The modeling of defects in the rotor-trains of turbomachinery – simulation-based diagnostics
The paper is devoted to the problem of the turbomachinery defects’ modeling. The numerical analysis of the proper model of the rotating system and its defect can give the symptoms of the defect. The presented computer software MESWIR is originally invented in the Institute of Fluid-Flow Machinery of...
Saved in:
| Published in: | Проблемы машиностроения |
|---|---|
| Date: | 2013 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інстиут проблем машинобудування ім. А.М. Підгорного НАН України
2013
|
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/99136 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The modeling of defects in the rotor-trains of turbomachinery – simulation-based diagnostics / S. Banaszek // Проблемы машиностроения. — 2013. — Т. 16, № 3. — С. 73-77. — Бібліогр.: 6 назв. — рос. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859625861801574400 |
|---|---|
| author | Banaszek, S. |
| author_facet | Banaszek, S. |
| citation_txt | The modeling of defects in the rotor-trains of turbomachinery – simulation-based diagnostics / S. Banaszek // Проблемы машиностроения. — 2013. — Т. 16, № 3. — С. 73-77. — Бібліогр.: 6 назв. — рос. |
| collection | DSpace DC |
| container_title | Проблемы машиностроения |
| description | The paper is devoted to the problem of the turbomachinery defects’ modeling. The numerical analysis of the proper model of the rotating system and its defect can give the symptoms of the defect. The presented computer software MESWIR is originally invented in the Institute of Fluid-Flow Machinery of PAS (Gdansk, Poland) and it is the effective tool for generation of diagnostic relations. It is based on the non-linear analysis of the rotating systems founded on hydrodynamic slide bearings. It uses a 3D Reynolds equation, FEM and the non-linear equation of motion. The MESWIR software can generate the kinetoststic characteristics of bearings and vibration of the entire system (the shaft and the bearings). It allowes a model-based diagnostics of a several classes of defects. A large power turbo-set is taken for example calculations. A dynamic state of the healthy rotor, in the form of vibration of bearings, is presented as a “base case” which is the reference for further analyzes. A two different defects were modeled: the bearing misalignment and the crack of the shaft. The calculated vibratory state of the bearings shows their symptoms in comparison with the base case.
Рассматривается проблема моделирования дефектов роторных машин. Показано, что с помощью численного анализа модели ротора и его дефекта можно определить признаки этого дефекта. Представлено программное обеспечение MESWIR, которое может генерировать кинетостатические характеристики подшипников и вибрации всей системы (вала и подшипников), что позволяет проводить диагностику дефектов различных классов. В качестве примеров приведены расчёты турбоагрегата большой мощности. Показаны результаты моделирования двух дефектов: смещение подшипника и поперечная трещина вала.
Розглядається проблема моделювання дефектів роторних машин. Показано, що за допомогою чисельного аналізу моделі ротора та його дефекту можна визначити ознаки цього дефекту. Наведено програмне забезпечення MESWIR, що може генерувати кінетостатичні характеристики підшипників і вібрації всієї системи (вала й підшипників), що дозволяє проводити діагностику дефектів різних класів. Як приклади наведені розрахунки турбоагрегату великої потужності. Показано результати моделювання двох дефектів: зсув підшипника й поперечна тріщина вала.
|
| first_indexed | 2025-11-29T11:48:21Z |
| format | Article |
| fulltext |
ВЫСОКИЕ ТЕХНОЛОГИИ В МАШИНОСТРОЕНИИ
ISSN 0131–2928. Пробл. машиностроения, 2013, Т. 16, № 3 73
УДК 539.3.534.1
Slawomir Banaszek, Ph. D.
The Institute of Fluid-Flow Machinery, PASci.
(Poland, Gdansk, e-mail: slawomir.banaszek@imp.gda.pl)
THE MODELING OF DEFECTS IN THE ROTOR-TRAINS OF
TURBOMACHINERY – SIMULATION-BASED DIAGNOSTICS
The problem of the turbomachinery defects modeling is considered. The numerical analysis of
the proper model and its defect can give the symptoms of the defect. The presented computer
software MESWIR can generate the kinetoststic characteristics of bearings and vibration of the
entire system (the shaft and the bearings), that allow carry out model-based diagnostics of a
several classes of defects. A large power turbo-set is taken for example calculations. A two
different defects were modeled: the bearing misalignment and the crack of the shaft.
Рассматривается проблема моделирования дефектов роторных машин. Показано, что
с помощью численного анализа модели ротора и его дефекта можно определить при-
знаки этого дефекта. Представлено программное обеспечение MESWIR, которое мо-
жет генерировать кинетостатические характеристики подшипников и вибрации всей
системы (вала и подшипников), что позволяет проводить диагностику дефектов раз-
личных классов. В качестве примеров приведены расчёты турбоагрегата большой мощ-
ности. Показаны результаты моделирования двух дефектов: смещение подшипника и
поперечная трещина вала.
Розглядається проблема моделювання дефектів роторних машин. Показано, що за до-
помогою чисельного аналізу моделі ротора та його дефекту можна визначити ознаки
цього дефекту. Наведено програмне забезпечення MESWIR, що може генерувати кіне-
тостатичні характеристики підшипників і вібрації всієї системи (вала й підшипників),
що дозволяє проводити діагностику дефектів різних класів. Як приклади наведені розра-
хунки турбоагрегату великої потужності. Показано результати моделювання двох де-
фектів: зсув підшипника й поперечна тріщина вала.
1. The numerical model of rotating shaft founded on slide bearings
Knowledge acquisition for critical machinery diagnostics means defining and describing
symptoms of defects - response of the machine to particular malfunctions. Relations between de-
fects and their symptoms are called “diagnostic relations” (fig. 1).
THEORETICAL
MODEL
DEFECTS
(INPUT DATA FOR
COMPUTATIONS)
SYMPTOMS
(RESULTS)
DIAGNOSTIC
RELATIONS
Fig. 1. The concept of model (computer simulation) based diagnostic relations.
ВЫСОКИЕ ТЕХНОЛОГИИ В МАШИНОСТРОЕНИИ
ISSN 0131–2928. Пробл. машиностроения, 2013, Т. 16, № 3 74
The computer code, originally invented in The Institute of Fluid-Flow Machinery, PASci.
in Gdansk, is called NLDW (first letters of Polish phrase “Non-Linear Rotor Dynamics”). It is the
effect of many years of experience of the research group under a leadership of Prof. Kicinski. The
entire model is described in details and verified in the monograph [1].
From the mathematical point of view, the dynamics of rotating machine is described by the
non-linear differential equations in a matrix form:
)(),(),( tPxxxKxxxDxM =++ &&&&& (1)
where: M – global matrix of inertia; D – global matrix of damping; K – global matrix of stiffness;
xxx &&&,, – generalized vectors of displacements, velocities and accelerations; P – generalized vector
of external excitations; t – time.
Equation (1) is the equation of motion of entire system, composed of a number of DOFs.
The rotor line is being modeled with beam finite elements with 6 DOFs per node. The properties of
the rotor depend on its geometry and material. The fig 2. shows the algorithm of the calculation.
The stiffness and damping of slide bearings are being calculated with the use of non-linear
model which encompasses 3D Reynolds equation, energy equation, conductivity equation, etc.
(fig. 3) The stiffness and damping coefficients can be defined as:
,,,, 21122211
x
W
c
y
W
c
y
W
c
x
W
c
yxyx
∂
∂
=
∂
∂
=
∂
∂
=
∂
∂
=
x
W
d
y
W
d
y
W
d
x
W
d
yxyx
&&&& ∂
∂
=
∂
∂
=
∂
∂
=
∂
∂
= 21122211 ,,, ,
where Wx, Wy are the components of oil film reaction and a dot over the symbol indicates the time
derivative.
The 3D Reynolds equation in the following form is the main equation describing the prop-
erties of bearings [2]:
τ∂
∂
+
∂
∂
−
∂
∂
−=
∂
∂
∂
∂
+
∂
∂
∂
∂ h
x
B
x
h
UA
z
p
z
A
x
p
x
1 ,
where: p – oil pressure, h – oil film thickness, µ – the lubricant viscosity, U1 – linear velocity of
bearing journal, τ – time, A, B – functions of the viscosity and the local film thickness.
The dependence of stiffness and damping coefficients of oil film on the instantaneous posi-
tion and transverse velocity of the vibrating bearing journal is the essence of slide bearing’s non-
linearity. That’s why the stiffness and damping coefficients, instantaneous positions of bearing
t = t + ∆t
ϕ (ωt) = ϕk + ϕd (ωt)
CALCULATION RESULTS
COUPLED NONLINEAR
LATERAL, AXIAL AND
TORSIONAL VIBRATIONS
ROTOR LINE WITH IMPERFECTIONS
(Pi – cracks, Ri – misalignments)
CALCULATIONS OF ROTOR ELEMENTS DEFLECTION AND
DISPLACEMENT
Pi = fp (ϕ) Ri = fr (ϕ)
nonlinear substructure
Check of convergence and accuracy
of calculation
NO YES
JOURNAL BEARINGS AND LABYRINTH SEALS
CALCULATION OF DYNAMIC CHARACTERISTICS
ci,k = fc (ϕ) di,k = fd (ϕ)
nonlinear substructure
FOUNDATIONS WITH SUPPORTS
INTRODUCTION OF DYNAMIC CHARACTERISTICS
Cmm = const Dmm = const
linear substructure
START
ω = const
t = 0
ϕ = ϕk
Fig. 2 The linear versus non-linear modeling. The algorithm of the dynamic’s calculation
ВЫСОКИЕ ТЕХНОЛОГИИ В МАШИНОСТРОЕНИИ
ISSN 0131–2928. Пробл. машиностроения, 2013, Т. 16, № 3 75
journals and instantaneous shape of the shaft line are being calculated iteratively for each time-step,
and for each time step the appropriate matrices are being actualized. Carrying out the calculations
for a number of subsequent revolutions of the shaft gives a result the time history of vibrations.
2. The example simulations of defects
The model described above allows to simulate the following defects:
− imbalance
− rotor misalignment
− load modification
− transverse crack
− support stiffness loss
− displacements of bearings (misalignment, skewness)
− thermo-elastic deformations of the bearing shells
− hydrodynamic instability
− modification of bearing properties (e.g. caused by the altered lubrication conditions).
First, one have to build a so-called “base-case” – the model and the response of the healthy
rotor. It is the reference model for
results of further calculations
when the defects would be simu-
lated.
Let’s take as an example,
the 200 MW turbo-set. Fig. 4 pre-
sents the FE mesh of its model.
The length of the rotor is about 28
m.
The dynamic state of the
object is presented in the form of
so-called “diagnostic cards”,
which show the orbits and spectra
of the bearings’ vibrations. Fol-
lowing figures present the diag-
nostic cards for the example de-
fects. The fig. 5 presents the diag-
Fig. 3. The slide bearing as a mechanical system: the stiffness and damping coefficients,
thermal flux, the algorithm of the slide bearing’s properties’ calculation
Fig. 4. The FE mesh of the turbo-set
ВЫСОКИЕ ТЕХНОЛОГИИ В МАШИНОСТРОЕНИИ
ISSN 0131–2928. Пробл. машиностроения, 2013, Т. 16, № 3 76
nostic card of the base case (healthy rotor) of the turbo-set and the case of the misalignment of the
bearing No.5 [3, 4]. As we can see, such misalignment (0.4 mm into the right) didn’t change the
vibration state of the machine significantly.
The following examples will testify, how the response of the system can depend on the po-
sition and orientation of the defect in the machine. The crack in the shaft will be the example defect
of the machine. The model of the crack in the MESWIR system is built with the use of simple bi-
nary model by Knott [1, 5, 6].Geometry of the element with a crack is presented in Fig. 6.
The stiffness of the element with the crack is modified for the additional flexibilities in-
duced by a crack and calculated from following relation:
Ke = Tt⋅(L + Ld)
-1⋅T,
where: Ke – the stiffness matrix of the element, L – the flexibility matrix of intact element, Ld – the
matrix of additional flexibility induced by the crack, T – the matrix of transformation, Tt – trans-
posed matrix of transformation, –1 – index denoting the matrix inversion.
The way of the crack incorporation into the program allows to model the influence of the
rotor spinning, the kinetostatic deflection of the shaft and the presence of the lateral-axial-torsional
vibrations’ couplings. The fig. 7 presents the two example cases of the crack in the generator: close
to the bearing and in the midspan.
We can observe the rise of sub-harmonic components of 1/3 X, which usually testify the
le/2
le
z
y
x
uy, ϕy
uz,ϕz
1
2
3
4
8 5
6
7
11
9
12
10
ux,ϕx
α
y
x
x dx
a
b
r
h
dα
Fig. 6: A scheme of beam element with a crack
Fig. 5. The diagnostic cards for the 200 MW turbo-set:
left – the base case, right – the misalignment of the bearing No.5
ВЫСОКИЕ ТЕХНОЛОГИИ В МАШИНОСТРОЕНИИ
ISSN 0131–2928. Пробл. машиностроения, 2013, Т. 16, № 3 77
hydrodynamic instability of the bearings. It is also interesting that the influence of the crack on the
absolute vibrations of the bush is stronger than the influence on the relative vibrations (journal-to-
bush).
3. Closing remarks
The paper shown only a very few examples of building the diagnostic relations in a way of
computer simulations. If a proper model of the machine is built, such a relations can be utilized in
the intelligent supervisory system in the power plant (as they were invented). They can also be util-
ized in the design process of the new machinery (units) or at the modernization. They can bring us
an information how can we affect the dynamic state of the machine at its exploitation.
Literature
1. Kiciński J. Rotor Dynamics / J. Kiciński. – Gdansk: IFFM, 2006.
2. Kiciński J. The Theory and Investigations of the Hydrodynamic Slide Bearings / J. Kiciński. – Wrocław:
Ossolineum, 1994.
3. Moczulski W. Knowledge Acquisition for Hybrid Systems of Risk Assessment and Critical Machinery
Disgnosis / W. Moczulski, K. Ciupke. – Radom: ITEE-PIB, 2008.
4. Rybczyński J. Acceptable Dislocation of Bearings in Turbine Set Considering Permissible Vibration and
Load of the Bearings / J. Rybczyński // Key Eng. Materials. – 2005. – Vol. 293–294. – P. 433–440.
5. Knott J. F. Fundamentals of fracture mechanics / J. F. Knott. – London: Butterworths, 1974.
6. Ostachowicz W. M. Coupled torsional and bending vibrations of a rotor with an open crack / W. M. Osta-
chowicz, M. Krawczuk. // Archive Appl. Mech. – 19921. – Vol. 62. – P. 191–201.
Поступила в редакцию
01.08.13
Fig. 7. Diagnostic cards for the example cases of the crack in the rotor:
left – crack close to the bearing No. 6, right – crack in the midspan
|
| id | nasplib_isofts_kiev_ua-123456789-99136 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0131-2928 |
| language | English |
| last_indexed | 2025-11-29T11:48:21Z |
| publishDate | 2013 |
| publisher | Інстиут проблем машинобудування ім. А.М. Підгорного НАН України |
| record_format | dspace |
| spelling | Banaszek, S. 2016-04-23T10:59:59Z 2016-04-23T10:59:59Z 2013 The modeling of defects in the rotor-trains of turbomachinery – simulation-based diagnostics / S. Banaszek // Проблемы машиностроения. — 2013. — Т. 16, № 3. — С. 73-77. — Бібліогр.: 6 назв. — рос. 0131-2928 https://nasplib.isofts.kiev.ua/handle/123456789/99136 539.3.534.1 The paper is devoted to the problem of the turbomachinery defects’ modeling. The numerical analysis of the proper model of the rotating system and its defect can give the symptoms of the defect. The presented computer software MESWIR is originally invented in the Institute of Fluid-Flow Machinery of PAS (Gdansk, Poland) and it is the effective tool for generation of diagnostic relations. It is based on the non-linear analysis of the rotating systems founded on hydrodynamic slide bearings. It uses a 3D Reynolds equation, FEM and the non-linear equation of motion. The MESWIR software can generate the kinetoststic characteristics of bearings and vibration of the entire system (the shaft and the bearings). It allowes a model-based diagnostics of a several classes of defects. A large power turbo-set is taken for example calculations. A dynamic state of the healthy rotor, in the form of vibration of bearings, is presented as a “base case” which is the reference for further analyzes. A two different defects were modeled: the bearing misalignment and the crack of the shaft. The calculated vibratory state of the bearings shows their symptoms in comparison with the base case. Рассматривается проблема моделирования дефектов роторных машин. Показано, что с помощью численного анализа модели ротора и его дефекта можно определить признаки этого дефекта. Представлено программное обеспечение MESWIR, которое может генерировать кинетостатические характеристики подшипников и вибрации всей системы (вала и подшипников), что позволяет проводить диагностику дефектов различных классов. В качестве примеров приведены расчёты турбоагрегата большой мощности. Показаны результаты моделирования двух дефектов: смещение подшипника и поперечная трещина вала. Розглядається проблема моделювання дефектів роторних машин. Показано, що за допомогою чисельного аналізу моделі ротора та його дефекту можна визначити ознаки цього дефекту. Наведено програмне забезпечення MESWIR, що може генерувати кінетостатичні характеристики підшипників і вібрації всієї системи (вала й підшипників), що дозволяє проводити діагностику дефектів різних класів. Як приклади наведені розрахунки турбоагрегату великої потужності. Показано результати моделювання двох дефектів: зсув підшипника й поперечна тріщина вала. en Інстиут проблем машинобудування ім. А.М. Підгорного НАН України Проблемы машиностроения Высокие технологии в машиностроении The modeling of defects in the rotor-trains of turbomachinery – simulation-based diagnostics Article published earlier |
| spellingShingle | The modeling of defects in the rotor-trains of turbomachinery – simulation-based diagnostics Banaszek, S. Высокие технологии в машиностроении |
| title | The modeling of defects in the rotor-trains of turbomachinery – simulation-based diagnostics |
| title_full | The modeling of defects in the rotor-trains of turbomachinery – simulation-based diagnostics |
| title_fullStr | The modeling of defects in the rotor-trains of turbomachinery – simulation-based diagnostics |
| title_full_unstemmed | The modeling of defects in the rotor-trains of turbomachinery – simulation-based diagnostics |
| title_short | The modeling of defects in the rotor-trains of turbomachinery – simulation-based diagnostics |
| title_sort | modeling of defects in the rotor-trains of turbomachinery – simulation-based diagnostics |
| topic | Высокие технологии в машиностроении |
| topic_facet | Высокие технологии в машиностроении |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/99136 |
| work_keys_str_mv | AT banaszeks themodelingofdefectsintherotortrainsofturbomachinerysimulationbaseddiagnostics AT banaszeks modelingofdefectsintherotortrainsofturbomachinerysimulationbaseddiagnostics |