— to separate rolling noise from other sources;
— to assess a threshold for the rail roughness by measuring multiple pass-bys.
The method is not for approval of sections of reference track in terms of acoustic rail roughness and
track decay rates, which are covered by EN 15610 and EN 15461, respectively.
The method is applicable to trains on conventional tracks, i.e. normal ballasted tracks with wooden or
concrete sleepers and on ballastless track systems.
The method has not yet been validated for:
— non-standard wheel types such as small wheels up to 600 mm diameter, resilient tram wheels;
— non-standard track types such as embedded rail or grooved rail;
The method is not applicable to track with rail joints.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
EN 15461, Railway applications — Noise emission — Characterisation of the dynamic properties of track
sections for pass by noise measurements
EN 15610, Railway applications — Noise emission — Rail roughness measurement related to rolling noise
generation
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EN ISO 266, Acoustics — Preferred frequencies (ISO 266)
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
pass-by time
t [s]
p
duration of vehicle pass-by from buffer to buffer
3.2
number of axles
N [-]
ax
number of axles in the selected train or part of train
3.3
one-third octave band frequency
f [Hz]
c
centre frequency of a one-third octave frequency band
3.4
one-third octave wavelength
λ [m]
centre wavelength of a one-third octave wavelength band
3.5
sound pressure signal
p(t) [Pa]
time signal of the sound pressure measured at a fixed point
3.6
equivalent sound pressure level spectrum
−5
L (f ) dB re 2.10 [Pa]
p
eq,Tp c
one-third octave spectrum of the sound pressure energy averaged over pass-by time t
p
3.7
acceleration signal
2
a(t) [m/s ]
time signal of the rail acceleration
3.8
equivalent vertical rail vibration level spectrum
−6 2
L (f ,V) dB re 10 [m/s ]
aeq,Tp c
one-third octave spectrum of the sound pressure energy averaged over pass-by time t at running
p
speed v
3.9
decay exponent
-1
β [m ]
decay exponent characteristic for the vibration decay in the rail
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3.10
vertical track decay rate
D (f ) [dB/m]
z c
decay rate of vertical rail vibrations along the rail head
3.11
lateral track decay rate
D (f ) [dB/m]
y c
decay rate of lateral rail vibrations along the rail head
3.12
combined effective roughness wavelength spectrum
−6
L (λ), dB re 10 [m]
Rtot
wavelength spectrum in one-third octaves of the combined effective wheel-rail roughness including the
contact filter
3.13
combined effective roughness frequency spectrum at speed v
−6
L (f ,v) dB re 10 [m]
Rtot c
frequency spectrum in one-third octaves of the combined effective wheel-rail roughness including the
contact filter
3.14
rolling noise transfer function
L (f ) [dB re 20 Pa/√m]
HpR,tot,nl c
transfer function in one-third octave bands between the sound pressure at a fixed point, 7,5 m, and the
combined effective roughness frequency spectrum, normalized to the axle density N /l
ax
4 Symbols and abbreviations
Symbol Definition Unit
ℓ length of train, vehicle or train part [m]
v train speed [m/s]
5 Instrumentation
Instrumentation for sound pressure measurement should comply with requirements in EN ISO 3095.
The whole measurement chain shall be capable of measuring in the frequency range 25 Hz to 10 kHz.
The signal sample rate for acceleration and sound pressure signals should be sufficient for the
frequency range required. A sample frequency of 25 kHz or 32 kHz is sufficient for a measurement
range up to 10 kHz.
The accelerometer type should be consistent with the expected vibration range and frequency range.
The accelerometer and its measurement chain shall be selected and adjusted to cover the typical
vibration range without signal clipping or overloading. Vertical railhead vibration can reach up to
2
5 000 m/s or more. The dynamic range shall be at least 70 dB.
The accelerometer and its connector shall be water tight especially if moisture can collect during the
measurement.
Optionally a thermometer should be available for measuring the rail temperature.
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6 Installation aspects
The accelerometer should be fixed to the rail by means of a glue
NOTE Magnetic fixing is also possible but may reduce the usable frequency range at higher frequencies.
General guidelines on mechanical mounting of accelerometers should be taken into account as set out
in ISO 5348.
Attention should be given to firm mounting as the resonance frequency of the accelerometer on its
mounting can drop below 10 kHz if not sufficiently stiff.
Overloading and potential loosening or detachment should be avoided and therefore continually
monitored during measurement.
Further information on installation aspects can be found in [10].
7 Measurement positions
For vertical track decay rate and combined roughness measurement a single accelerometer is mounted
under the longitudinal axis of the rail foot or under the side of the rail head (with angle plate, see
Figure 1), next to a sleeper. For lateral decay rate measurement an accelerometer is mounted on the
outer side of the rail head. If the transfer function is measured then a microphone is positioned at 7,5 m
from the track centreline and at 1,2 m above the rail surface directly opposite the accelerometer. The
number of accelerometers may be increased if required, for example to measure the combined
roughness on the other rail or along the track to take potential track variations into account.
a) Cross section of the rail, wheel
b) Example of position a
flange on the left side
Figure 1 — Suitable positions for measuring vertical railhead vibration a and b
Mounting underneath the side of the railhead (b) should include an angle stud to ensure vertical
positioning of the accelerometer. Position c indicates the position for lateral railhead vibration
measurement, if required.
The measurement cross-section shall not be close to unusual rail support conditions, in particular:
1) there shall be no pumping sleeper within a distance smaller than 3 m to the accelerometer;
2) there shall be no missing or damaged rail clip (or fastener of any other type, if necessary) on the
supports directly adjacent to the accelerometer location;
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3) the accelerometer shall not be located within 5 m of a weld;
4) the accelerometer shall not be located within 40 m of an expansion joint.
8 Measured quantities
— Pass-by time t of train or train part;
p
— train speed v;
— vertical railhead acceleration signal a(t);
— sound pressure signal at 7,5 m p(t);
— optionally axle trigger signal z(t) should be recorded during the measurements;
— optionally the rail temperature should be recorded during the measurements.
9 Test procedure
During a whole pass-by of a train the following is recorded:
— vertical railhead vibration (acceleration signal) including the approach and departure of the train;
— sound pressure time signal, if a transfer function is required;
— train speed v;
— train length ℓ, usually determined from known vehicle lengths;
— number of axles N , counted or estimated from the vibration or trigger signal;
ax
— optionally the axle trigger signal z(t).
If the lateral decay rate is to be determined, then also lateral railhead vibration shall be registered.
The vertical track decay rate and, if required, the lateral track decay rate shall be averaged over several
pass-bys of one or more trains, rejecting outlier curves, see Clause 11.
An indicative result (which shall not be considered as a valid result) of the combined roughness and
transfer function can be obtained from a single pass-by.
The measurement uncertainty can be reduced by:
— averaging results over three or more pass-bys of the same train;
— averaging results over two or more train speeds of the same train at least 10 % apart.
Combined roughness can be measured either on a single rail or on both rails depending on the purpose
of the measurement.
10 Data processing
The vertical (and if required lateral) rail acceleration time signal is processed by the method described
in Clause 11 to determine the track decay rate.
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The combined roughness is derived from the vertical decay rate and the equivalent rail vibration level
L over pass-by time t according to the method set out below. The transfer function is derived
aeq,tp p
according to Clause 14 from the equivalent sound pressure level L (f ), the combined roughness
p
eq c
L (f ,v) and the number of axles per unit length N /ℓ.
Rtot c ax
11 Method to determine the track decay rate from rail vibration
11.1 General
The track decay rate (both vertical and lateral) shall be determined by the energy iteration method
described in 11.2. Alternative methods analysing the slope of the time signal are described in Annex C.
The slope methods described in Annex C generally do not eliminate the contributions from other wheels
and can therefore give an underestimation of the decay rate. In addition, where manual interaction is
required during processing, more errors can occur in selecting the location of the defining points. The
energy method takes the contributions of other wheels into account and is less sensitive to manual
inputs as long as the wheel positions are correctly specified. Examples of results from the slope
methods compared to the energy method are given in B.3.
Results shall be averaged over at least 3 pass-bys. The average shall be the arithmetic mean of track
decay rate levels in each one-third octave frequency band. Results differing by more than 5 dB in any
one-third octave frequency band should be rejected, at least in the frequency range concerned.
11.2 Energy iteration method
The energy iteration method to derive the decay rate from the vibration time signal is analogous to the
hammer impact method described in EN 15461, with the difference that the moving wheel provides the
excitation instead of a hammer, and the track has a real load. Also the signal energy is higher than when
using a hammer.
The rail vibration amplitude due to a single wheel is assumed to be described by an exponential
function:
−βx
A x ≈ A 0 e (1)
( ) ( )
Where
x is the position away from the contact point along the rail;
A(x) is the vibration amplitude along the rail;
A(0) is the instantaneous amplitude at the position of the wheel contact point;
β is a decay exponent.
The decay rate D in dB/m can be given as:
z
β
De20 log≈ 8,686β db/m (2)
[ ]
( )
z 10
This decay rate is derived from the evaluation of the ratio of the integrated vibration energy over a
length L , potentially including the whole train pass-by versus the integrated vibration energy over a
2
short length L directly around the wheels. L is taken as the shortest axle distance in the train (or part
1 1
of the train). A common minimum wheel distance is 1,8 m, in which case the analysis length L extends
1
from – 0,9 m to + 0,9 m around each wheel position. The wheel position is determined by a wheel
trigger signal or manually from the acceleration signal. In the latter case, a sufficiently high signal
sampling rate is required to accurately locate the axle positions, see Clause 8.
11
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The integrated squared vibration over a length L around all N wheels is, using Formula (1):
1
L /2
N N 1 βL N
1
2
1−e
22 −β x 2
(3)
A A Ae(0) d 0x A ( )
( )
∑∑nL, n ∑ n
L 1 ∫
1
∑
β
n 1 n 1 n 1
−L /2
1
Similarly, the integrated squared vibration over a long length L incorporating all N wheels is:
2
N −βL N N
2
2
11−e
−β x 22
Ae0 d 0x A≈ A0 (4)
( ) ( ) ( )
( )
∑ n ∑ nn∑
∫
ββ
n 1 nn11
L
2
The approximation at the right hand side in the above formula is valid for sufficiently large L , e.g. a
2
train length or the length of a (group of) vehicle(s).
2 2
The quantities A and A can be determined straightforwardly from measured acceleration signals.
L1 L2
Σ Σ
The transducer time signal is passed through one-third octave band pass filters resulting in a filtered
time signal. Then, for each frequency band, the integrated squared vibration is determined over every
wheel over length L (time T ), see Figure 2a and for the whole pass-by (whole train) for L (time T).
1 x 2
2 2
Using Formulae (3) and (4) the vibration energy ratio R of A and A for each one-third octave
L1 L2
Σ Σ
band frequency f is given as:
c
2
Af
( )
c
L
1
∑ −βL
1
Rf ≈−1 e (5)
( )
c
2
Af
( )
c
L
2
∑
12
=
== =
=
= ==
= ==
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Key
2
Y
acceleration in m/s
X time in s
a) Unfiltered time signal of whole pass-by with total integration time T indicated
Key
2
Y
acceleration in m/s
X time in s
NOTE The integration is applied to the bandpass-filtered time signal for each one-third octave band.
b) Selected part of time signal indicated showing integration time T around each wheel
x
Figure 2 — Time signal of vertical rail vibration
The T interval contains mainly energy from the single wheel, but also contributions from other wheels,
x
particularly the nearby ones. T should be chosen to be slightly shorter than the shortest distance
x
between wheels over the whole train to avoid overlap in energy summation.
From Formula (5) and Formula (2) the vibration decay rate D (TDR) is determined from:
z
13
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8,686
(6)
D f =−−ln 1 Rf
( ) ( ( ))
z cc
L
1
The measured vertical rail acceleration level potentially contains contributions from all wheels. So the
pass-by slopes of the vibration level are also affected by these contributions and need to be adjusted
accordingly. This can be done by the following iteration procedure illustrated in Figure 3:
— A formula for estimating the decay exponent β(f ) at each band frequency is based on Formula (5),
c
similar to Formula (6). The vibration energy ratio R(f ) is determined for the whole train pass-by or
c
selected part of it as in Formula (5), and multiplied by N/w (f ), where N = number of axles and
k c
w (f ) = weighting coefficient.
k c
Rf N
( )
c
ln 1−
wf
( )
k c
β f = − (7)
( )
k c
L
1
A starting estimate for the initial decay exponent β (f ) is obtained with w = 2 N. This initial condition
1 c 1
w = 2 N assumes that half the vibration energy at each wheel is from other wheels.
1
— The subsequent iterations are then calculated until the decay exponent β (f ) is stable to within
i c
0,5 dB, which is often achieved after four iteration steps k = 2 to 5:
NN
−−2β xx
k−1 ji
(8)
wf( ) = e
k c ∑∑
ji11
where
is the distance between the current wheel j and another wheel i
xx−
ji
The weighting coefficient w represents a sum of the squared contributions from all wheels, viewed
k
from each wheel and then summated over all wheels. If the decay exponent is large, the effect of
adjacent wheels is small and w quickly converges to w = N. If the decay is small then w becomes
k k k
larger. Sufficient convergence is often achieved within around four steps.
The effect of the decay rate on the exponential vibration amplitude of each wheel is shown in
Figures 4a, 4b and 4c. The overlap between the amplitude envelope curves of individual wheels
increases significantly for medium or low decay rates.
14
= =
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NOTE ε (f ) is taken at 0,1
c
Figure 3 — Flowchart for the energy iteration procedure
15
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Exponential pass-by envelope curves and summated curve, decay rate = 0,5 dB/m
a) — Simulated envelope curves of vibration of individual wheels and summated amplitude of all
wheels for low decay rates
Exponential pass-by envelope curves and summated curve, decay rate = 4 dB/m
b) Simulated envelope curves of vibration of individual wheels and summated amplitude of all
wheels for medium decay rates
16
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Exponential pass-by envelope curves and summated curve, decay rate = 10 dB/m
c) Simulated envelope curves of vibration of individual wheels and summated amplitude of all
wheels for high decay rates
Key
Y 2
amplitude in m/s
X time in s
Figure 4 — Simulated envelope curves of vibration of individual wheels and summated
amplitude of all wheels
Examples of the iteration procedure are shown in Figures 5a and 5b, with convergence towards a
relatively low decay rate and a high decay rate. The lowest curve is the initial value with four iteration
steps above it.
17
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a) Convergence of a decay rate applying the iteration procedure for a low decay rate
b) Convergence of a decay rate applying the iteration procedure for a higher decay rate
Key
Y track decay rate in dB/m
X frequency in Hz
NOTE The initial curve is the lowest.
Figure 5 — Convergence of a decay rate applying the iteration procedure
12 Method to determine the combined roughness from vertical railhead
vibration
The combined roughness for the whole train or part of a train with length ℓ is determined by the
following formula:
18
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Df
( )
z c
L f ,v L f ,v+10 lg − A f− A f− 40 lg 2p f (9)
( ) ( ) ( ) ( ) ( )
Rtot c aeq,tp c 1 c 2 c c
8,686N
ax
L (f ,v) is the equivalent acceleration spectrum in one-third octave bands measured during the
aeq,tp c
pass-by of train during time t with length ℓ and N axles, running at speed v.
p ax
A is the difference between the spectrum measured at the actual measurement pos
...
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