Weryfikacja opracowanych metod Autor: Urbanek J., Jabłoński A., Barszcz T.

Weryfikacja opracowanych metod
Autor: Urbanek J., Jabłoński A., Barszcz T.
Sprawozdanie z wykonania zadania nr 10 projektu
badawczego IP2012 061572 pt. „Opracowanie
nowatorskich
narzędzi
analizy
sygnałów
wibroakustycznych generowanych przez maszyny
wirnikowe pracujące w ekstremalnie zmiennych
warunkach operacyjnych”
W trakcie realizacji zadania 10, zespół badawczy, na bazie zebranych sygnałów
wibroakustycznych, zweryfikował opracowane metody oraz zaprezentował ich
przykładowe wykorzystanie. Najbardziej pracochłonną czynnością w ramach
realizacji zadania było wyodrębnienie danych o pożądanych cechach spośród
danych zarejestrowanych w poprzednim zadaniu badawczym. Wyniki
zastosowania opracowanych narzędzi przedstawione w raporcie uznajemy za
bardzo atrakcyjne w kontekście oczekiwanych rezultatów.
2014-6-30
Urbanek J., Jabłoński A., Barszcz T
opracowanych metod
ssswedfsdfUrbanek J., Jabłoński A., Barszcz T., Weryfikacja
0
IP2012 061572
Opracowanie nowatorskich narzędzi analizy sygnałów wibroakustycznych
generowanych przez maszyny wirnikowe pracujące w ekstremalnie zmiennych
warunkach operacyjnych
Outline
1
2
Introduction .......................................................................................................................................... 2
Angular temporal components ............................................................................................................. 3
2.1
Theoretical background ................................................................................................................ 3
2.2
3
Blind separation .................................................................................................................................... 7
3.1
Theoretical background ................................................................................................................ 7
3.2
4
5
6
7
8
Application .................................................................................................................................... 4
Application .................................................................................................................................... 8
Conclusions ......................................................................................................................................... 12
APPENDIX A – Additional verification ................................................................................................. 13
APPENDIX B – Additional verification ................................................................................................. 17
APPENDIX C – Additional verification ................................................................................................. 20
APPENDIX D – Additional verification ................................................................................................. 24
1
Urbanek J., Jabłoński A., Barszcz T., Weryfikacja opracowanych metod
IP2012 061572
Opracowanie nowatorskich narzędzi analizy sygnałów wibroakustycznych
generowanych przez maszyny wirnikowe pracujące w ekstremalnie zmiennych
warunkach operacyjnych
1 Introduction
This report consists of the validation of the proposed methods within the Research
project IP2012 061572. The goal was to verify the utility of the proposed approach on
real-life signal influenced by extremely changing operation regime of speed and load.
The validation is performed on two industrial objects, namely wind turbine and
printing machine. The description of these objects is included in this document. The
methods that are to be verified were described in details in reports No. 7 and 8, and
are as follows:


Identification of spectral-components of angular temporal signal in highly
changing operation conditions,
Deterministic-random separation of such signals as an exemplary application of
the proposed methodology
Both methods are based on the new class of non-stationary signals – general angular
temporal ones, that was introduced in Report No. 6.
Each example is preceded by short description of each of the methods. The finally,
the report is concluded.
2
Urbanek J., Jabłoński A., Barszcz T., Weryfikacja opracowanych metod
IP2012 061572
Opracowanie nowatorskich narzędzi analizy sygnałów wibroakustycznych
generowanych przez maszyny wirnikowe pracujące w ekstremalnie zmiennych
warunkach operacyjnych
2 Angular temporal components
2.1 Theoretical background
The concept of the angular-temporal spectrum (ATS) was initially described in Report
No. 7. The introduced tool returns the distribution of signals components in bifrequency domain of and . The stands for is the frequency related to anglefixed events (preferably expressed in orders, so related to single rotation of the
element), while denotes events occurring with time-fixed instances (expressed in
Hz). Proposed ATS is expressed as follows:
(
where
(
(
)
(
)
)|
(
∫
(1)
)
(2)
) is an angular-temporal normalized signal x(t) and is expressed by:
(
For
(
) denotes angle-synchronized short-time Fourier transform of signal
) given by:
(
where
∫ |
)
(
(
))
( )
( )
( )
(3)
( ) being a windowing function with non-zero values between
⁄ and ⁄
and ( ) denoting angle-fixed time increments used for positioning of the window.
Additionally, we define ( ) as a local angular-temporal mean value of signal x(t)
as:
(
)
∫
(
)
(
⁄
)
⁄
( )
(4)
3
Urbanek J., Jabłoński A., Barszcz T., Weryfikacja opracowanych metod
IP2012 061572
Opracowanie nowatorskich narzędzi analizy sygnałów wibroakustycznych
generowanych przez maszyny wirnikowe pracujące w ekstremalnie zmiennych
warunkach operacyjnych
( ) beinglocalized angular-temporal standard deviation of x(t) defined as:
and
(
(
)
)
⁄
√ ∫
( ( )
(
)
( ( ))
(5)
⁄
The purpose for transformation of signal x(t) into its angular-temporal normalized
version (
) is to remove amplitude fluctuations between different time
periods T and as a result obtain standardized distributions for each instances of
angle-synchronized short-time Fourier transform. Amplitudes of (
) and
|
(
)|
magnitudes of
are now expressed by the units of local standard
) preserves
deviation (
). It can be seen that transformed signal (
( ) has a
both angular and temporal character of analyzed signal as time window
fixed time length yet is being shifted with equal angular instances. Therefore, Fourier
transform over will produce angle-synchronized short time Fourier transform (eq.2)
that can be interpreted as a frequency-shifting filterbank for which each frequency
component is observed in angle-fixed intervals. It was shown in Chapters 4 and 5 of
Report No 7, on both simulated and experimentally derived signals.
2.2 Application
The proposed method has been applied to signals described in the Report No. 7.
The main time-consuming preprocessing activity within the current task was to select
signals characterized by expected high fluctuations. Exemplary recorded signal is
presented in Fig 1 . The presented case is difficult, since we observe severe variation
of rotational speed and load that influence amplitude and phase of the vibration
signal.
4
Urbanek J., Jabłoński A., Barszcz T., Weryfikacja opracowanych metod
IP2012 061572
Opracowanie nowatorskich narzędzi analizy sygnałów wibroakustycznych
generowanych przez maszyny wirnikowe pracujące w ekstremalnie zmiennych
warunkach operacyjnych
.
Fig 1 Recorded vibration signal on driven end bearing
The angular-temporal spectrum calculated for the exemplary signal is presented in the Fig 2
as a colormap. Vertical axis represents the frequency of angle-fixed cycles (Orders) of the
analyzed signal while horizontal axis represent frequency of time-fixed components.
Therefore, horizontal lines marked with red arrow in the Fig 2 correspond to phenomena
occurring cyclically once every half of revolution (order No. 1); yet, exciting time-fixed
components within the frequency range between 5 kHz and 6 kHz (like 0.41 order FTF
pointed with orange arrow and 3.66 order BPFO pointed with yellow arrow).
Additionally, higher harmonics of angle-fixed components due to the overall shape of the
each pulse. The zooms are used to magnify particular phenomena appearing in the signal.
For detailed characteristics of the turbine see Report No.7, section 3.2.
5
Urbanek J., Jabłoński A., Barszcz T., Weryfikacja opracowanych metod
IP2012 061572
Opracowanie nowatorskich narzędzi analizy sygnałów wibroakustycznych
generowanych przez maszyny wirnikowe pracujące w ekstremalnie zmiennych
warunkach operacyjnych
Fig 2 Angular-temporal spectrum recorded vibration signal on driven end bearing (top) with zooms: between
0-1 [ords] (middle) and 3-4 [ords]
The magnitude of the resulting angular temporal spectrum is expressed in the units of the
local standard deviation (
) due to applied amplitude normalization and is to be
interpreted relatively (to the reference data).
More examples of the implementation of the angular-temporal spectrum to real data is
illustrated in appendixes.
6
Urbanek J., Jabłoński A., Barszcz T., Weryfikacja opracowanych metod
IP2012 061572
Opracowanie nowatorskich narzędzi analizy sygnałów wibroakustycznych
generowanych przez maszyny wirnikowe pracujące w ekstremalnie zmiennych
warunkach operacyjnych
3 Blind separation
3.1 Theoretical background
A method for blind separation of vibration signals into component related directly to
shaft rotation and component containing excitation of structural resonances and
noise was described in details in Chapter 2 of Report No. 8. When considering
vibration signals generated by machinery operating under varying load and speed, it
is inherently prohibited to consider separation into deterministic and random
components, as all of signal components are random in nature as both: frequency
and amplitude of the signal depend on operational parameters. However, following
well established philosophy of discrete-random separation (DRS) separation, the
concept of extracting components generated during the rotation of unbalanced parts
of kinematic chain (e.g. shafts) from the rest of the signal, that is mainly excitation of
local resonances (e.g. by faulty rolling element bearings) and random noise unrelated
to machine operation is illustrated.
When vibration signal is generated by machinery under constant speed and load we
assume components related to unbalanced elements to be time deterministic as they
can be characterized by certain frequency related to rotational speed and amplitude
that is also constant in time. For varying operational condition assumption of time
determinism is no longer valid; however, we can assume that frequency of observed
machine-related components is constant when observed in angle-fixed time intervals
(presented in angular domain). Additionally, we can assume that instantaneous
amplitude of the signal is characterized by smooth variations related to varying speed
and load. Therefore, we can assume that signals generated by unbalanced element of
rotating machinery operating under varying operational conditions fall into class of
generalized angular deterministic signals.
Signal x(t) is called a “generally angular deterministic” for given phase increments
7
Urbanek J., Jabłoński A., Barszcz T., Weryfikacja opracowanych metod
IP2012 061572
Opracowanie nowatorskich narzędzi analizy sygnałów wibroakustycznych
generowanych przez maszyny wirnikowe pracujące w ekstremalnie zmiennych
warunkach operacyjnych
with given angular period
when its’ transformation to
( ) meets the following
criterion:
( )
Where
(
)
(6)
( ) is normalized (z-scored) version of signal x( (t))= ( ) for
and
the angular period :
( )
( )
where
( )
( )
( ) is localized angular standard deviation of
( )
and
( )
√ ∫
( ( )
( ) for the period :
( ( )))
(8)
( ) being a localized angular mean of x(t) for the angular period
( )
∫
( )
(9)
Therefore, signal x(t) can be transformed into ( ) by changing the domain
from temporal to angular and normalizing the instantaneous amplitude as presented
in eq.2. Such transformation will produce the signal that is angularly deterministic, so
DRS techniques can now be applied in the same way as for signals generated under
constant operational conditions.
3.2 Application
The proposed reasoning is presented using data collected with vibration-based
CMS installed on the gearbox of the commercially used printing machine, which is a
supplementary data collection with respect to data recorded within realization of the
task No. 9. The drive of this machine consists of 28-stage gearbox (2 bevel and 26
parallel) supported using 84 rolling element bearings. In the proposed design of CMS
three accelerometers, namely LZ_1, PZ_2 and PX_3 are mounted as presented in
Fig 3.
8
Urbanek J., Jabłoński A., Barszcz T., Weryfikacja opracowanych metod
IP2012 061572
Opracowanie nowatorskich narzędzi analizy sygnałów wibroakustycznych
generowanych przez maszyny wirnikowe pracujące w ekstremalnie zmiennych
warunkach operacyjnych
z26
z25
z20
z18
z22
z21
z19
z17
z28
z23
z24
z12
z16
z11
z10
z9
z13
z15
z27
z8
z7
PZ_2
z6
z14
z5
PX_3
z4
LZ_1
z3
z2
z1
KF
M
1:1
Fig 3 Scheme of the printing machine’s gearbox with marked accelerometer’s position and
direction
The rated speed for this machine is equal to 2000 [RPM]. During the measurement
the increase of speed from 275 to 415 [RPM] (Fig 4 - bottom) was observed and
recorded using accelerometer PZ_2. It was faced in accordance to the axis of rotation
of parallel stages of the gearbox. The sensor with the frequency range of 25[kHz] and
sensitivity equal to 100 [mV/g] was used. Together with the vibration signal, the
rotational speed of the driving shaft was recorded. The time duration for acquired
vibration signal was 10 [s].
Instantaneous load was not recorded during this measurement. Therefore its profile
remains unknown. However, under the assumption that changes of rotational speed
and load are correlated, we have selected cut-off frequency for envelope calculation
simply as
(| ̇ |).
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Urbanek J., Jabłoński A., Barszcz T., Weryfikacja opracowanych metod