Acta Polytechnica CTU Proceedings


doi:10.14311/APP.2018.20.0005
Acta Polytechnica CTU Proceedings 20:5–9, 2018 © Czech Technical University in Prague, 2018

available online at http://ojs.cvut.cz/ojs/index.php/app

BTT & RFLB - THE OPTIMUM SET FOR STEAM TURBINE
BLADES MONITORING

Miroslav Balda

Research and Testing Institute, Tylova 46, 30100 Plzeň, Czech Republic
correspondence: balda@vzuplzen.cz

Abstract. BTT, Blade Tip Timing system, is a commercially available system generating files of
precise times of blade tips when passing sensors attached in a machine stator. RFLB, Residual Fatigue
Life of Blades, is a postprocessor of those files evaluating estimates of fatigue lives of all blades fitted
to the wheel. The set reduces a danger of unexpected blade failures.

Keywords: BTT, RFLB, fatigue, blades, maintenance.

1. Introduction
Fatigue of materials is a very complicated phe-
nomenon, which influences the quality of structures
seriously. The bigger the structure is, the more impor-
tant are the consequences of possible fatigue damages.
The typical structures, in which any fatigue cracks
should not occur, are turbomachines. Any unexpected
breakdown caused by the fatigue generates extreme
losses of energy production. This is the reason why
manufacturers of turbomachinery devote enormous
care to a design of fatigue-save parts of a machine
and to material testing. To common tests belong also
fatigue tests of most exposed parts of the machine,
blades of a turbine.

The blades are working at rather complicated oper-
ational conditions like high radial stress from centrifu-
gal forces and extreme velocity of wet steam turbulent
flow exciting them to vibrations accompanied by al-
ternating stresses. Dynamic stresses at critical points
of blades may initiate material damage, which results
in a crack propagation when cumulated. Since this
phenomenon may end in a total breakdown of a blade
followed by an unplanned shutdown of the machine,
producers of turbomachines arm their products with
systems, which are able to monitor blades at their
critical places.

2. Blade Tip Timing – BTT
The current monitoring systems used for that purpose
are denoted as BTT – Blade Tip Timing systems
because they are based on time measurement of blade
tips when passing sensors (see Fig. 1).

A BTT system consists of a set of sensors placed at
the stator of the turbine above tips of blades of the
selected wheel. Outputs of ns sensors are connected
to control inputs of their own counters of precise clock
pulses. As soon as a tip of the vibrating blade passes
a sensor, the sensor generates a pulse which initiates
a transfer of the current content of the counter to its
memory. There is still one sensor and the counter and
its memory which counts pulses generated by a datum

fixed at a shaft. At the end of the measurement,
the contents of all memories are sent to ns + 1 files.
The measured data, series of times, are processed off-
line into natural frequencies of blades and histograms
of position magnitudes and other parameters of the
measurement.

3. Residual Fatigue Life of
Blades – RFLB

An application of a system RFLB has in principle
three main stages:
• measurement of material properties,
• modal analysis of the blade to be measured,
• long time monitoring in situ in a power plant.
All stages are very important for the final statement
about the residual fatigue life of all measured blades.

3.1. Material properties
There are two material tests necessary for RFLB sys-
tem, the tensile test, and the high cycle fatigue test.
The result of the tensile test is shown in the form of
the diagram made by a testing device in Fig.2. It
may be accepted as a limiting case of the fatigue test
during which the specimen has been broken at the
half of the loading cycle.
The high cycle fatigue (HCF) test is a different

one. Usually, a set of 8 - 10 specimens are loaded
by harmonic processes of different amplitudes σam
up to breaks after Nam loading cycles [1]. The result
of the test is a regression line to couples (Nam,σam),
called SN curve [2], which becomes a straight line
when drawn in a diagram with axes log Nam, log σam
(see Fig. 3).

3.2. Modal analysis
Good information on the blade as an object of mon-
itoring is very important. The detailed numerical
analysis of the blade fitted in the wheel is made by a
FEM program. Results of the analysis should contain
the solution of the eigenvalue problem, e.g. natural

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http://dx.doi.org/10.14311/APP.2018.20.0005
http://ojs.cvut.cz/ojs/index.php/app


Miroslav Balda Acta Polytechnica CTU Proceedings

Figure 1. BTT system with ns probes (sensors).

frequencies and corresponding natural modes for a
set of nodal diameter numbers. Moreover, it is also
important to have frequency response functions of cir-
cumferential deflection of a blade tip to stress tensors
at critical places of the blade.

3.3. Monitoring by the RFLB
The software system RFLB complements the system
BTT by estimating fatigue lives of blades. It exploits
the information contained in the BTT output files for
the purpose totally.

Such a complicated system, as the RFLB is, should
be split into modules fulfilling special tasks. The
interactive MATLAB program RFLB is built as a
flexible one as possible with respect to events occurring
in power plants. The system contains about 30 scripts
and functions.
The control module – RFLB organizes, in a

cooperation with the operator, the function of the sys-
tem RFLB. At first, the operator informs the module
where to find the parameters of the blade, material,
and results from the modal analysis. The operator
may also interrupt the normal automatic run of the
RFLB when needed. There are many reasons for do-
ing so. A typical situation occurs when the operator
wants to look into the protocol or wants to plot the
result of some past measurement. Then, the program
breaks the normal sequence of commands, fulfills the
requirement of the operator, and continues just in
the place, where has been interrupted. This behav-
ior ensures the control module of the program. The
module RFLB initiates the run of the RFLB with all

new blades. It also enables to change some blades
without a loss of continuity in the cumulation of dam-
ages of other blades. The same holds after a break in
processing.
The module BTT is a driver for a continuous

run of the system. It distributes tasks to specialized
functions. The first of them is function getdata which
reads the files generated by systems BTT. There are
served files from two BTT systems, Starman and
Hood. The function getdata is the only one which
should be rebuilt if another BTT system was applied
for measurements. The reason for it is that the output
files of systems BTT are not standardized.
The main role of function getdata is creating a

vector composed of key-phasor times of once per rev-
olution pulses from the red probe in Figure 1 and a
hyper-matrix (3D array) of times from all sensors and
blade tips of the wheel. One vector of the 3D array
is seen from Figure 4. Since the measured data are
in the standard form, so the rest of the RFLB system
does not need any change. At the end of the func-
tion getdata, all-time series are Fourier transformed
into aliased Fourier spectra by fast Nieslony’s func-
tion rainflow [3]. The resulting Fourier spectra are
aliased in frequency due to the deep under-sampling
of blade tip signals.
Frequency aliasing has to be eliminated by a spec-

trum reconstruction. This is implemented by function
reconstr. It is well known that under-sampled signals
defy reconstruction by normal way. Fortunately, there
is additional information at disposal. That is a set
of natural frequencies obtained during the numerical

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vol. 20/2018 BTT & RFLB - The Optimum Set for Steam Turbine Blades Monitoring

Figure 2. Material T671 - tensile test.

0.5 1 10 100 1000 10000 100000 1e+06 1e+07

400

500

600

700

800

900

1000

1100

1200

1300

1400

1500

1600
1700

Number of cycles N
a

S
tr

e
s

s
 a

m
p

li
tu

d
e

 σ
a

Material T671

σ
m

=0 − Woehler

σ
m

1

 = 450 MPa

σ
m

2

 = 600 MPa

R
m

R
02

σ’
a0

σ’
a450

σ’
a600

σ
c

Figure 3. T671 SN curves, σm = 0, 450, and 600 MPa.

Figure 4. Vector of measured and reconstructed samples of one blade tip deflections.

7



Miroslav Balda Acta Polytechnica CTU Proceedings

Figure 5. Aliased DFT of all blades in the wheel.

modal analysis. The natural frequencies recalculated
to the aliased ones serve for identification of eval-
uated peaks in DFT. The frequency bands around
DFT peaks coinciding with aliased natural frequen-
cies are moved on places corresponding real natural
frequencies of the reconstructed spectra.
In Figure 5, there are positions of aliased natural

frequencies shown in upper parts of the diagram by
red ticks and order numbers. The upper frequency
of the reconstructed Fourier spectra is chosen by an
order higher than the speed frequency, which is the
sampling frequency fs, say, fS = 25 fs. The rest of
the aliased spectra is spread within the reconstructed
spectra under user wishes. The last stage of the re-
construction is the inverse Fourier transform of the
reconstructed spectra, what returns reconstructed sig-
nals in much higher resolution as seen in Figure 4.
If the moving of the spectrum bands was done with
care, the reconstruction is successful, what is seen
from Figure 4.

As soon as the reconstructed signals are ready, rel-
ative damages in critical places of the blades can be
estimated by function damage. Unfortunately, it is
the most time-consuming operation, because of each
blade signal has to undergo rain-flow analysis, what is
a decomposition of each signal into full cycles, followed
by a recalculation of time data into circumferential
deviations and then to stress state in critical places
on blades.

For the purpose, the elements of the stress tensors
obtained during modal analysis, are used for evaluat-
ing an effective (damaging) stress σd of kth loading
cycle in the following form

σ̃d,k,n = ∆tk ×
[
σ̃2x + σ̃

2
y + σ̃

2
z (1)

− 2µ (σ̃xσ̃y + σ̃yσ̃z + σ̃zσ̃x)

+ k2c (τ̃
2
xy + τ̃

2
yz + τ̃

2
zx)
]1/2

n
,

Figure 6. Relative damages of all blades.

where kc =σc/τc ≈
√

2(1 + µ) and symbols with tilde
are dynamic components of a stress tensor in the crit-
ical point corresponding to nth mode of vibration.
Time-series of damaging stress course are decomposed
into a set of full cycles and half cycles by a rain-
flow procedure getting thus stress amplitudes σak and
mean stresses σmk needed for an estimation of elemen-
tary damage dk in kth cycle by a fatigue hypothesis.
The most common one is the hypothesis of Pålmgren-
Miner [4, 5] respecting an influence of σm [6]:

dk,PM = 1/Nam = 2
(

sa
s′a0 − sm

)w
, (2)

where fictive amplitude s′am replaces either σ′am or

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vol. 20/2018 BTT & RFLB - The Optimum Set for Steam Turbine Blades Monitoring

τ′am. It is evident from Figure 3 that its values are
given by the positions of intersections of a particular
SN curve with the line Nam = 0.5. For all family of
SN curves holds that s′am = s′a0 − sm. This property
of SN curves of steels saves time and money because
it canceled the necessity of making expensive tests of
prestressed materials.
The system RFLB cumulates elementary relative

damages defined by equation (2), so it is able to yield
information on the total relative damage D ≤ 1 of
any blade of the wheel to the operator at any moment.
In case, the damage D reached a chosen amount, the
system issues an alarm message. Residual fatigue
life, defined as L = 1 − D, says how much time still
remains to break down.

4. Conclusions
The article has shown the advantages gained by a com-
bination of a hardware system BTT with the software
system RFLB. Installation of the set of both items
in power plants for monitoring blades in potentially
uncertain turbine stages may be very effective for the
reliability of a machine because it diminishes a danger
of unexpected breakdowns and enables to plan times
of maintenance and a number of spare blades in store.

List of symbols
dam relative damage of a cycle with σa and σm
D total relative damage
fn natural frequency [Hz]
fs sampling frequency [Hz]
fS sampling frequency of reconstructed spectra [Hz]
fN Nyquist frequency = fs/2 [Hz]
L relative residual fatigue life
Nam number of cycles to failure under σa and σm
Rm material strength [MPa]

Rp yield limit [MPa]
s either σ or τ [MPa]
t time [s]
Ts sampling period = 1/fs [s]
w exponent of Woehler’s curve
µ Poisson’s ratio
σ stress in tension [MPa]
σa amplitude of a stress cycle [MPa]
σm mean stress of a stress cycle [MPa]
σam amplitude of a cycle by mean stress [MPa]
σ′am intersection point of SN curve with N = 0.5 [MPa]
τ stress in torsion [Mpa]

Acknowledgements
The author appreciates a kind support of his research
from the Technological Agency of The Czech Republic via
the Center of Competence No. TE01020068, Center of
research and experimental development of reliable energy
production

References
[1] J. Chvojan: A test of material T671 high cycle fatigue

(In Czech), VZÚ Plzeň, Testing record No. 846/2003
[2] ČSN 42 0368: Fatigue testing of metals. Statistical
evaluation of fatigue test results of metals (In Czech),
Czech Normalizing Institute, Prague, 1973.

[3] A. Nieslony: Rainflow Counting Algorithm.
MathWorks, File Exchange, file No. 3026, 2003

[4] A. Pålmgren: Die Lebensdauer von Kugellagern, VDI
Zeitschrift (68), pp. 339-341, 1924.

[5] M.A. Miner: Cumulative damage in fatigue, Trans.
ASME, Journal of Applied Mechanics, (12) pp.
A159-A164, 1945.

[6] M. Balda: Fatigue life assessment of prestressed
material, Engineering Mechanics, C. Fischer & J.
Náprstek eds., ITAM CAS CZ, Proc. Conf. Engineering
Mechanics, Svratka, May 14-17, 2018

9


	Acta Polytechnica CTU Proceedings 20:5–9, 2019
	1 Introduction
	2 Blade Tip Timing – BTT
	3 Residual Fatigue Life of Blades – RFLB
	3.1 Material properties
	3.2 Modal analysis
	3.3 Monitoring by the RFLB

	4 Conclusions
	List of symbols
	Acknowledgements
	References