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Poznan University of Technology
FACULTY OF TRANSPORT ENGINEERING
The vibrodiagnostics of the metro tunnel escalator drive gearbox
Vitalii BoikoStudent of Double Master`s Degree Program
Promotor:
prof., DrTechSc, Yuriy Danylchenko
Reviewer:
dr hab. inż. Roman Barczewski
Poznań 2019
CONTENTS
INTRODUCTION...........................................................................................................................................5
1. THE STUDY OF THE INFORMATION BOUND WITH THESIS.......................................................................7
1.1. The analysis of the typical faults of gearboxes performance............................................................7
1.2. The gearbox elements condition monitoring vibrodiagnostics methods........................................11
1.3. Methods of the vibration signal processing....................................................................................22
2. JUSTIFICATION OF THE CHOSEN DIAGNOSTICS METHOD......................................................................28
2.1. Measuring scheme.........................................................................................................................28
2.2 Measuring equipment and software...............................................................................................30
2.3. Signal processing sequence............................................................................................................33
2.4. Post-processing of the obtained data.............................................................................................36
3. EXPERIMENTAL RESEARCH OF DYNAMICS OF THE ESCALATOR DRIVE GEARBOX..................................40
3.1. Research and analysis of the vibration state of a good performance gearbox...............................40
3.2. Development of the method of identifying faults of gearbox components....................................55
4. IMPLEMENTATION OF THE RESULTS OF THE STUDY..............................................................................65
4.1. The way of implementation............................................................................................................65
4.2. The idea of the project...................................................................................................................65
4.2. Technological audit.........................................................................................................................67
4.3 Analysis of market opportunities for project launch.......................................................................67
4.4. Development of market strategy of the project.............................................................................74
4.5 Development of the marketing program of the start-up project.....................................................76
5. CONCLUSIONS.......................................................................................................................................79
6. BIBLIOGRAPHY.......................................................................................................................................81
2
STRESZCZENIE
Wibrodiagnostyka przekładni napędowej tunelowych schodów ruchomych metra
Praca magisterska dotyczy diagnozowania stanu technicznego przekładni
napędowej schodów ruchomych metra. Serwis schodów ruchomych metra w
Kijowie wyznaczył zadanie techniczne polegające na utrzymaniu sprawności
przekładni napędowej schodów ruchomych przy minimalnych kosztach. Aby
spełnić ten warunek, wybrano stosunkowo tanią i dokładną metodę diagnozowania
stanu przekładni napędowej opartą na pomiarach i analizie drgań
(wibrodiagnostykę). Badania realizowane w ramach niniejszej pracy dotyczyły
procesów akustycznych, drganiowych i termalnych związanych z powstawaniem
uszkodzeń elementów przekładni. Przedmiotem badań było określenie symptomów
diagnostycznych bazujących na wynikach parametryzacji drgań generowanych
przez przekładnię, które umożliwiają detekcję uszkodzeń jej elementów.
Celem pracy było opracowanie skutecznej metody identyfikacji uszkodzeń
elementów przekładni napędowej schodów ruchomych, wykorzystującej sygnały
drganiowe. W ramach pracy wykonano następujące zadania: analiza literaturowa
związana z tematem pracy, uzasadnienie wykorzystania wybranych metod
przetwarzania sygnału, badania eksperymentalne i analizy uzyskanych danych,
wdrożenie zaproponowanej metodyki jako projektu startowego. Na podstawie
wyników badań opracowano metodę diagnostyki drganiowej przekładni napędowej
tunelowych schodów ruchomych metra.
Słowa kluczowe: dynamika, wibrodiagnostyka, przekładnia napędowa, ruchome
schody.
3
ABSTRACT
The vibrodiagnostics of the metro tunnel escalator drive gearbox
This master thesis concerns condition monitoring of the gearbox of the
metro tunnel escalator. Kyiv metro escalator service set a technical task of
maintaining the technical efficiency of the escalator drive gearbox with minimal
costs. In order to satisfy this condition a relatively cheap and accurate method of
condition monitoring of the gearbox was chosen. The method is based on
measurements and analysis of vibrations signals (vibrodiagnostics). The research
carried out in this work concerned acoustic, vibration and thermal processes related
to the formation of defects of the escalator gearbox components. The subject of the
study was the determination of diagnostic symptoms, based on parameterization of
vibration signals generated by gearbox, that allow us to detect faults of gearbox
elements. The purpose of the work was to develop an effective method of
identifying defects of components of a gear box using vibration signals. The
following tasks were performed while completing the work: literature analysis
related to the topic of work, justification of the use of selected signal processing
methods, experimental research and analysis of the obtained data, implementation
of the proposed methodology as a startup project. Based on the results of the
research, a method for vibrodiagnostics of the gearbox of the metro tunnel
escalator drive gearbox has been developed.
Key words: dynamics, vibration diagnostics, gearbox, tunnel escalator.
4
INTRODUCTION
Traditional methods of defectoscopy of reducers for lifting and transporting
machines, which do not belong to non-destructive methods of controlling the
condition of the drive, require time and partial disassembly of the drive elements.
Such methods reduce the efficiency of the drive and increase the cost of its
maintenance. In addition, there is a problem of determination of the reason of the
defect and the place of its formation. The same problem is shared by the
diagnostics of the gearboxes of the metro tunnel escalator drives. In addition, the
need to provide the necessary passenger capacity per hour does not allow to stop
the machine often. Vibrodiagnostics is a relatively cheap, convenient and highly
precise method for condition monitoring of the escalator gearbox. Therefore, the
technical task of ensuring the good performance state of the gearbox of the metro
tunnel escalator with minimal possible costs was set.
The work comprises processing and analysing the signal of a gearbox with
good performance, to develop a method for detecting defects in damaged gearbox
components in the high-frequency region and to determine the most suitable
parameters for measuring the signal from the gearbox, such as the location of the
the sensor on the gearbox, the orientation of the sensor in space and the signal
measurement time.
The goal of the master's thesis is to develop a method for identifying defects
of the reducer of the drive of the metropolitan escalator by using the vibration
diagnostics. Tasks associated with this purpose are:
1. Collection and analysis of materials related to the vibration analysis and the
identification of defects of the gearbox components;
2. Justification of the use of the drive gearbox diagnostics method;
3. Experimental researches and analysis of the received results;
4. Creation of a plan for implementation of the methodology as a startup project.
5
The object of the research is the process of defects of the elements of the
gearbox of the metro tunnel escalator drive formation, which causes increased
noise, vibration and, as a result, high rates of the gearbox components wear.
The subject of the study is the vibrational signal obtained from the gearbox
of the metro tunnel escalator drive and, especially, the diagnostic signs of defects
in the spectrum obtained from this signal.
The spectra, obtained by the transformation of the signal from the good
performance and damaged gearboxes, were processed and analysed. Computer
models of the intermediate shaft and the intermediate shaft cover were designed in
CAD software. These models were later analysed in CAE Ansys to detect the
natural frequencies of these elements. Modelling is used to confirm the results of
the analysis of the vibration signal. The results of the spectral analysis and
modelling were used to develop the method of vibration diagnostics of the
elements of the gearbox of the metro tunnel escalator drive. The precise and
relatively cheap analysis method of the state of the metro tunnel escalator drive
gearbox was created.
The author of this thesis developed a method of diagnostics of defects of the
reducer of the drive of the metro escalator by analysing the vibration spectrum.
6
1. THE STUDY OF THE INFORMATION BOUND WITH THESIS
1.1. The analysis of the typical faults of gearboxes performance
The escalator drive consists of an engine, coupling and gearbox. The scope
of this work is the study of the state of the gearbox itself. Therefore, let's analyse
below the typical faults of the gearboxes performance.
Defects can be hidden due to the material used, the technology of
manufacturing and assembling the components of the gearbox, operating
conditions (including wear, in particular, from cold welding and the development
of microscopical cracks in the macro ones; the inconsistency of the actual
operating conditions with depicted on the design stage ones), etc.
For example, during the gearbox assembly a technological method such as
the creation of a strained-deformed engagement state is used in order to obtain
joint without gaps after the forging. The same method is used for bearings
installation. In other words, deformations can be created deliberately.
The theory of reliability, as a rule, suggests the sudden refusal, which is
characterized by a jump-like change in the values of one or more parameters of an
object. In reality, it is necessary to analyse other failures, for example, a resource
failure, resulting in the object acquiring a border condition state, or operational
failure, which arises because of the violation of established rules or conditions of
maintenance.
In evaluations and reliability analysis, the terms "element" and "system" are
widely used.
The term “element” refers to a part of a complex object, which has an
independent characteristic of reliability, used in calculations and performs a certain
personal function for a complex object own interest, which in relation to the
element is a system. For example, the bearing plays the role of an element in the
gearbox, and in relation to the rolling bodies (rollers), the bearing is a system.
7
From the above example, it can be seen that, depending on the level of the problem
to solve and the degree of binds between the analysed devices, a particular object
can in one case be a system, and in another - an element.
So when analysing the bearing, it can be "decomposed" into many elements:
rings (outer and inner ones), cage, rolling bodies (rollers, balls). On the other hand,
for a gearbox the bearing is more conveniently represented as an element, which
has its own characteristics of reliability, describing standards and technical
documentation, maintenance requirements.
Below we will describe certain defects, like those of gears, and bearing units
- all these elements determine the efficiency of the gearbox.
Widespread use of gear transmissions in machines and mechanisms of
various fields of technology, including high-speed and heavy-loaded gears
operating in low and high temperatures, the impact of tough environment and
radiation, inevitably related to the development of damage to the gear teeth due to
transmitted loads, speed of rotation, heat treatment, conditions of production and
maintenance, which eventually leads to the failure of the gearbox performance [2].
Of the various types of gear failure gear breakage or tooth decay is the most
basic. Breakage of the tooth due to static overload is known from the XVIII
century [3]. At steel producing plants and railways there were major accidents
caused by the breakage (destruction) of teeth. In the middle of the XIX century, the
breakage was described as jump-like developing defect moving from surface to
core. In the second half of the XIX century, the resistance of the materials was
introduced two coefficients, which characterize the absolute breakage and cyclic
bending stresses that result in the breakage. Later, the concept of fatigue strength
was introduced. At the threshold of the 20th century there was a fatigue breakage
of the tooth.
The creation of generators and steam turbines in the middle of the XIX
century lead to increase in requirements for wear resistance of the teeth.
8
At the end of the XIX century, the first illustrated album, containing
examples of gear faults, appeared.
Gear harness became known with the use of gearings in aircraft engines in
the early XX century, and especially in cases of grinded gear wheels.
Widespread use of grinding in the gear production drew the attention of
manufacturers to the problem of grinding cracks. The study of the temperature in
the engagement, which is on average 250...450 °C, and in some cases reaches 1200
°C, has begun due to harness problems.
Edge transitions (stress concentrators) and defects of the material became the
cause of 50% of all failures of gearbox gears. In the 1940s a technological
sequence of gear machining was developed, that established the best results in
terms of their endurance (coking, grinding, hardening).
In order to strengthen the tooth markers and prevent the formation of stress
concentrators, beginning from mid-1940s the usage protuberance cutters to form
smooth lines from the working surfaces to the transitional curves of the teeth
bottom land has begun.
Fatigue is known from the end of the 19th century, when it was first
discovered on the rolling paths of ball bearings. To resist it, actions were proposed:
- protection of transmissions from overloads (safety couplings),
- use of synthetic types of lubricants,
- grinding wheels to increase the load capacity.
In the 1920s, the corrosion that arose under the influence of lubricants, and
then the existence of corrosion fatigue of the material in the presence of lubrication
were revealed. In the XXI century, the first data appeared on biocorrosion, which
develops when using oils (most of the mineral, transmission and, less relatively,
synthetic) and reduces their usage interval.
9
In connection with the active use of heat treatment in the manufacture of
gears, it was time to pay serious attention to cracks after the quenching.
About 16% of all premature bearing failures are associated with improper
mounting, usually caused by excessive force applied, resulting from the lack of
proper tools. For effective mounting and dismounting of bearings mechanical,
hydraulic or thermal methods are required.
Despite the fact that the use of so-called bearing lubricants involves getting
rid of these problems, about 36% of premature bearing failures are related to the
wrong choice of lubricant.
In reality, any bearing, with any deviations of the properties of the lubricant
from the required parameters, will fail long before it will reach the time of resource
exhaust.
Bearings are precision products that cannot work reliably under conditions
of contamination of the cavity of the bearing and lubricant with foreign particles.
Since sealed and lubricated for entire lifespan bearings make up a relatively small
proportion of the bearings installed in the machines, at least 14% of their
premature failures are associated with pollution problems.
When machinery is overloaded or improperly serviced, the bearings fail
prematurely due to fatigue, which causes about 34% of all their premature failure.
Such failures can be prevented, because damaged and overloaded bearings
deliver "alarm signals" that can be detected using the devices for monitoring the
state of machines [4]. The range of such devices includes portable devices,
stationary systems and software for periodic (offline) or continuous (online)
monitoring of the key parameters of the operation of industrial equipment [5,6].
10
1.2. The gearbox elements condition monitoring vibrodiagnostics methods
When recording and analysing vibration signals generated by gearings, it is
necessary to take into account the main characteristic features of their work. These
features are described below.
The first one comprises, that the vibration signal from the gearing contains
synchronous components (harmonics), proportional to the reciprocating frequency
of rotor rotation (gears), and non-synchronous, associated with resonance
processes and not proportional to the rotor's rotational frequency. All the main
power of the vibration signal from the gearing is concentrated in a rather high-
frequency region.
The tooth mesh frequency of the gearing f z is equal to the product of the
shaft rotation frequency of the rotor on the number of teeth on it and can reach one
or even ten kilohertz. In practice, during recording vibration signals, assuming
their further application for the diagnostics of the condition of gears, it is desirable
to begin with the recording of maximal high frequencies, which will definitely
benefit later.
The components inherent to the very process of engagement created by a
pair of teeth in the transmission of a torque, have a low energy level and that is the
second feature. There are two reasons for this. First, the energy released in the
process of rolling the teeth, by itself, is not very large. Secondly, the location of the
installation of vibration sensors, due to the design features of the gearboxes, is far
from the zone of engagement.
As a result, the vibration transmission path of the engagement is quite large
and the signals in it fade gradually. Therefore, at least, it is necessary to use for
diagnostics the state of the gear vibration velocity signals, and in most cases, to
increase the informativity of vibration signals, it is necessary to use vibration
acceleration.
11
The amplitude of the harmonic components in the spectrum, caused by
vibrations from the gearings, depends to a large extent on the transferred load,
which is the third important feature. At the gearbox idle speed, the coupling
harmonics are visible very badly. As the forces transmitted by the gearing increase,
vibrations increase from the engagement process. This feature of the engagement
requires, if possible, comparative measurements under the same, preferably large,
load.
If the load is small - the defects of the gearing may not reveal themselves.
Several measurements used to construct a temporary trend performed at different
loads of the gearbox make all these measurements completely inappropriate for
comparison with each other for the search in the gearbox for changes, on the other
hand.
Vibrations from the engagement are non-stationary in the way, that they
have in their composition several phases of "rotation", more precisely, "slipping"
the tooth across the tooth, which differ in different types of gears, that makes the
fourth feature. Each of these phases generates the vibration of its natural
frequency, not related to the frequency of interference. Moreover, each of the teeth,
due to its specific differences from other teeth, generates its own frequencies. All
this supplements the fact that the pairs of "mutually rolled" teeth are constantly
changing, since the gears have not the same number of teeth.
All these important features result in the appearance of vibrations of a non-
uniform "residual noise" near the tooth mesh frequency. With this term in
technology is usually called a mixture of vibrations of different frequencies. The
ideal source of "white noise" is the falling water in the waterfall, which gave the
name of this term. Truth is, that there is a version that as many colours in the
amount give a white colour, and in the white noise all fluctuations are formed.
Such an interpretation of the origin of the term "white noise", with a more detailed
consideration, is less relevant to reality.
12
"White noise" consists of a lot of frequencies, and in a white colour, several
fixed frequencies are mixed. On the spectrum of vibration, "white noise" defines
itself in the form of raising the overall level of the whole spectrum in a fairly wide
band of frequencies near the characteristic gear mesh frequency. The "white noise
itself" consists almost entirely of non-synchronous random components.
Fifth feature is, that very often, the overall rise of the spectrum from "white
noise" occurs not only at the gear mesh frequency, but also at the frequency of its
own resonances of the elements of the gearing or gearbox. This is due to the
following reasons. Micro strikes in the gear excite a rather wide range of
vibrations, but the maximum amplitude of it will be, which fully corresponds to the
standard physical depiction of process, at the frequency of the resonance of one or
another closely located element of the gearbox. This frequency of own resonance is
determined by the design of the gearbox.
To use the diagnostics of the state of the gear pair is not at the frequency of
engagement, but on the frequencies of the own resonance of the elements of the
reducer, is necessary in high-speed multipliers, where the frequency of engagement
itself can be very high. As a result, it will be very heavily faded in the construction
elements, and it is sometimes impossible even to record this frequency on the
bearing mounts.
Resulting from the unique features of the gearing, the most informative
component in the spectrum of the vibration signal is one with frequency f z, the
frequency of which is equal to the product of the rotation frequency of the shaft
and the number of teeth in the gear located on this gearbox shaft. It’s amplitude is
usually very sensitive to the load transmitted by means of the gearbox.
The diagnostics specialist should not be frightened by the possible high
amplitude of this harmonic, especially as a result of the very first measurement of
vibration on this gear. The permissible value of this parameter is difficult to
normalize. The amplitude of the gearing harmonic f z on the spectrum of the
13
vibration signal depends on quite a lot parameters, the main of which can be
considered:
- quality of manufacturing a gearing, its hardening, polishing of working
surfaces,
- quality, sufficiency and purity of lubricant,
- the value of the gearbox load by the load moment transmitted from the
engine to the actuator.
The result is that almost always the first vibration measurement on bearings
of a gearbox or multiplier is not diagnostic, but evaluative, especially if it concerns
the local maxima of the harmonics of the gear mesh frequency.
The main attention on the "first" measurement of vibration and the
diagnostics of the state of the gearing, which is carried out at a certain level of
loading, should be given not to the peak of the f z, but to other, more important
features and parameters of the spectrum. This variety of features of the spectrum of
vibration, characteristic of some defects are characterizing the condition of the
gearbox. Often, it is just the external, not so noticeable features of the shape of the
spectrum, which, even with small amplitudes, can alarm the significant defects of
gearings.
The most serious attention when analysing the spectra of vibration signals
should be paid to:
- presence in the vibration spectrum near the main harmonic of tooth mesh,
sidebands from the gear mesh frequency f z, located to the left and to the
right of the main peak,
- relative magnitude of the amplitude of these harmonics of the tooth mesh
frequency, measured in relation to the amplitude of the peak of the gear
mesh frequency,
14
- the magnitude of the frequency step of queueing side harmonics of the
tooth mesh frequency, indicating how many these side lobes are shifted
relative to each other, and with regard to the fundamental harmonic.
- phenomena in the spectrum of the characteristic hump of "white noise"
near the gear mesh frequency. If there are several harmonics of this
frequency, then the humps can be near them; the diagnostic focus is the
averaged level of these humps relative to the harmonic of the gear mesh
frequency, and its harmonics, as well as the mutual relations between them.
-appearance of the peaks and humps of the "white noise" located in the
zones, which at first glance are not related to the frequency of engagement,
which do not have a simple substantiation of the arising vibrations, in the
spectrum of the vibration signal.
Let's try to explain again the causes of the appearance of peaks and humps of
"white noise" in different zones of the spectrum of the vibration signal, at first
glance, in no way associated with the gear mesh frequency and its harmonics.
It is necessary to understand well that virtually every defect of the gearing,
every wear, leads to the loss of "smoothness" of the engagement work. Instead of
uniform teething, a dynamic process is observed. It is accompanied by periodic
alternating loads, caused by violation of the working surfaces of the gearing.
When sufficiently serious, and sometimes even weak blows happen to be
applied the gearing, the gears and the design of the gearbox are affected by a force
shock impulse. This impact excites mechanical vibrations in structure elements,
which, in general, are extinct by exponential law. The frequency with which the
structure elements will oscillate or the frequency of "internal filling" of such fading
vibrations, is determined by structure own mechanical resonance with the vibrating
element. Usually, this frequency is not strictly fixed, but is a set of closely spaced
frequencies, the ratio of amplitudes of which looks rather random.
15
Figuratively speaking, the internal design of the gearbox is a resonance
circuit in which the fading vibrations are excited by the dynamic impacts caused
by the process of transmission of torque by means of the gearing. If we now obtain
the vibration spectrum of a structure with such a resonant circuit, then on it, along
with the peak at the gear mesh frequency, there will be a peak or hump with a
"white noise" located at the frequency of the own resonance of the construction
element. Often within the spectrum of vibration from the gearing this resonant
peak by its amplitude, and even more so in terms of power, is even more
significant at the peak of the harmonics of the tooth mesh frequency. Not rare, the
spectrum includes several such resonance peaks at the frequencies of various
elements of the gearbox.
This resonant harmonic peak (hump), excited at the natural frequency of the
internal elements of the reducer, is convenient to use for assessing the state and
diagnostics of defects in reducers. In practice, there are many cases where, due to a
number of specific features, it is not possible to record the gear mesh frequency,
and it is necessary to use harmonics in the resonant zones.
This usually refers to high-speed multipliers, where the tooth mesh
frequency is high, and the level of vibration signal quickly fades in the structure
base elements on the path to the vibration sensor. It is quite convenient, and
sometimes only possible, to use such an approach for diagnostics of very slow-
moving gears, where too often there are problems with recording the gear mesh
frequency, but due to the large dimensions of gearings [7].
Now let’s describe typical faults of bearings.
To the "bearings faults" all defects of support bearings of aggregates, and the
supporting posts themselves are related. Since the most widely used are the rolling
and sliding bearings, the features of diagnostics of defects of these types of
bearings are described here.
16
Rolling bearings of different types and brands, ball and roller, radial and
radial-thrust, single-row and double-row, etc. are widely used in rotating
equipment for different purposes. Without exaggeration, it can be said that most of
the repairs of equipment, especially of low and medium power, are made due to
defects in the support roller bearings. Therefore, the fast assessment of the
technical condition of such bearings, the diagnostics of their defects, as well as the
prediction of the possibility of their further maintenance, is the one of the most
important tasks in the work of the services of vibration diagnostics.
To assess the technical condition of bearing defects, various authors and
companies have developed many different methods. Naturally, all these methods,
different in their theoretical prerequisites, have different complexity, require
different equipment and can be used for various purposes. Of course, the summary
information obtained as a result of the use of these methods has different
informativity and authenticity.
Diagnostics of defects by the general level of vibration is included in the
widespread simplest practice of assessing the general technical state of rotating
equipment by the general level of the vibration signal. Such diagnostics is carried
out by technical personnel without special vibration training. For such a diagnosis
of defects in rolling bearings it is quite enough to use the simplest vibration meter
that measures the overall level of vibration.
Such a method for searching the defects in roller bearings allows defects to
be detected only at the very last stage of their development, when they already
cause or have already led to the deterioration of the bearing condition, an increase
in the overall level of vibration.
The criteria of the technical condition, and the degree of development of
defects in this method, are fully oriented to the corresponding normative values of
the levels of vibration adopted for this mechanism. Defective in this diagnostic
method is considered a roller bearing whose vibration exceeds the general
17
normative level for the unit. This is a sign of the defective state of a controlled
rolling bearing. With such a threshold increase in the level of vibration measured
on the support bearing, maintenance staff must make a decision about the
possibility of further unit maintenance or stopping the equipment and replacement
of the bearing.
The first signs of the defect of the bearing are found during the inspection of
the equipment by personnel rather late by this method of diagnosis, in about a few
months, weeks or even days, depending on a number of features of the operation of
the bearing, until the full wear of the bearing is reached. Despite such a late
detection of defects, and somewhat sceptical attitude to this method, this method of
controlling rolling bearings is widely used in practice and gives good results in
those cases.
The method has the greatest advantages when:
-The main task of diagnostic testing of equipment is to prevent accidents and
their consequences, even if diagnostic information about the defect is
received at a rather late stage.
- The replacement of the bearing can be executed at any time, without any
harm to the work of the controlled installation and technological cycle of the
whole enterprise, without disturbing the overall process.
- If the cycles of repair work on a controlled equipment are such, that the
remaining life span of the bearings with a diagnosed defect, albeit minimal,
always exceeds the working time before it is put into repair for other
reasons.
The advantage of this, the simplest method of diagnostics of defects in
rolling bearings by the general level of vibration, is the fact that its use does not
require virtually any additional training of the attendant, and often the operating
staff. Additionally, the cost of technical equipment required for this diagnostic
method is minimal.18
If the company had not previously performed any work on vibration
diagnostics, this method of diagnosis proves to be the most effective in its
implementation. Application of all other methods of diagnostics of roller bearings
always requires a large initial investment, and gives an economic effect only at
later stages of work.
Most specialists in vibration diagnostics, if they are beginning to engage in
work with roller bearings, expect the greatest reliability and the greatest effect
when introducing diagnostics by means of the classical vibrational spectrum. Such
spectra, in contrast to the vibration signal waveform spectra, are also used to
diagnose roller bearings. They are often called “direct” spectra
Unfortunately, their optimistic expectations are not destined to come true.
Not only is the diagnostic procedure itself quite complicated and controversial, the
reliability of most practical diagnostics of the condition of rolling bearings
obtained by using such "direct" spectra of vibration signals is unexpectedly low.
The "surprise" of such a paradox is programmed in advance and lays in the
special requirements of the diagnostics of the spectra of vibration signals. Mistakes
in diagnoses are predicted before and consist in the fact that the classical spectrum
is, in its definition, the distribution of the power of the output temporal vibration in
the frequency region. For this reason, the appearance on the spectrum of the
characteristic harmonics of one or another element of rolling bearings should be
expected only if the defect develops to such an extent that the power of its
harmonics will be comparable to that of the "mechanical" harmonics associated
with the imbalance, offset. Only in this case on the spectrum one can confidently
diagnose the "bearing" harmonics, when they will have not only great amplitude
but also significant power.
In order to increase the sensitivity of this diagnostic method to "bearing
harmonics" with low power, different methods are used, for example, the
amplitudes of harmonics in the analysed spectra are represented on a logarithmic
19
scale. This certainly helps, but to a certain extent, when the harmonics are already
beginning to disguise the general "white noise", which in vibrating signals has a
significant amplitude.
It can be said that the diagnosis by the spectra of the vibration signals can
confidently identify the defects of rolling bearings, starting only from the end of
the first stage of their development, and more often from the middle of the second
zone. Moreover, even at this level, the diagnostics of "direct" spectra of vibration
signals is a rather uneasy matter, and has a number of specific requirements.
It is quite clear that once the diagnostics of rolling bearings, more often, is
carried out during the analysis of dynamic processes, then the vibration
accelerayion signal must be recorded, in which these processes are more
significant. Although in some diagnostic methods it is necessary to analyse the
energy component of vibrations, which should be used for measurements in the
dimension of vibration velocity.
Now the main features of the defects of bearings in the initial vibration
signals, and in the "direct" spectra of power obtained on their basis will be
described. There are several such characteristic features.
First, it is the presence in the recorded vibration signal of clearly visible
periodic shock processes. Each impact that occurs when rolling the defect zone by
the bodies of rolling of the bearing, is characterized by a whole set of parameters.
These include the maximum impact amplitude, the frequency of free vibrations
occurring, and their fading rate.
Secondly, it is the presence in the spectrum of the vibration signal of a large
number of "non-integral" components or harmonics with fractional numbers of the
shaft rotation frequency. The frequencies of these inertia harmonics are determined
by the bearing ratios. In addition, with certain types of bearing defects, these
harmonics themselves create their own families and harmonics at the frequencies
of mutual impact, which further complicates the diagnostic procedure.
20
Third, it is the presence in the spectrum of the vibration signal of broadband
"uplifts", peculiar energy humps near bearing frequencies, and the frequencies of
their own resonances of elements of mechanical construction. Identifying the cause
of these humps in the spectrum, as well as connecting their parameters with the
primary defects of bearing rollers, is very difficult.
When conducting a further analysis of the received vibration signal, it is
represented in the frequency and time domain. Time analysis of the signal allows
to observe the change of the signal in time, analyse the change in amplitude, as
well as increase of the influence of higher harmonics on the signal. Analysis in the
frequency domain allows spectral analysis, which makes it possible to detect the
effect of separate individual frequency components to the resulting signal.
At the first stage of the development of the defect in the spectrum, along
with the first, mechanical, harmonics of the frequency of rotation of the rotor, a
peak appears on the characteristic frequency of the defect of one or another bearing
element. At this stage, the characteristic harmonic is already well visible on the
spectrum and allows you to precisely identify the defective element.
Further development of the defect leads to the appearance of harmonics from
the characteristic bearing frequency. Normally there are harmonics of a double and
triple multiplicity of the main frequency of the bearing defect. Along with each
such harmonic, the left and right sides will also have side frequencies, the number
of pairs of which can be quite large. The more developed the defect, the more side
harmonics and the harmonics of the defect frequency appear in signal. The wear of
a bearing with such a spectrum is already evident and can cover almost the entire
working surface of the bearing; it has already become a complex defect, affecting
several elements of the bearing. The bearing needs to be replaced or to be
intensively prepared for such a procedure.
This is the last stage in the development of bearing defects. Friction wear is
high and rotor rotation is difficult. The wear of the bearing reaches such a stage,
21
when the characteristic frequency of the defect is due to the deterioration from the
wear becomes unstable, the lateral harmonics will encounter the same fate. The
imposition of many harmonic families, each of which consists of the main
frequency and lateral harmonics, creates a rather complicated picture. If in these
families the basic harmonics differ slightly in frequency, then the sum of
amplitudes of all these neighbouring frequencies represents a general rise in the
spectrum, the "energy hump", covering a frequency range, which includes all the
harmonics of all families from all existing defects in the roller bearing [7].
1.3. Methods of the vibration signal processing
A number of methods is used to process a vibration signal. Further, several
methods will be observed to conclude which of them is more suitable for the work
task. This depends of complexity of it, obtained results and the elements that are
being diagnosed. The most commonly used signal processing method is the Fourier
transform.
The Fourier transform for a continuous signal h( t) is the Laplace transform
of a certain function f , which is defined by the expression [7]:
H ( f )=∫−∞
+∞
h(t)exp (− j 2πft )dt=F {h(t)} (1.1)
In this formula, H (f ) is called the Fourier transform with continuous time (or
continuously temporary Fourier transform, CTFT). The value of f in the complex
sinusoid exp (− j2πft ) corresponds to the frequency, which is measured in hertz, if
the value of t is measured in units of time (in seconds). In fact, the CTFT identifies
the frequencies and magnitudes of those complex sine waves, to which some
arbitrary oscillations are decomposed. The inverse Fourier transform is determined
by the expression:
h ( t )=∫−∞
+∞
H (f )exp (− j 2πft )df=F−1 {h(t )} (1.2)
22
The process of the Fourier transform is explained on Fig. 1.1.
23
Fig.1.1. General example of the Fourier transform: complicated input signal is
decomposed to simple periodic components, frequency and amplitude of which are
being depicted on spectrum [14]
When digitizing a time signal, the effect of redistribution of energy between
frequency components (the leakage phenomena) may be observed, if the sample
length does not contain the integer number of signal cycles. The result of such an
inaccurate presentation of the implementation of the output time signal is the
erosion of the frequency peaks. If you apply the appropriate window functions, you
can reduce the leakage effect. The most commonly used is the Hann window
(Hanning), which gives good results for stationary processes, but applications of
the windows of another kind can also be used.
For transition processes, the best result can be obtained by using a
rectangular window. The Hamming window allows for more sharp peaks than in
the case of Hanning, but increases the level of side petals (leakage of energy). On
the contrary, the Blackman window and its modification, the Blackman-Harris
window, provides a reduced level of side petals, but with increased blurring of the
central peak. The flattop window allows for a more accurate estimation of
amplitudes than Hanning, but it is impossible to distinguish weak signals in the
24
vicinity of a powerful frequency peak. The flattop window gives the widest peak
with side petals, similar to Hanning, but the smooth peak of the peak allows you to
determine most accurately the relationship between the amplitudes when changing
the frequency. By smoothing the sampling errors, the window functions also
improve the spectral representation of nonstationary signals (for example, the
cascade spectrum). A flattop window that retains the most accurate correlation
between the amplitudes of different harmonic signals can be used in calibration
procedures.
Depending on the frequency of the signal to get one realization of the
spectrum (Fourier transform), the implementation of a signal from the fraction of a
second to a few seconds is required. However, for a modulated signal, to reliably
estimate of the average amplitude may take longer. Therefore, a very important
function of the analyser is the averaging of several consistent spectra. In the
presence of one channel of data transmission (measurement channel) averaging is
carried out by the amplitudes of the frequency components without taking into
account phase relationships. To conduct averaging of the complex spectrum (real
and imaginary parts), it is necessary to synchronize the spectra using an additional
signal associated with the phases of motion of the machine parts.
Also, for the processing of the vibration signal, an analysis of the envelope
curve spectrum is used (mainly applied to bearings, but can be used for processing
other elements of the gearbox).
Diagnostics on the spectrum of envelope curve vibration is one of the most
complex methods of diagnostics of the machine elements (gears, bearings), if we
compare them with each other in terms of the complexity of mathematical
processing and the physical interpretation of the results.
The method is based on two rather simple prerequisites. First, depending on
which element of machine, for example rolling bearings, there was a defect (inner
and outer rings, rolling body, cage), the frequency of impact in the signal (the
25
frequency of "rolling" of the defect in the bearing operation) will change. This
frequency is uniquely associated with the geometric dimensions of the bearing and
the rotational speed of the supported rotor. Secondly, after each impact in the
bearing, there will be free damped oscillations that last for quite a long time. These
oscillations should be broadband, take a wide range of frequencies that are needed
to rebuild the method from interference by rebuilding bandpass filters.
In fact, the processing of vibration signals is carried out in this way. With a
bandpass filter (analogue or digital), a narrow range of frequencies is allocated
from the whole signal. At the same time, the question of a specific choice of the
desired frequency band is given to the user, which immediately complicates the
work of even a specialist of middle-level qualification, not to mention beginners.
The received signal is recorded by a digital detector (an envelope signal is being
built), and from it the usual spectrum is obtained.
The resulting diagnosis of the bearing condition is made on the basis of an
analysis of the ratio of amplitudes of "bearing" harmonics in the spectrum of the
bypass signal. It is important to clearly understand that the received spectrum is not
built around all signal, but only through its narrowband sample. Therefore, the
amplitudes of harmonics are not in the "exact" value of vibration acceleration, but
in units of relative modulation of the signal. It also significantly complicates the
interpretation of the results and the final diagnosis.
In addition to the disadvantages listed above, this method has another very
significant drawback, which complicates the correct determination of the bearing's
remaining resource. If a defect occurs on a bearing ring, and this happens most
often, then at the first stage of its development there is a proportional increase in
vibrational characteristics. At some stage of the development of the defect, a
process begins when, in the spectrum of the envelope curve signal, the signs of the
development of the defect (the level of modulation of the signal by the bearing
harmonics) begin to decrease. The defect is being developed, and the diagnostics
gives an improvement in the bearing condition. After some time, this 26
"improvement of the bearing" stops and restores the proportionality between the
degree of development of the defect and its features in the spectrum of the
envelope curve signal. The most unpleasant thing here is that this "abnormal
diagnostic zone" can take up to half of the total time from the moment of the defect
to the realisation of the bearing failure. The physical explanation of this
phenomenon is quite simple. At the first stage of the development of the ring
defect, all the energy of the shock occurs in the contact area of one rolling body
with the defect zone. As the zone grows, there is a situation in which the rolling
body passes through the defect zone, but the impact force decreases due to the fact
that at this time the rotor rests on two other rolling bodies, located on both sides of
the defect zone. As they run around the clip outside the defect area, the impact
force decreases and may, as observed in practice, decrease by two to three times.
The result of this is understandable - the diagnostic system gives a proportional
improvement of the rolling bearings.
All of the above complexity of the application of this method of diagnostics
(and also the great difficulties that arise when setting the thresholds of the state of
the bearing on the level of modulation) significantly limit the scope of the
application of the spectrum of bypass vibration. Its main purpose is to control the
most responsible and expensive bearings. Only for them it is possible to conduct
the whole complex of measures connected with periodic, rather frequent control,
and also with definition of correct norms and thresholds of a state. For a massive
survey of a large number of bearings, the method is not suitable because it allows
us to confidently detect defects in bearings only at rather late stages of their
development. In the initial and "middle" phases of development of defects the
reliability of the received diagnoses decreases to 30 - 50%, which is obviously
insufficient [7].
Conclusions:
-the most damages in the gearbox occur in gearings and bearings,
27
- the method of vibrational spectra analysis will be used for the analysis of
defects,
- due to insufficient functionality of the existing methods of signal
processing, their disadvantages and complexity, it was decided to develop
another method of analysis based on fast Fourier transforms, filtering using
window functions and averaging the signal,
-unlike gears, the analysis of bearing defects is associated with additional
complexity, so for the analysis of defects data it is necessary to develop a
separate method,
-for the analysis of gear defects, the vibration spectra analysis will be
applied according to known diagnostic features from the reference book [1].
28
2. JUSTIFICATION OF THE CHOSEN DIAGNOSTICS METHOD
2.1. Measuring scheme
The object of the study is the gearbox of the ET-2 escalator drive, elements
of which are called out on the Fig. 2.1.
Fig. 2.1. Elements of the escalator drive
The next scheme for sensor installation is used for obtaining of the vibration
signal from the escalator drive gearbox (Fig. 2.2):
Fig. 2.2. Block-scheme for recording the vibration signal
29
The signal is being sent from the vibration acceleration sensor, installed on
the adhesive base (bee wax) on the housing of the gearbox or on the shaft cover,
and then being amplified (the signal is a voltage, proportional to vibration
acceleration). Then, after the signal went through the amplifier, the signal is sent to
an analog-to-digital converter, where the electric signal is converted into digital
one. Next, this signal is transferred to the computer for further processing and
analysis.
Sensors according to vibration diagnostics standards must be connected in
three orthogonal directions: axial and two radial ones (vertical and two horizontal)
[8]. In our case, we use the scheme depicted below (Fig. 2.3).
Fig. 2.3. Scheme of sensors mount onto the investigated gearbox of the escalator
drive (1, 2, 3 - measurement points: 1 - on the clutch with brake wheel, 2 - on the
cover of the input shaft, 3 - on the cover of the intermediate shaft, A - axial
direction, V - vertical direction, H - horizontal direction)
30
2.2 Measuring equipment and software
To measure the signal, the following set of equipment is used:
- accelerometer PCB 353B15 (Fig. 2.4, a),
- an amplifier PCB 480E09 (Fig. 2.4, b),
- an analog signal transmitted from the sensor is processed using an
analog-to-digital converter NI USB-9215 (Fig. 2.4, c).
Images are taken from the official site of these components developers.
a) b)
c)
Fig. 2.4. Measurement equipment: a) accelerometer, b) the signal amplifier, c) analog-to-digital signal converter
31
Tab. 2.1. Characteristics of the PCB353B15 accelerometer (Fig. 2.4, a) [9]
Characteristic Value and units
Sensitivity (± 10%) 1.02 mV/(m/s2)
Measurement range ± 4905 m/s2
Frequency range (± 5 %) 1-10000 Hz
Frequency range (± 10 %) 0.7-18000 Hz
Frequency range (± 3 dB) 0.35-30000 Hz
Resonance frequency ≥ 70 kHz
Nonlinearity of the amplitude characteristic ≤ 1%
Relative coefficient of transverse
transformation≤ 5%
Overload limit ± 98100 m/s2
Temperature range of operation between -54 and +121 ͦ C
Time of operation < 5 s
Height 10.9 mm
Weight 2 g
Sensitive element quartz
32
Tab. 2.2. Characteristics of the signal amplifier PCB 480E09 (Fig. 2.4, b) [10]
Characteristic Value and units
Channel quantity 1
Frequency range (-5 %, ampl. rate ×1, ×10) 0.15-100000 Hz
Frequency range (-10 % ampl. rate ×100) 0.15-50000 Hz
Temperature range between 0 and 50 ͦ C
Power supply (DC) 25-29 V
Type of connectors BNC
Dimensions (l x h x w) 6.1×10×7.4 cm
Weight 0.3 kg
Tab. 2.3. Characteristics of the National Instruments USB-9215 Analog-to-
Digital Converter (Fig. 2.4, c) [11]
Characteristic Value and units
Channel quantity 4
ADC resolution 16 bit
Sampling frequency 20000 Hz
Operating voltage range (on sensor) ± 10 V
Time of conversion 4.4 μs
Type of connectors BNC
Measurement accuracy 0.082%
Dimensions (l x h x w) 14.2×2.5×8.8 cm
Weight 0.275 kg
33
To process the vibration signal, we use the software DASYLab, which by
means of graphical programming allows you to quickly build a circuit to process
the signal. For post-processing of the spectrum we use the program Microsoft
Excel, which has a convenient tool for working with charts and tables. To
determine the natural frequency of the gearbox elements of the escalator, we will
use the CAE Ansys software. CAD Kompas 3D is used to virtually design gear
components.
2.3. Signal processing sequence
The signal after the conversion is packed into the .mat file. For processing in
DASYLab, the signal needs to be converted to the .asc format, after converting it
in MATLAB, we upload the file to the target workspace (Fig. 2.5).
In the program, the signal is loaded into the Read module, and after the
signal is processed using the following algorithm.
1. Vibration signal is sent to the filter, where several first blocks of the signal are
cut off (the Separate module).
2. After this, the signal passes through one of two windows (the Hann window -
for high-resolution spectra (for frequency refinement), a rectangular window for
a low-resolution spectrum). Low and high resolution spectra differ by the
spectra resolution parameter:
∆ f=f sn (2.1)
where: ∆ f – spectra resolution; f s – sampling frequency, Hz;n – number of
samples in the time window.
34
Fig. 2.5. A block scheme of signal processing in DASYLab to obtain spectra of different resolutions
Fig. 2.6. An example of implementing a signal transformation into a low resolution spectrum in DASYLab35
When passing through the window, the signal is multiplied by the window
function, after which it is filtered by it. Below are the formulas for the
rectangular (2.2) and Hann (2.3) windows:
w (n )=1(2.2)
w (n )=0.5−0.5 ∙ cos ( 2πnN−1
) (2.3)
where: w – window function, N – size of the time window(for high resolution -
32768, for low resolution - 512 samples), n = 0, 1, … (N-1) (module: Data
Window).
3. After passing through the “data window” module, the signal passes through the
Fourier transform and we obtain the amplitude spectrum. The transformation of
the signal is performed using fast Fourier transforms, which represent a kind of
number of effective algorithms for calculating the Fourier series [17] (used in
DASYLab in the FFT module (two channels are for vibration acceleration and
vibration velocity spectra respectively, in the work used only vibration
acceleration spectra)). Fast Fourier Transform is a method of calculating a
discrete Fourier transform for a computer (the formula for the discrete
transformation is given below) [17]:
X ( f )= ∑n=−∞
+∞
x (n )exp (− j2 πfnT ) ,−1/(2T )≤ f ≤1/ (2T ) (2.4)
where: X ( f ) – conversion result, frequency function (amplitude-frequency
spectrum); f – frequency, Hz; T – sampling interval, s, x (n ) – discrete signal n
intervals of time T . Sampling allows to break the spectrum at time intervals,
with an infinite number of which it is possible to restore the original amplitude-
frequency spectrum.
4. Then, after receiving the spectra over the entire length of the signal, the values
of the spectral amplitudes are averaged (module Block Average) and then we
36
obtain the desired averaged spectrum (step 5). (Vibration velocity signal also
multiplied by specific rate in module Ariphmetic)
After that, the .asc files that we get at the output are converted to .csv files, after
which we get the ability to edit spectra in the Microsoft Excel environment.
2.4. Post-processing of the obtained data
To analyse the output data of a normally working gearbox, we use
descriptions of diagnostic characteristics of the defects in the reference book [1].
To confirm the results of the analysis, it is necessary not only to compare the
results with the high-resolution spectrum, but also to carry out simulation in Ansys.
The formulas for the excitation frequencies of the reducer elements taken from the
reference book [1] are written below:
f r=n
60 (2.5)
f z=f r ∙ z (2.6)
f FTF=12f r(1−
Db
D pcosβ) (2.7)
f IR=12f rN (1+
Db
D pcosβ) (2.8)
f ¿=12f r N (1−
Db
D pcosβ) (2.9)
f BS=D p
2Dbf r[1−(Db
D p )2
(cosβ )2] (2.10)
D p=Do+Di
2 (2.11)
where f r – shaft rotation frequency, Hz, n – shaft rotation speed, rpm, f z – gear
mesh frequency, Hz, z – number of teeth of the gear, f FTF – frequency of rotation of
rolling bodies around the bearing axis, Hz, f IR – frequency of passage of rolling
bodies on the inner ring, Hz, f ¿ – frequency of passage of rolling bodies on the
37
outer ring, Hz, f BS – frequency of rotation of rolling bodies around their axes, Hz,
N – number of rolling bodies in the bearing, Db – diameter of rolling bodies, mm, D p – bearing middle diameter, mm, cosβ – cosine of the contact angle of rolling
bodies and paths of rolling, Do – diameter of the outer ring of the bearing, mm, Di -
diameter of the inner bearing ring, mm.
We conduct an analysis of natural frequencies by the forms of oscillation in
the Workbench ANSYS environment. First, in the Engineering Data fill the data on
the material (Fig. 2.8): Jung's module, thermal and mechanical characteristics.
Then we load CAD 3D Model in Model module of ANSYS, preferably in
Parasolid format. Then we continue editing in the Mechanical environment (Fig. 2.
9). In this environment, we set the nature of the relationships between the assembly
elements in the Connections section.
Fig. 2.7. Modal analysis in Ansys
38
Fig. 2.8. ANSYS Engineering Data module
39
Fig. 2.9. ANSYS Mechanical (module window)
40
Next, for our purposes, we will use a standard breakdown on the finite
elements of the Mesh module. Next, we set restrictions, elastic or fixed, depending
on the elements. For elements with elastic (elastic support) stiffness is calculated
using the formula:
K=СS (2.12)
where K, N/m3 – contact stiffness of the support, C, N/m – coefficient of stiffness
of the support, S, m2 – contact area of support.
In the Solve module, we calculate the total deformation for three forms of
vibration and start the solvation process, after that we will obtain the result.
To analyse the spectrum from the damaged gearbox, there is need to filter
out the important part of the signal, highlighting only those frequencies that
describe defects in the gearbox.
For this I propose my method of analysis, which consists in the linearity
processing of the spectrum at rotational frequencies, frequencies of excitation and
the natural frequencies of the individually investigated elements. Frequencies are
planned to be selected by the sampling method, multiplicities of 5, 10, etc. for
more clean spectrum.
Conclusions:
- the necessary measuring equipment and the measurement scheme was chosen to
measure the reliable signal;
- the chosen method of signal processing (implemented with DASYLab modules),
which allows obtaining the accurate spectra,
- selected methods of spectral analysis of a normal gearbox and the method of
analysis of damaged gear are proposed;
- to confirm the results of the analysis, simulation in ANSYS is used to detect the
natural frequency of the gear components.
41
3. EXPERIMENTAL RESEARCH OF DYNAMICS OF THE
ESCALATOR DRIVE GEARBOX
3.1. Research and analysis of the vibration state of a good performance
gearbox
To analyse the gearbox of the metro tunnel escalator drive, it is necessary, to
find the excitation frequencies of individual elements of the gearbox, that needs to
be diagnosed. The following tables describe the excitation frequencies in the first
approximation:
Tab. 3.1. Frequencies of excitation of shafts and gears in the first
approximation
Den
otat
ion
Gear number 1 2 3 4 5 6
Number of teeth 24 106 27 116 22 72
Shaft number 1 2 3 4
n, rpm 725 164 164 38,2 38,2 11,7
Multiplied
harmonicsShaft rotation frequency, Hzf r
I 12,08 2,74 2,74 0,64 0,64 0,19
II 24,17 5,47 5,47 1,27 1,27 0,39
III 36,25 8,21 8,21 1,91 1,91 0,58
IV 48,33 10,94 10,94 2,55 2,55 0,78
Multiplied
harmonicsTooth mesh frequency, Hzf z
I 290 290 73,87 73,87 14,01 14,01
II 580 580 147,74 147,74 28,02 28,02
III 870 870 221,6 221,6 42,03 42,03
IV 1160 1160 295,47 295,47 56,04 56,04
42
Tab. 3.2. Frequency of excitation of bearings elements in the first approximationD
enot
atio
n
Parameter Roller with cylindrical
rollers 42624
Ball radial single row
324
Roller radial spherical
double row 3624
Ball radial single row
330
Roller radial
spherical double row
3634
Ball radial single row 156
Roller radial spherical double
row 3003160
Quantity of bearing per shaft 2 1 2 1 2 1 2n Shaft rotation frequency rpm 730 165 165 38,5 38,5 11,8 11,8 Shaft input intermediate intermediate. low-speed low-speed output outputDi Inner diameter of the bearing mm 120 120 120 150 170 280 300Do Outer diameter of the bearing mm 260 260 260 320 360 420 460
β Angle of contact of bodies and rolling bodies races 0 0 14 0 14 0 10
N Number of rolling bodies 13 8 14 8 16 12 28D p Center bearing diameter mm 190 190 190 235 265 350 380Db Diameter of rolling bodies mm 36 42,86 38 50,8 46 41,28 36f r Rotor rotation frequency Hz 12,17 2,75 2,75 0,64 0,64 0,2 0,2
f FTFFrequency of rotation of rolling bodies around the bearing axis
4,93 1,07 1,34 0,25 0,31 0,09 0,11
f IRFrequency of passage of rolling bodies on the inner ring
94,07 13,5 19,81 3,12 5,25 1,31 2,52
f ¿
Frequency of passage of rolling bodies on the outer ring
64,1 8,53 18,76 2,01 5,01 1,04 2,96
f BSRotating frequency of rolling bodies 30,95 5,8 6,88 1,41 1,85 0,82 1,03
43
With characteristic excitation frequencies in the first approximation, we
continue with the analysis of the transformed signals received.
The signals were obtained by means of accelerometers (sensors) installed at
several points on the gauge for a 2 (3) series of measurements. The connection
scheme is shown in the figure (Fig. 3.1).
Fig. 3.1. Scheme of sensors placement on the gearbox of escalator drive (1, 2, 3 -
measurement points: 1 - on the coupling with the brake wheel, 2 - on the cover of
the input shaft, 3 - on the cover of the intermediate shaft, A - axial direction,
V - vertical direction, H - horizontal direction)
Fig. 3.2. Kinematic scheme of gearbox of the metro tunnel escalator drive
44
In order to meet the conditions for the reliability of the measurement,
namely:
- absence of higher harmonics of rotor rotation frequency;
- the average level of vibration in the band should be compared with the
level of noise in the range of low and medium frequencies and exceed the
level of its own noise no less than 15 ... 20 dB [1].
To do this, we cut off the first measurement point as not satisfying the
conditions of the study.
The spectra of signals from the second and third points are depicted on the
Fig. 3.3, Fig. 3.4.
Tab. 3.3. Local maxima on the spectra obtained from the second and third
points of sensors location
Measurement point 2 3
Direction of
measurementAxial Vertical Axial Vertical
Loca
l max
ima
freq
uenc
ies
in
asce
ndin
g or
der (
Hz)
f I 74 74 111 74
f II 186 186 186 186
f III 779 259 260 408
f IV 1113 371 408 594
f V 779 594 779
f VI 779 854
f VII 1039 1039
f VIII 1188 1150
45
Fig. 3.3. Spectrum of vibration acceleration; measurement point #2, a - axial
direction, b - vertical direction, local maxima indicated by arrows
46
Fig .3.4. The spectrum of vibration acceleration; measurement point #3, a is axial
measurement; b is vertical measurement; peak frequencies are indicated by arrows
47
Study of spectra from the second and third points is depicted below.
The analysis revealed the presence of a peak at the excitation frequency of
the 2nd engagement f z2 I=74Hz. This signals a possible existing defect in the gear
that transmits the movement from the intermediate shaft to the low-speed one. On
spectra were also found peaks at multiple frequencies k f z2 I, k=1,5; 2,5. This
indicated a possible defect of the variable stiffness of the teeth in the engagement.
For a more detailed analysis, high-resolution spectra were used, in which peak
harmonics were found to be k f z2 I, where k=0,5; 1; 1,5; 2; 2,5 (Fig. 3.5).
Fig. 3.5. High resolution spectrum of vibration acceleration; measurement
point #2, a - axial direction, b - vertical direction, multiplied harmonics marked
with arrows
48
Fig. 3.6. Spectrum of high resolution of vibration acceleration; measurement point #3, a - axial direction, b - vertical direction, black rectangle – peak (axial) and fall
(vertical) at a frequency of 1208-1210 Hz
49
For the final confirmation of the existence of the defect found, we searched
natural frequencies of the intermediate shaft (Fig. 3.7) for three modes of vibration
(the natural frequencies of other shafts were found earlier). The shaft is fixed
elastically at the places of installation of bearings with a stiffness of 1.15 ∙1019 Nm3
and limited in the axial direction of movement (because the shaft is fixed in the
housing and secured to prevent axial displacement). The links are placed in the
Connections section between the wheels and the shaft. The results of the analysis
are shown in the Tab. 3.4.
Tab. 3.4. Natural frequencies of the intermediate shaft in three forms of
oscillation
Vibration mode Frequency (Hz)
1 188,23
2 432,2
3 438,27
50
Fig. 3.7. Deformation by the modes of vibration of the studied intermediate shaft: the upper left image is the first form, the
upper right is the second form, the bottom is the third, the red rectangle indicates natural frequencies
51
The natural frequency of the intermediate shaft coincides with the 2.5 times the
gear mesh frequency of the second gear, also at this frequency there is the root
harmonic of the studied spectrum. Thus it is possible to confirm the presence of a
defect of varying stiffness of the teeth in the second gearing and the presence of
parametric resonant vibrations of a multiplied teeth mesh frequency with natural
engagement frequency. This leads to detachable shock modes, that cause wear of the
profile of the teeth, increased noise transmission and the appearance of new
components in the vibration spectrum of the reducer [1].
In the spectrum of the vibration acceleration signal obtained from the
measurement at the third point, the local maximum of the signal was found at a
frequency of 1150-1188 Hz when measured in the axial direction (the sensor is
located on the cover of the intermediate shaft). At the same frequency when
measured vertically (the sensor is on the gearbox housing), local maximum is not
found. When searching for high-resolution spectra, a more precise frequency value of
1208-1210 Hz was found (Fig. 3.6). This indicates that this frequency may
correspond to the cover of the intermediate shaft on which the sensor is installed. To
check this assumption, we searched natural frequency for three forms of vibration
(Fig. 3.8). The cover is fixed elastically through the holes for elastic bolts with a
stiffness of 2.64 ∙1017 Nm3 .
52
Fig. 3.8. Deformation according to the modes of vibration of the studied shaft cover: the upper left image is the first form, the
upper right is the second form, the bottom is the third, the red rectangle indicates natural frequencies
53
Tab. 3.5. Natural frequencies of the intermediate shaft cover in three modes of
vibration
Vibration mode Frequency (Hz)
1 1209,2
2 1563,1
3 1573,1
Thus it is confirmed that the peak occurring at frequencies 1208-1210 Hz on
the high-frequency charts in the axial direction is the frequency of the intermediate
shaft cover (see Tab. 3.5).
After we have confirmed the defects in the gearbox and found the accurate
value of the gear mesh frequency, it is necessary to clarify the data of the first
approximation of the excitation frequencies of the shafts, gears and bearings:
f z2 I=74,22Hz=¿ f r2 I=f z2 I
z3=74,22
27=2,85Hz (3.1)
n2=f r 2 I ∙60=2,85∙60=164,93 rpm (3.2)
n1=n2∙z2
z1=164,93 ∙ 106
24=728,5 rpm (3.3)
where: n1 , n2 – the rotation speed of the input and intermediate shaft respectively, rpm,
and z1, z2 , z3 – is the number of teeth on the first, second, third gears, respectively.
Thus, the excitation frequencies in the second approximation are as follows depicted
in Tab. 3.6 and Tab. 3.7.
54
Tab. 3.6. Frequencies of excitation of shafts and gears in the second
approximationD
enot
atio
n
Gear number 1 2 3 4 5 6
Number of teeth 24 106 27 116 22 72
Shaft number 1 2 3 4
n, rpm 728,5 165 165 38,4 38,4 11,7
Multiplied harmonics Shaft rotation frequency, Hzf r
I 12,14 2,75 2,75 0,64 0,64 0,20
II 24,28 5,50 5,50 1,28 1,28 0,39
III 36,43 8,25 8,25 1,92 1,92 0,59
IV 48,57 11,00 11,00 2,56 2,56 0,78
Multiplied harmonics Tooth mesh frequency, Hzf z
I 291,40 291,40 74,22 74,22 14,08 14,08
II 582,80 582,80 148,45 148,45 28,15 28,15
III 874,20 874,20 222,67 222,67 42,23 42,23
IV 1165,60 1165,60 296,90 296,90 56,31 56,31
55
Tab. 3.7. Frequency of excitation of bearings elements in the second approximation
Den
otat
ion
Parameter Roller with cylindrical
rollers 42624
Ball radial single row
324
Roller radial spherical
double row 3624
Ball radial single row
330
Roller radial
spherical double row
3634
Ball radial single row 156
Roller radial spherical double
row 3003160
Quantity of bear. per shaft 2 1 2 1 2 1 2
n Shaft rotation frequency rpm 728,5 165 165 38,4 38,4 11,7 11,7
Shaft input intermediate intermediate. low-speed low-speed output output
DiInner diam. of the bearing mm 120 120 120 150 170 280 300
DoOuter diam. of the bearing mm 260 260 260 320 360 420 460
β Angle of cont. of bod. & r.b.r 0 0 14,00 0 14 0 10
N Number of rolling bodies 13 8 14 8 16 12 28
D pCenter bearing diameter mm 190 190 190 235 265 350 380
DbDiameter of rolling bodies mm 36 42,86 38 50,8 46 41,28 36
f r Rotor rotation frequency Hz 12,14 2,75 2,75 0,64 0,64 0,20 0,20
f FTFFrequency of rotation of roll. bod. ar. the bear. axis 4,92 1,06 1,34 0,25 0,31 0,09 0,11
f IRFreq. of pass. of roll. bod. on the inner ring 93,87 13,48 19,77 3,11 5,24 1,31 2,52
f ¿
Freq. of pass. of roll. bodies on the outer ring 63,97 8,52 18,72 2,01 5,00 1,03 2,95
f BS Rot. frequency of roll. bod. 30,89 5,78 6,87 1,41 1,84 0,82 1,03
56
Thus, the frequency of excitation of the gearbox components was calculated,
which depends on the actual speed of the engine shaft rotation.
3.2. Development of the method of identifying faults of gearbox components
During the previous studies, an analysis of the signal from the damaged
escalator gearbox was performed on request of the escalator service of the Kyiv
metro company. On the researched escalator after the repair (replacement of the
gearing) there were high levels of noise and vibration. After the diagnosis, it was
discovered that the reason for this was an error in the installation of shafts and the
defect was found in the ball bearing located on the intermediate shaft. This
spectrum is depicted below (Fig. 3.9).
There are areas highlighted with black that have local maxima. These are
high-frequency areas with frequencies above 1000 Hz. On the spectra of a
normally working gearbox, there are no significant peaks in these areas, so it was
assumed that these peaks are responsible for defects in the bearing unit. It was
necessary to develop a methodology that would help identify these peaks, as
bearing defects.
Fig. 3.9. Spectrum of damaged gearbox
57
First, let’s compare spectra from normal performance reducer, investigated
in chapter 3.1 and damaged performance one. This comparison depicted on Fig.
3.10.
Fig. 3.10. Compared spectra obtained from measurements from normal
performance reducer described by black dashed line and damaged reducer
described by blue solid line
As can be seen, in the high frequency area beyond 1000 Hz there are local
maxima on the spectrum. There can be concluded, that these maxima are
describing bearing defects, that were almost absent in normal performance reducer.
In this thesis, I propose a technique that filters the spectrum at frequency
frequencies of the excitation of the inner and outer ball bearing rings and the own
frequency of the shaft cover.
First check the main peaks of the graph for the frequency multiplicity of the
inner and outer rings of the ball bearing.
58
Tab. 3.8. Frequencies of main local maxima in relation to the excitation
frequencies of bearing rings elements
Peak frequency (Hz) f IR=13,5Hz f ¿=8,5Hz
68 5,037 8
177 13,11111 20,82353
461 34,14815 54,23529
1081 80 127,2
1343 99,48148 158
2000 148,1481 235,2941
2868 212,4444 337,4118
4299 318,4444 505,7647
6369 471,7778 749,2941
6522 483,1111 767,2941
9390 695,5556 1104,706
9478 702 1115
As we can see there are some non-fractional components of multiplied
frequencies of the bearing inner and outer ring, that signals of possible defects
there.
Now, let’s filter the spectrum by ten times the harmonics of the excitation
frequencies of the inner and outer rings: The tenth harmonic frequency was
selected by a sampling method from a number of rates from one to ten, because the
spectrum obtained allowed to effectively analyse the signal for defects in the target
element of the gearbox.
59
Fig. 3.11. The gearbox spectrum filtered by a frequency of 85 Hz
Fig. 3.12. Filtered spectrum (blue) on one graph with the original one (orange)
60
Fig. 3.13. The gearbox spectrum filtered by a frequency of 135 Hz
Fig. 3.14. Filtered spectrum (black) depicted with the original one (orange)
61
Fig. 3.15. Root peaks of two coincident spectra (highlighted by blue ovals)
As we can see, the root harmonics of the original spectrum and the spectrum
filtered by ten times the harmonics of the frequency of the inner ring coincide
exactly in high frequency zones (Fig. 3.15). Thus, we can assume that there is a
pronounced defect of the strong deterioration of the inner ring. By the spectrum
filtered by the harmonics of the outer ring (Fig. 3.11), we can assume the presence
of less serious wear of the outer ring. Now we will check the spectrum filtered by
the harmonics n f c (n = 0,5; 1; 1,5; 2…) (f c – shaft cover natural frequency) (Fig.
3.16):
Fig. 3.16. The gearbox range is filtered by natural shaft cover frequency,
f c=188Hz
62
Fig. 3.17. Filtered spectrum (violet) superimposed on the original (orange)
As we can see, the natural frequency of the shaft cover is present in all
high-frequency zones (Fig. 3.17). In this way, it can serve as a diagnostic feature of
a defect in the bearing, in the presence of a high frequency zone.
Finally, let's show the spectra filtered by ten times the harmonics of the inner
and outer rings and natural shaft cover frequency:
63
Fig. 3.18. The combination of filtered spectra: spectrum filtered with multiplied by
85 Hz frequencies – light-blue (below), the spectrum filtered with multiplied by
135 Hz frequencies – black (in the middle), the spectrum filtered by f c=188Hz
frequency – violet (from above), the coincidences are highlighted in dark blue
rectangles
64
The repair protocol mentioned the frequency of the bearing of the first shaft
with short cylindrical rollers. This frequency is checked with the method suggested
in the work on Fig. 3.19
Fig. 3.19. Filtered spectrum (black - spectrum along the inner ring, green - by the
outer ring), imposed on the original (pale pink)
Thus in the figure there is a partial coincidence of the bearings of the input
shaft frequencies and areas of maximum peaks. As a result, we can assume a
moderate wear of the inner and outer bearing rings. Given the lower amplitude
level than in the case of a ball bearing, it can be assumed that the wear of the
bearing is moderate.
Conclusions:
The technique of analysis of the vibration signal has shown its effectiveness in
the analysis of a working gearbox.
It is recommended to conduct measurements in the axial and vertical directions
for more accurate information about gearbox to be obtained.
The optimum signal measurement time for the successful averaging of the
spectrum is determined - 200s.
65
The analysis of defects of the gearbox components in high-frequency areas, in
particular bearings, with the proposed method of filtering the signal, which on
the example of a known defect of a bad performance gearbox has shown its
effectiveness;
There is a recommendation to filter the spectrum of the gearbox by multiplied
inner and outer ring frequencies of the bearing and the natural frequency of the
shaft cover for detection of the bearing defects.
With the help of this method, the defects in the high frequency area of the
spectrum were successfully linked to the known from repair report defects of
the bearing elements in bad performance gearbox.
The method of identifying defects of the gearbox components has shown its
efficiency in this case.
66
4. IMPLEMENTATION OF THE RESULTS OF THE STUDY
4.1. The way of implementation
Research results are interesting to the users of lifting vehicles. As already
mentioned above, the escalator service of the Kyiv metro station set a technical
task of sustaining the normal performance state of the gearbox. Thus, in the field of
mechanical engineering there is a demand for similar projects. Therefore, it was
decided to implement the research results as a startup project. This project is
estimated using method described in reference book [16]
4.2. The idea of the project
In this section, the idea of a startup project is being described with the help
of Tab. 4.1.
Tab. 4.1. Description of the project
Project content Areas of application User benefits
The service of
vibrodiagnostics of
escalator drive gearboxes is
offered
Mechanical
Engineering, Civil
Engineering
1) Maintenance of
machines performance
2) Improved
performance due to fast
review
3) Cost savings
Implementation of the idea is possible provided that the necessary measuring
equipment and software are available. The following table depicts an analysis of
the benefits of the idea compared with the competitive one (Tab. 4.2).
67
Tab. 4.2. Weak, strong and neutral state respectively to competitor and
customer demands by characteristics of the idea
№
Technical and economic
characteristics of the
idea
Weak Neutral Strong
1.Estimation of the
project priceCompetitor — My project
2Accuracy of work
execution— My project Competitor
3
The depth of study of
the vibration
characteristics of the
gearbox
— Competitor My project
The Tab. 4.3 shows a comparison of my project's performance with the
competing ones. Indicators are divided into three groups: they have worse values
(W), the same values with competitors (N) and those that prevail competitor
characteristics (S).
Tab.4.3. Quality evaluation of project characteristics
№ Technical and economic
characteristics of the ideaThe idea of the project
1Increase of the reliability of the machine
workStrong
2 Cost of service from the client side Strong
68
3 Necessity of provision of initial capital Weak
4.2. Technological audit
This section analyses the technological feasibility of a project. The Tab. 4.4
below discusses the ways of the technological implementation of the idea.
Tab. 4.4. Technological audit
№ The idea of the projectWay of
implementation
Existence
of
technology
Availability
of
technology
1
Service on
vibrodiagnostics of
gearboxes of escalators
Usage of the
necessary measuring
equipment and
diagnostics method
to support the
reliable performance
of the gearbox
exists available
The way of implementation and opportunities are available
4.3 Analysis of market opportunities for project launch
This section analyses the possibility of introducing a product into the
market, depicting the threats of the project, paying attention to the market
environment, customer needs and opportunities of competitors.
The Tab. 4.5 below contains the analysis of demand, the dynamics of market
development and its volume.
69
Tab. 4.5. Preliminary description of the potential market
№ Indicators of the market situation Characteristic
1 Number of major participants, units 2
2 Total sales, UAH 500 000 UAH
3 Market dynamics (qualitative assessment) stable growth
4 Availability of entrance restrictions material
expences
5 Specific requirements for standardization and
certificationexist
6 Average rate of profitability in industry (or market)
(derived from statistics), %46
The market is relatively attractive to the project. The Tab. 4.6 analyzes
potential customers, their specific features and product requirements.
Tab. 4.6. Characteristics of potential customers
№ The need for the
market
Target
audience
Differences in the
behavior of various
potential target
groups of clients
Consumer
requirements
for the product
1. Support of
machine working
ability
General
Mechanical
Engineering
Financial capacityAccuracy,
economy and ease of use
70
Taking into account the mood of potential clients, it is necessary to conduct
an analysis of the market environment, namely analysis of the factors that threaten
or contribute to the success of the project.
Tab. 4.7. Threat factors
№Factor
Possibility
description
Possible action of
the company
1.
A more effective
and accurate
method of
condition
monitoring is
introduced on the
market Reduced demand
for use
Improvement of
the existing
methodology,
introduction of new
elements in the
analysis
2.High initial
investments
Consider the
possibility of an
initial loan,
attracting
additional
investment
Tab. 4.8. Positive factors
№ FactorPossibilities
description
Possible action of the
company
1. Great need for technologyIncreasing
demand
Active work with
clients
2. Relatively small operating costs Savings of funds Increase profits
71
It is then necessary to analyze the market conditions.
Tab. 4.9. Step-by-step analysis of competition in the market
Features of the
competitive environment
What does this feature
mean
Influence on enterprise
activity
Type of competition is
oligopoly
A small presence of
companies in this niche
business
Favorable market
conditions
National level of
competition
The market is open and
much of it is not covered
by competitors
Possibility of
unproblematic
expansion of presence
in the market
Intra-industry
characteristic
Mainly ongoing research
is conducted to develop
more accurate and simple
methods of analysis
The market needs
constant improvement
of technology
Price competition
Constant work is
underway to reduce the
cost of technology
It is necessary to
develop a cost-effective
method
Vivid intensity
We consider as
competitors of a company
with a similar product
Dependence on the
market
72
Porter's Five-Power Model [16] is a concept of the five main factors that
affect the attractiveness of the market, given the nature of the competition:
- present competitors,
- potential competitors,
- availability of substitute goods,
- competition between suppliers for power in the market,
- consumers.
For each factor, it is necessary to ensure a strong position to ensure the
necessary capital turnover and influence on other market participants. Let's
examine the competition in the industry by Porter.
Tab. 4.10. Porter competition analysis
Components
of the
analysis
Direct
competitors
in the
industry
Potential
competitorsClients
Substitute
products
None
Possible
occurrence
in the future
Efficiency,
economy and
accuracy
There are no
effective
substitutes
ConclusionsLow
intensity
At the
moment,
there is little
influence on
the market
Customers are
developing
technical tasks,
thus forming the
market, it is
necessary to
consider
Do not
threaten our
project
73
Tab. 4.11. Justification of the factors of competitiveness
№ Competitiveness Factor Substantiation (giving factors that make a
factor in comparing competitive projects is
significant)
1 Economical Relatively small costs in the application of the
technique
2 Accuracy of analysis Customer requirements for workability
3 Analysis speed Efficiency in response to emergencies
Based on the above factors, we will analyse the strengths and
weaknesses of the project.
Tab. 4.12. Comparative analysis of strengths and weaknesses "Methods of
vibration diagnosis of the gear unit of the escalator"
№ Competitiveness
Factor
Points
1-20
The rating of competitor's products in
comparison with the project "Method of
vibration diagnostics of gear reducer of
escalator drive"
-3 -2 -1 0 1 2 3
1 Economical 20 ●
2Accuracy of
analysis20 ●
3 Analysis speed 20 ●
74
The final analysis of the feasibility of a project is determined by a SWOT [16]
analysis (identification of strengths and weaknesses, opportunities and threats to
the project).
Tab. 4.13. SWOT-analysis of the startup project
Strengths: project economy and
measurement accuracy
Weaknesses: the need for further
refinement of the methodology
Opportunities: occupy a large part
of the market
Threats: putting into operation
more effective alternatives
The ways of launching the project into the market are being developed using
this method.
Tab. 4.14. Alternatives to the market introduction of the startup project
№Alternative to market behavior
Probability of
obtaining
resources
Terms of
implementation
1
Immediate introduction of the
existing technique on the
market to occupy the entire
niche
High 2-3 months
2
Improvement of technique,
carrying out of additional
experiments, certification
High 2 years
From the two alternatives we will choose a second, because the customer's
requirements for the accuracy of the analysis are constantly increasing, moreover,
additional details may be added when implementing this alternative. Also, this will
allow in the future to occupy most of the market.
75
4.4. Development of market strategy of the project
This section defines the behaviour when introducing a product on the
market. We start with the choice of the target group.
Tab. 4.15. Selection of target groups of potential consumers
№Description of the
profile of the
target group of
potential clients
Readiness
of
consumers
to accept
the
product
Tentative
demand
within the
target group
Intensity of
competition in
the segment
Ease of
entering a
segment
1Mechanical
EngineeringReady High Low
Relatively
complex
2Civil Engineering
and maintenanceReady
Higher than
average
Lower than
averageSimply
To operate in the selected segment, you need to develop a basic development
strategy.
Tab. 4.16. Definition of the basic development strategy
Selected alternative to
project development
Market
coverage
strategy
Key competitive
positions according
to the chosen
alternative
Basic
development
strategy
AlternativeCoverage of
80-95%Competitor №1
Product
specialization
strategy
76
The strategy of specialization is described in reference book [16]. After that
we defined the strategies. competitive behaviour:
Tab. 4.17. Definition of the basic strategy of competitive behavior
Is the project a
"pioneer" in the
market?
Will the company
search for new
customers, or take
away existing
competitors?
Will the company
copy the main
characteristics of
the competitor's
product, and
which?
Competitive
behaviour
strategy
Yes Yes
Copy only
commonly used
ideas
Imitator
strategy
Used behaviour strategy depicted in reference book [16]. As a result of the
work we received the basic strategy of development and competition in the market,
selected target groups of clients, with whom we work.
77
4.5 Development of the marketing program of the start-up project
First, it is necessary to form the marketing concept of the product. Therefore,
we will analyze the results of the previous analysis.
Tab. 4.18. Identify key benefits of the concept of a potential product
№Need
Benefit offered by
the product
Key benefits relatively
to competitors
1Cost effectiveness of
goodsReduce the cost Improved efficiency
2
Increased demand in the
field of mechanical
engineering and
machine operation
Accurate and fast
results of analysis
Perfect analysis
technique
We continue with development of the three-dimensional marketing model of the product.
78
Tab. 4.19. Description of the three levels of the product model
Levels of product Essence and components
I. Product as was plannedAccuracy and cost-effectiveness of
analysis
ІІ. Real product
Properties / characteristics
1. Technological,
2. Economical.
Quality: The theory is confirmed by
means of modelling and experiments
Name: Advanced system of vibration
analysis
ІІІ. Product with
reinforcements―
How the potential product will be protected from copying: due to the
uniqueness of the idea and patent law
Determine the price limits for setting the price for our service. This analysis was conducted through the search of targeted information through the Internet.
Tab. 4.20. Determination of price limits
The level of
prices for
substitute
goods
The price level
for analogue
goods
The level of income of
the target group of
consumers
The upper and lower
limits of the price of a
product / service
-2000-9000
UAH/mth2500000 UAH1) 2000/9000 UAH/mth
1)UAH – Ukrainian Hryvna
79
Next the path of optimal distribution of goods to be determined
Tab. 4.21. Formation of the sales system
Specifics of purchasing
behavior of target clients
Sales functions to
be performed by the
supplier of the
product
The depth
of the
distribution
channel
Optimal sales
system
Service on a regular
basis
Informing and
executionDeep Own sales system
The last step is to create a concept for marketing communications
Tab. 4.21. The concept of marketing communications
Specif
icity of the
behaviour of
target clients
Communi
cation channels
used by target
customers
Key
positions selected
for positioning
The
task of an
advertisement
Conce
pt of
advertising
appeal
Custo
mized for
conversation
Internet
and intra-
industry
communication
Advertisin
g on the Internet
and working with
clients of the
target group
Extendi
ng targeted
customers
The
product
provides the
best
precision
and cost-
effectiveness
Conclusions
Introduction of research results is profitable and expedient.
Need constant cooperation with clients to ensure the success of the goods.
Marketing strategy for bringing the idea to the market is selected.
80
The idea has important advantages in the market of equipment condition monitoring due to its uniqueness.
81
5. CONCLUSIONS
The task of ensuring the reliable performance of the gearbox of the tunnel
escalator of the subway was set. The goal was to develop a method for identifying
the defects of the gearbox of the metropolitan escalator drive by the method of
vibration diagnostics. Within the framework of the program for accomplishing this
goal, four tasks were set.
The first task involved collecting materials on the topic of the master's
thesis. The typical defects of the reducer, methods of their vibration diagnostics
and methods of processing the vibration signal were analysed. After analysing the
materials, the advantages and disadvantages of various methods of vibration
diagnosis were identified. As a result, a method based on the transformation of the
vibration signal into the spectrum was chosen as a tool, and it was decided to
develop its own defect identification method for the analysis of the damages of the
gearbox.
The measuring equipment and software were selected for signal recording
and processing purposes, and a measurement scheme was chosen for reliable
results. Vibration signals processing and analysis schemes were also proposed, and
their implementation with the help of software was established.
After carrying out of experimental researches, methods of processing and
analysis of vibration signals were applied to them. Measurement parameters of the
signal from the escalator drive gearbox were established, as well as the suitability
for applying the technique of processing the vibration signal was confirmed. The
method of analysis of the vibration signal of the damaged reducer proposed in this
thesis has shown its effectiveness in practice, and analysis of the elements of the
escalator allowed to confirm the reliability of both methods.
The marketing research of the idea was conducted and it proved that the
implementation of the results of this work is profitable and effective.
82
Therefore, I believe that the tasks set for implementation in the framework
of the master thesis are fully implemented. For further research the problems that
remain are: modelling of the defect formation process and construction on this
basis of a system of structural monitoring of the state of the gearbox of the metro
escalator.
83
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