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

6. BIBLIOGRAPHY

1. Klyuiev V. Non-destructive monitoring: Reference book, B. 7: Method of acoustic emission. Vibrodiagnostics, V. Klyuiev. – М.: Mechanical Engineering, 2005. – 829 p.

2. Starzhynskiy V. Observation of possible failures of electrical drive gearboxes performance, V. Starzhynskiy, E. Shalobaiev, D. Surikov, T. Tolochka., Tula SU periodic magazine. Technical sciences. – 2011. – №5. – P. 277–285.

3. Xieier-Tos H. The History of gearing failures // Couplings and transmissions, 1996. – №1. – P. 29–32.

4. H. Budienkov, O. Niedzviezkaya Usage of the acoustic emission methods for gearing diagnostics // Couplings and transmissions, 1997. – №1. – P. 40–52.

5. Shalobaiev E. Method of a complex study and diagnostics of friction units in equipment // International symposium papers «Hydrodynamic lubrication theory": in 2 b. B. 2. – М.: Mechanical Engineering -1, 2006. – P. 343–353.

6. Podmastieriev K. Electroparametrical methods of the rolling support complex diagnostics, K. Podmastieriev. – M.: Mechanical Engineering, 2001. – 376 p.

7. Rusov V. Diagnostics of the equipment of the revolving equipment by the vibration signal, V. Rusov. – Perm, 2012. – 252 p.

8. ISO 10816-1:2016 Mechanical vibration - Measurement and evaluation of machine vibration - Part 1: General guidelines.

9. PCB Model 353B15 Specifications // PCB Piezotronics.

10. PCB Model 380E09 Specifications // PCB Piezotronics.

11. NI USB-9215 Series User Guide and Specifications // National Instruments – Internet address: http://www.ni.com/pdf/manuals/371568e.pdf. – access date: 01.03.2019.

12. Barszcz T. Fault Detection Enhancement in Rolling Element Bearings Using the Minimum Entropy Deconvolution / T. Barszcz, N. Sawalhi. // Archives of Acoustics. – 2012. – №37. – P. 131–141.

13. Thanagasundram S., A fault detection tool using analysis from an autoregressive model pole trajectory, S. Thanagasundram, S. Spurgeon, F. Schlindwein. // Journal of Sound and Vibration. – 2008. – №317. – P. 975–993.

84

14. All about Vibration Measuring Systems // IMW Corporation – Internet address: http://www.imv.co.th/e/pr/vibration_measuring/chapter03/. – access date: 01.03.2019.

15. Marple Jr. S., Digital Spectral Analysis // Dover Publications. – 2019 – 432 p.

16. Solodkiy V. Guidelines for organizational moments of Master Thesis // Igor Sikorsky KPI. – 2016. – 64 p.

17. Medvedev S., Perov M. Fourier transform and classic digital spectral analysis // Special practicum in radio physics and electronics. NNGU. – 2001.

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