CHAPTER-I

OBJECTIVE AND SCOPE OF THE PROJECT

1.1 INTRODUCTION

In the early days, equipment maintenance was conducted only when

equipment actually failed. The work was more “fix it” than maintenance. Shortly

thereafter, came the recognition that performing regular maintenance and

refurbishment tasks on equipment could keep equipment operating longer between

failures. This became known, variously, as Periodic Maintenance, Calendar Based

Maintenance or Preventive Maintenance (PM). The goal was to have most of the

equipment be able to operate most of the time until the next scheduled maintenance

outage. This approach is also outdated. Now Condition monitoring has made good

progress in recent years maintenance is being carried out based on condition of

machine which reduces the cost of unnecessarily opening of equipment. Most of

the defects encountered in the rotating machinery give rise to a distinct vibration

pattern (vibration signature analysis techniques)Vibration Monitoring is the ability to

record and identify vibration “Signatures” which makes the technique so powerful

for monitoring rotating machinery. Vibration analysis is normally applied by using

transducers to measure acceleration, velocity or displacement. The choice largely

depends on the frequencies being analyzed.

Condition monitoring has made good progress in recent years in identifying

any types of deterioration in plant machinery, so that pro-active maintenance can

be performed, improving overall plant productivity. Vibrations are found almost

Everywhere in power plants. Rotating machinery vibrates due to unbalances,

misalignments and imperfect bearings; Vibration, in general, reduces equipment

life and, in extreme cases, can result in equipment damage or even catastrophic

failures. On the other hand, existence of vibration can also be used to diagnose

equipment problems and provide.

1

1.2 OBJECTIVE OF THE PROJECT

The new generation of condition monitoring and diagnostics systems differs by

the detailed solution of diagnostic problems that allows making a step from machine

vibration state monitoring to the monitoring of the machine technical condition. Most

rotating machine defects can be detected by such a system much before dangerous

situations occur.

The aim of vibration monitoring is the detection of changes in the vibration

condition of the object under investigation during its operation. The cause of such

changes is mainly the appearance of a defect. The number of such points can be reduced

to one or two for each object to be monitored if there is a common casing.

The main objective of this project is to identify the causes of significant vibrations

developed in the main pump driving end and main pump non driving end and to rectify

those vibrations by proper action and to develop an simple ANN for the fault diagnosis

boiler feed pump.

1.3 ORGANIZATION OF THE WORK

The project is organized into following activities:

Chapter I highlights the importance, objective of the study and methodology of the work.

Chapter II deals with the information from the research papers.

Chapter III gives the introduction of maintenance strategies, predictive maintenance

procedure, and condition monitoring techniques and briefly about the vibration

monitoring.

Chapter IV describes the theory regarding basics of vibration, vibration instrumentation,

and DATAPAC 1500 the instrument used for the vibration analysis.

Chapter V deals with the vibration analysis procedure and fault diagnosis of the

machinery.

Chapter VI gives the overview of the artificial neural networks, back propagation

algorithm and application ANN to vibration analysis.

Chapter VII deals with the case study of the BOILER FEED PUMP. The vibration

spectrum analysis and the experimentation and the fault diagnosis of the machine.

Chapter VIII presents the application of ANN for the fault recognition on BFP.

Chapter IX lists out the results, conclusions and future scope of the work.

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CHAPTER-II

LITERATURE REVIEW

2.1 INTRODUCTION

A literature survey was taken up to review present status of research in the field of

condition monitoring. Machine condition monitoring is gaining importance in industry

because of the need to increase reliability and to decrease the possibility of production

loss due to the machine breakdown. The use of vibration and acoustic emission signals is

quite common in the field of condition monitoring of rotating machinery. By comparing

the signals of a machine running in the normal and faulty conditions. Detection of faults

like unbalance, rotor rub, shaft misalignment, gear failure and bearing defects is possible.

These signals can also be used to detect the incipient failures of the machine components,

through the online monitoring system, reducing the possibility of catastrophic damage

and the down time. Some of the recent works in this area are.

R.K BISWAS, [1] Scientist and head, condition monitoring group, CMERI,

DURGAPUR. Presented paper on “Vibration based condition monitoring of rotating

machines” states that Condition Monitoring is defined as the collection, comparison and

storage of measurements defining machine condition. Almost everyone will recognize the

existence of a machine problem sooner or later. One of the objectives of Condition

Monitoring is to recognize damage that has occurred so that ample time is available to

schedule repairs with minimum disruption to operation and production. In this aspect

vibration is probably the best operating parameter to judge dynamic condition of

machines. Condition monitoring is essentially a screening process in which

measurements and other data are compared to pre-established norms for the purpose of

recognizing abnormal variations.

A machine seldom breaks down without warning. The signs of impending

breakdown are almost present long before the catastrophic failure. Vibration signals

define the dynamic property of the machine including various faults of machine like

bearing instability, unbalance, coupling misalignment, looseness, rubs, etc. Vibration

3

characteristics also define early indication of defects on components such as rolling

element bearing and gears.

M.Todd, S.D.J.McArthur, G.M.West, J.R.McDonald, S.J.Shaw. J.A.Hart [2]

paper on “the design of a decision support system for the vibration monitoring of

turbine generators” they discussed about the Condition Monitoring (CM) systems

monitor the health of expensive plant items such as turbine generators. They interpret

turbine parameters by signaling an alarm when pre-defined limits are breached. This is a

time consuming and laborious process due to the volume of data interpreted for each

alarm. In order to reduce the burden of alarm assessment, a Decision Support System

(DSS) is proposed. The DSS will feature a Routine Alarm Assessment (RAA) module

which provides an initial analysis of the alarms, highlighting those with no further

operational consequence and enabling the expert to focus on those which indicate a

genuine problem with the turbine. The implementation of an RAA prototype is discussed

along with how this will act as a foundation for a full alarm interpretation and fault

diagnostic system.

David Clifton,[3] St. Cross College, December, 2005 made research on

“Condition Monitoring of Gas-Turbine Engines” This report describes preliminary

research into condition monitoring approaches for modern gas-turbine aircraft engines,

and outlines plans for novel research to contribute to machine learning techniques in the

condition monitoring of such systems. A framework for condition monitoring of aircraft

engines is introduced, using signatures of engine vibration across a range of engine

speeds to assess engine health. Inter- and intra-engine monitoring approaches are

presented, in which a model of engine normality is constructed using vibration data from

other engines of its class, or from the test engine itself, respectively.

T.W. Verbruggen[4] a book on “Wind Turbine Operation & Maintenance

based on Condition Monitoring”. This report is part of the project entitled WT_Ω

(WT_OMEGA = Wind Turbine Operation and Maintenance based on Condition

Monitoring) which has been carried out in co-operation withLagerwey the Wind Master,

Siemens Nederland, and SKF.

4

A Ramachandra, S B Kandagal, [5] worked on “Prediction of Defects in

Antifriction Bearings using Vibration Signal Analysis” Condition monitoring of

antifriction bearings in rotating machinery using vibration analysis is a very well

established method. It offers the advantages of reducing down time and improving

maintenance efficiency. The machine need not be stopped for diagnosis. In order to

prevent any catastrophic consequences caused by a bearing failure, bearing condition

monitoring techniques, such as, temperature monitoring, wear debris analysis, oil

analysis, vibration analysis and acoustic emission analysis have been developed to

identify existence of flaws in running bearings. Among them vibration analysis is most

commonly accepted technique due to its ease of application.

Sadettin Orhan, Nizami Aktu¨rk, Veli C¸ elik,[6] worked on “Vibration

monitoring for defect diagnosis of rolling element bearings as a predictive

maintenance tool: Comprehensive case studies” Vibration monitoring and analysis in

rotating machineries offer very important information about anamolies formed internal

structure of the machinery. In this study, the vibration monitoring and analysis case

studies were presented and examined in machineries that were running in real operating

conditions. Failures formed on the machineries in the course of time were determined in

its early stage by the spectral analysis. It was shown that the vibration analysis gets much

advantage in factories as a predictive maintenance technique.

Peter W. Hills, Mechanalysis (India) Limited, India, “A more intelligent

approach to rotating equipment monitoring”,[7]. Proactive condition management of

rotating machinery is not new to the power sector and is applied widely but with varying

degrees of success. The financial benefits have long been recognized and widely

reported, but the cost of implementation, required expertise and continuity of the systems

remain as constraints to its broader use. To date, the focus of condition monitoring of

rotating equipment has been on detecting the mechanical aspects of a machine, such as

imbalance, alignment, etc, with little attention being paid to the on-line detection of its

electrical system.

Cornelius [8], Scheffer, describes the paper on “Pump Condition Monitoring

through Vibration Analysis” It is well-known that vibration analysis is a powerful tool

5

for the condition monitoring of machinery. This especially applies to rotating equipment

such as pumps. Through the years a variety of vibration-based techniques have been

developed and refined to cost-effectively monitor pump operation and the onset of

failures. This paper is an overview of a variety of vibration-based condition monitoring

techniques for pumps. In some instances these techniques are also applicable to improve

the operation and efficiency of pumps. Specific aspects to consider when taking vibration

measurements on pumps are for instance where to take readings, which type of probe to

use, what frequency range should be used, what the settings on the analyzer should be,

etc.

Sheng Zhang, Joseph Mathew, Lin Ma, Yong Sun and Avin Mathew,[9]

presented a paper on “Statistical condition monitoring based on vibration signals”.

Designing control limits for condition monitoring is an important aspect of setting

maintenance schedules and has been virtually ignored by researchers to date. This paper

proposes a novel statistical process control tool, the Weighted Loss function CUSUM

(WLC) chart, for the detection of condition variation. The control limit was designed

using baseline condition data, where the process was fitted by an autoregressive model

and the residuals were used as the chart statistic. The condition variation is reflected by

the changes of mean and variance of the statistic’s distribution against baseline condition,

which can be detected by a single WLC chart. The approach was evaluated using a case

study which showed that the chart can detect faulty conditions as well as their severity.

The proposed approach has the advantage of requiring healthy baseline data only for the

design of condition classifiers. It is applicable in numerous practical situations where data

from faulty conditions are unavailable.

P. Caselitz, J. Giebhardt,[10], presented a paper on “Condition Monitoring

and Fault Prediction for Marine Current Turbines”. This paper introduces the

concept of condition monitoring and fault prediction for marine current turbines. It will

describe the required hardware to perform condition monitoring measurements and some

appropriate fault prediction algorithms specific for marine current turbines. Furthermore,

concepts for communication and data base handling will be introduced. For the above

mentioned items, some relevant standards and technical guidelines will be addressed.

6

Steven M. Schultheis,[11], Charles A. Lickteig, presented a paper on

“RECIPROCATING COMPRESSOR CONDITION MONITORING”. This paper

will discuss risk-based decision making in regard to measurements and protective

functions, online versus periodic monitoring, proven and effective measurement

techniques, along with a review of both mechanical- and performance-based

measurements for assessing machine condition. Case histories will also be presented to

demonstrate some of the concepts.

Peter W. Hills,[12] Mechanalysis (India) Limited, India presented a paper on

A more intelligent approach to rotating equipment monitoring in the journal The

article is based on the paper ‘Intelligent Condition Management On-line’ The majority of

condition monitoring regimes for power plants’ rotating equipment is focused the

detection of mechanical faults, with little attention paid to electrical faults in equipment.

This could be about to change with the introduction of an on-line monitoring system that

‘learns’ to detect both types of fault.

L. B. Jack, A. K. Nandi,[13] presented a paper on “Feature Selection for ANNs

using Genetic Algorithms in Condition Monitoring”. The work presented in this paper

the work presented in this paper is based around experimental results per- formed on

vibration data taken from a small test rig which was tested with a number of

interchangeable faulty roller bearings. This is used to simulate the type of problems that

can commonly occur in rotating machinery. Rolling elements, or ball bearings, are one of

the most common components in modern rotating machinery; being able to detect

accurately the existence of a fault in a machine can be of prime importance in certain

areas of industry.

Ms S Wadhwani, Dr S P Gupta, Dr V Kumar, [14] “Wavelet Based

Vibration Monitoring for Detection of Faults in Ball Bearings of Rotating

Machines” this paper describes the application of wavelet transform (WT) for detection

of bearing damage from the vibration signal of the bearing. The wavelet transform

approach enables instant to instant observation of the contribution of different

frequency components over the full spectrum from. Actually, wavelet transform acts as a

mathematical microscope in which one can observe different parts of the signal by

7

adjusting the focus. A new technique combining the WT with neural network for

detection and classification of ball bearing fault in a three phase, 3.75 kW inductions

motor is presented in this paper. The method is tested successfully for three faulty

bearing conditions: crack in inner race, crack in outer race and defect in balls.

Zhigang TIAN, [15] “An Artificial Neural Network Approach for Remaining

Useful Life Prediction of Equipments Subject to Condition Monitoring”. Accurate

equipment remaining useful life prediction is critical to effective condition based

maintenance for improving reliability and reducing overall maintenance cost. An

artificial neural network (ANN) based method is developed for achieving more accurate

remaining useful life prediction of equipment subject to condition monitoring. The ANN

model takes the age and multiple condition monitoring measurement values at the present

and previous inspection points as the inputs, and the life percentage as the output.

Techniques are introduced to reduce the effects of the noise factors that are irrelevant to

equipment degradation. The proposed method is validated using real-world vibration

monitoring data.

N.M. ROEHL C.E. PEDREIRA" H.R. TELES DE AZEVEDO [16] presented

a paper on “Fuzzy art neural network approach for incipient Fault detection and

isolation in rotating machines”. A neural network approach for on-lie detection and

isolation of faults in rotating machines is proposed. The methodology is based on

clustering of shaft vibration monitoring data by using fuzzy art neural networks. Fault

isolation is obtained by retrieving stored associations among known physical faults and

clusters. The proposed scheme is implemented to detect and isolate different operation

modes in a hydro generator.

P.A.L. Ham, B.Sc.C.Eng..F.I.E.E. [17] “Trends and future scope in the

monitoring of large steam turbine generators” Current practices in the monitoring of

large steam turbine generators are briefly discussed, consideration being given to the

traditional range of turbine supervisory equipment, and the more extended facilities

which are sometimes now associated with rotating machinery, such as vibration

monitoring, together with the more generalized data logging systems now specified by

some Utilities. Consideration is given to the possible range of parameters and equipment

8

areas which may now be incorporated into a monitoring scheme, and attention is drawn

to the advances in display technology and operator interfaces which are now possible at

moderate cost. In a concluding section, a range of monitoring functions which could be of

wide general application in the field of steam turbine generators is discussed.

2.2 SUMMURY

This literature review presents an overview of the vibration based condition

monitoring of the rotating equipments in the thermal power plants. This literature review

also contains the review methodologies of the predictive maintenance technology.

9

CHAPTER-III

MAINTENANCE STRATEGIES

3.1 INTRODUCTION

General industrial profitability is effected both by on stream functions and

maintenance costs. Any system must account for the optimum maintenance that can be

performed by an organizational setup. Maintenance besides trying to better its own

efficiency and mechanical performance must solve the problem of failure.

3.2 CLASSIFICATION OF MAINTENANCE STRATEGIES

Maintenance strategies are classified by three developmental stages:

  1. Break down maintenance

  2. Preventive maintenance

3. Predictive maintenance

3.2.1 Break Down Maintenance

This provides the replacement of defective part or machine after the machine

becomes incapable of further operation. Break down maintenance is the easiest method to

follow and it avoids the initial costs on training personnel and other related upfront costs.

Draw backs of the break down maintenance are

1. Failures are untimely.

2. Since machine is allowed to run till to failure repair is more expensive, sometimes total

replacement is required.

3. Failures may be catastrophic. Hence loss will be more.

4. Production loss will be more, as it requires more time to restore normalcy.

5. It reduces the life span of the equipment.

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3.2.2 Preventive Maintenance

In preventive maintenance, maintenance is scheduled on calendar or hours to run

and is performed irrespective of machine conditions.

  Advantages:

  1. Damage to machine is less.

  2. Down time of machine is reduced by 50-80%.

  3. Lower expenses of overpay may same as much as 30%.

  4. Increases the equipment life expectancy.

  5. Reduces maintenance cost by reducing the

I. Capital spending by 10-20%.

                                          II. Labor cost by 10%.

                                          III. Material cost by 30%

  6. Improve the employee’s safety.

  7. Preventive maintenance results in a catastrophic failure and down time is required

to complete all schedule maintenance costs.

Disadvantages:

1. periodically dismantling of each and every critical machine is expensive and time

consuming.

2. It may lead to unnecessary inspections even on healthy machine also which may

further lead to more complications.

3. It is difficult to predict time interval between inspections, which ultimately may

lead to break down maintenance.

Fig: 3.1 Failure rate or bath tub curve

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  Preventive maintenance alone cannot eliminate break down. The causes of

equipment failure change with the passage of time fig: shows the failure rate curve which

is also called as life span characteristic curve or bath tub curve. Failure rate is taken on

ordinate and time is taken on abscissa. When the equipment is new there is a high failure

rate due to design and manufacturing errors. Failure rate is increases once again since the

equipment approaches the end of its failure.

3.2.3 Predictive Maintenance

Predictive maintenance (PdM) techniques help determines the condition of in-

service equipment in order to predict when maintenance should be performed. This

approach offers cost savings over routine or time-based preventive maintenance, because

tasks are performed only when warranted.

Predictive maintenance or condition-based maintenance, attempts to evaluate the

condition of equipment by performing periodic or continuous (online) equipment

condition monitoring. The ultimate goal of PdM is to perform maintenance at a scheduled

point in time when the maintenance activity is most cost-effective and before the

equipment loses optimum performance. This is in contrast to time- and/or operation

count-based maintenance, where a piece of equipment gets maintained whether it needs it

or not.

Most PdM inspections are performed while equipment is in service, thereby

minimizing disruption of normal system operations. Adoption of PdM can result in

substantial cost savings and higher system reliability. Trending and analyzing machinery

parameters we can detect the developing problems in early stages. Hence repair works

can be carried out before failure of a machine

Advantages:

Shut down can be done at convenient times.

Work schedule can be prepared for mobilizing men, tools and replacement parts

before shut down reducing machinery down time.

Identifying problem, costly trial and error procedures to solve a problem can be

avoided.

Machine in good running condition can run continuously as long as problem

develops.

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Disadvantages: 

Requires skilled labor. 

It is costly affair.

Predictive Maintenance Program:

For all machine common characteristic is vibrations and hence vibrations become

a powerful tool in implementing predictive maintenance program. The vibration

predictive maintenance program has four steps:

1. detection

2. analysis

3. correction

4. confirmation 

Detection

  First select all available critical machines in the plant.  prepare a schedule for all

these machines for data collection identify bearing locations of the machine train motor

non drive end, MNDE, FNDE, FDE, PNDE, PDE, etc. identify the directions where

vibration data is collected like h, v, a etc. define which vibration parameters are to be

collected via displacement, velocity, acceleration etc. after doing all these, start collecting

vibrating data and related data and record them. Collect the data for every fortnight or

monthly or so .by trending and interpreting the data identify source of vibrations.

Analysis

  After identifying the source of vibrations analyze to pin point the root cause for

vibrations. This can be achieved by eliminating process. Follow confirmative procedures

in support of analysis

Correction

Open and inspect the machine at a convenient time and make necessary corrections.

Confirmation

After corrections put the machine in service and again collect vibration data and look for elimination of the source.

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3.3 CONDITION MONITORING

3.3.1 Introduction

Condition monitoring pre-supposes knowledge of machines condition and its rate

of change, which can be ascertained by selecting a suitable parameter for measuring

deterioration and recording its value at intervals either on a routine or continuous basis.

This is done while the machine is running. The data obtained may then be analyzed to

give a warning on failure. This activity is called as condition monitoring.

Condition monitoring essentially involves regular inspection of equipment

using human sensory facilities and a mixture of simple aids and sophisticated instruments

The central emphasis is however on the fact that most inspections should be preferably

done while the machine is running.

Condition monitoring is concerned with the analysis and interpretation of

signals from sensors and transducers installed on operational machinery, employing

sensors positioned outside the machine, often remove from the machine components

being monitored, normally does the monitoring of a machine condition and health, using

established techniques, the analysis of information provided by the sensor output and

interpretation of the evaluated output is the needed to establish what actions to be taken.

Condition monitoring can also be a test and quality assurance, system for

continuous processes as well as discrete component manufacture. It maximizes the

performance of the company’s assets by monitoring their condition and ensuring that they

are installed and maintained correctly, it aims of detecting condition leading to

catastrophic breakdowns and loss of service, reducing maintenance overhauls, fine

turning of operating equipment increasing production and operating efficiency and

minimizing the replacement parts inventory. This is because a readily monitor able

parameter of deterioration can be found in every plant, Machinery and probabilistic

element in future prediction is highly reduced or almost eliminated thus maximizing the

items life by minimizing the effect of failure

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3.3.2 Condition Monitoring Techniques

There are only seven main techniques of condition monitoring.

They are:

a) Visual monitoring

b) Contaminant or debris monitoring

c) Performance and behavior monitoring

d) Corrosion monitoring thermograph

e) Sound monitoring.

f) Shock pulse monitoring.

g) Vibration monitoring.

a. Visual Monitoring

Visual monitoring involves the inspections and recording of surfaces to detect

Such as surface cracks and their orientation. Oxide films, weld defects and the presence

of potential sources such as sharp notches or misalignment.

b. Contaminant Monitoring

Debris analysis is well proving in all types of industrial and works on the

principle of taking or known quantity. Sample example: a gear box, then for analyzing

the amount and type of foreign particles present in the sample. This will be show such

problems, as gear wear, to the sample detects particles of gear material .oil analysis

differs from debris analysis so for as this technique allows an assessment of the actual

condition of the oil in use. That is whether the oil quality is good enough for the

application after period of use or it is burnt or exceeded its useful use.

c. Performance and Behavior Monitoring

Performance and behavior monitoring involves checking the performance of

machine or component to see whether it is behaving correctly. Monitoring the

performance of the bearing by measuring its temperature to see whether it is carrying out

its function.

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d. Corrosion Monitoring

Corrosion monitoring has actually applied to the fixed plane containing

aggressive material to monitor the rates of internal corrosion of walls of the equipment. It

is the system systematic measurement of corrosion or degradation of an a item of

equipment, with the aim of assisting and understanding the correct corrosion process of

obtaining information for the use of controlling corrosion

e. Thermography

Thermograph is a rapidly developing; it provides color cameras and videos,

clean indicator of heat loss, hot spot, cold spot, such as switchgear or any piece of plant

or production where temperature or its effects is important, it can be used both as

maintenance tools or a quality assurance tool. Shock pulse method is unique technique

for monitoring the true operation of the bearing by measuring the pressure wave

generated by the instantaneous mechanical impact.

f. Sound Monitoring:

Human operators are normally highly sensitive to the detection of defects as a

result of sudden change of sound due to the looseness of component results of wear or

slackening of fastening are particularly susceptible to such forms monitoring The most

widely available micro phones for sound or piezoelectric moving coils and condensers.

16

g. Vibration Monitoring:

Vibration monitoring measures the frequency and amplitude of vibrations. It is

Known that readings will change as machinery wear sets in. such readings can be

interpreted as indicators of the equipments condition, and timely maintenance actions can

be scheduled accordingly. Electrical machines and mechanical reciprocating or rotating

machines generate their own vibration signatures (patterns) during operation. However

such raw signals contain a lot of background noise, which makes it difficult or even

impossible to extract useful, precise information by simply measuring the overall signal.

It is thus necessary to develop an appropriate filter to remove the operationally and

environmentally contaminated components of signals (the background noise) so as to

reveal the clear signals generated by the events under study. To capture useful condition

monitoring data, vibration should be measured at carefully chosen points and directions.

Vibration monitoring is a well established method for determining the physical

Movements of the machine or structure due to imbalance mounting an alignment this

method can be obtained as simple. Easy to use and understand or sophisticated real time

analysis, vibration monitoring usually involves the attachment of a transducer to a

machine to record its vibration level special equipments is also available for using the

output from sensor to indicate nature vibration problem and even its precise cause.

Transducers for the measurement of vibrations employ electromagnetic

electrodynamics, capacitive, piezoelectric, or strain gauge principles out of these

piezoelectric accelerometers is most widely used since the recent past, Among the

monitoring techniques vibration monitoring as gained considerable importance because

of following fundamental factors

1) All rotation and reciprocating machines vibrate either to a smaller or greater

extent machines vibrate because of defects or incurrence in system

2) When inaccuracies or more it results in increased vibration each kind of defect

provides a vibration characterized in the unique way.

Therefore vibration characteristics reveal the health condition of machine.

17

CHAPTER-IV

BASICS OF VIBRATION

Definition

Vibration can be defined as simply the cyclic or oscillating motion of a machine

or machine component from its position of rest. Vibration refers to mechanical

oscillations about an equilibrium point. The oscillations may be periodic such as the

motion of a pendulum or random such as the movement of a tire on a gravel road.

Fig 4.1 basic vibration representation

Vibration is occasionally "desirable". For example the motion of a tuning fork, the

reed in a woodwind instrument or harmonica, or the cone of a loudspeaker is desirable

vibration, necessary for the correct functioning of the various devices.

More often, vibration is undesirable, wasting energy and creating unwanted sound

– noise. For example, the vibration motions of engines, electric motors, or any

18

mechanical device in operation are typically unwanted. Such vibrations can be caused by

imbalances in the rotating parts, uneven friction, the meshing of gear teeth, etc. Careful

designs usually minimize unwanted vibrations.

4.1 What Causes Vibration?

Forces generated within the machine cause vibration. These forces may be one that

Change in direction with time, such as the force generated by a rotating

unbalance.

Change in amplitude or intensity with time, such as the unbalanced magnetic

forces generated in an induction motor due to un equal air gap between the

motor armature and stator (field).

Result in friction between rotating and stationary machine components in

much the same way that friction from a rosined bow causes a violin string to

vibrate.

Cause impacts, such as gear tooth contacts or the impacts generated by the

rolling elements of a bearing over flaws in the bearing raceways.

Cause randomly generated forces such as flow turbulence in fluid handling

devices such as fans, blowers and pumps, or combustion turbulence in gas

turbines or boilers.

4.2 What is Machine Vibration?

Most of us are familiar with vibration; a vibrating object moves to and fro, back

and forth. A vibrating object oscillates. We experience many examples of vibration in our

daily lives. A pendulum set in motion vibrates. A plucked guitar string vibrates. Vehicles

driven on rough terrain vibrate, and geological activity can cause massive vibrations in

the form of earthquakes.

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Fig 4.2 Examples of vibration

There are various ways we can tell that something is vibrating. We can touch a

vibrating object and feel the vibration. We may also see the back-and-forth movement of

a vibrating object. Sometimes vibration creates sounds that we can hear or heat that we

can sense.

What is machine vibration? Machine vibration is simply the back and-forth

movement of machines or machine components. Any component that moves back and

forth or oscillates is vibrating. Machine vibration can take various forms. A machine

component may vibrate over large or small distances, quickly or slowly, and with or

without perceptible sound or heat. Machine vibration can often be intentionally designed

and so have a functional purpose.

At other times machine vibration can be unintended and lead to machine damage.

Most times machine vibration is unintended and undesirable. This book is about the

monitoring of undesirable machine vibration. Shown below are some examples of

undesirable machine vibration.

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Fig 4.3 vibrating parts

4.3 Vibration and Machine Life

Your first question may be: "Why worry about a machine's vibration?" obviously,

once a machine is started and brought into service, ft will not run indefinitely. In time, the

machine will fail due to the wear and ultimate failure of one or more of its critical

components. And, the most common component failure leading to total machine failure is

that of the machine bearings, since it is through the bearings that all machine forces are

transmitted. Of course, the next question is: "How long will be bearings last?" Although

an exact answer to this question is impossible, the manufacturers of rolling element

bearings attempt to estimate bearing life using the following calculation:

L 10 LIFE (HOURS) = 16.666/ RPM X (RATE / LOAD)3

Where: RPM = Machine rotating speed in Revolutions per Minute

RATE = the rated load capacity of the bearing (lbs.)

Load = the actual load to which the bearing is subjected.

This includes not only the static load due to the weight of the rotor, but the

dynamic load due to forces of unbalance, misalignment, etc., FORCES THAT CAUSE

VIBRATION.

According to this calculation to estimate bearing life, doubling the rotating speed

from, say 1800 RPM to 3600 RPM, would cut bearing life in half. However, by cutting

the load on the bearing by one-half would increase its service life by eight times (2-cubed

21

or 2 x 2 x 2 = 8). Of course, this estimate of bearing life does not take into consideration

other factors such as inadequate lubrication, lubricant contamination or damage from

improper storage or installation techniques.

From the above calculation, it can be seen that bearing load, including dynamic

load from vibratory sources such as unbalance and misalignment, has a significant effect

on bearing life and, ultimately, machine life. Further, the amount of vibration exhibited

by a machine is directly proportional-to the amount of force generated. In other words, if

the unbalance force is doubled, the resultant vibration amplitude will be doubled also. Or,

if the unbalance force is cut in half the unbalance -generated vibration will be cut in half

also. Therefore, the answer to the question: "Why worry about a machine's vibration?" is

simple:

1. Increased dynamic forces (loads) reduce machine life.

2. Amplitudes of machinery vibration are directly proportional to the amount of dynamic

forces (loads) generated. If you double the force, you double the Vibration.

3. Logically then, the lower the amount of generated dynamic forces, the lower the levels

of machinery vibration and the longer the machine will perform before failure

It's that simple. Low levels of vibration indicate low vibratory forces which, in turn,

results in improved machine life.

With few exceptions, when the condition of a machine deteriorates, one of two possibly

both things will generally happen:

The dynamic forces generated by the machine will increase in intensity, causing

an increase in machine vibration. Wear, corrosion or a build-up of deposits on the

rotor may increase unbalance forces. Settling of the foundation may increase

misalignment forces or cause distortion, piping strains, etc.

The physical integrity (stiffness) of the machine will be reduced, causing an

increase in machine vibration.

Loosening or stretching of mounting bolts, a broken weld, a crack in the

foundation, deterioration of the grouting, increased bearing clearance through

wear or a rotor loose on its shaft will result in reduced stiffness to control even

normal dynamic forces, Thus, it should be obvious that an increase in machinery

vibration is a positive indicator of developing problems. In addition, each

22

mechanical or operational problem generates vibration in its own unique way. As

a result, it is also possible to identify the specific nature of the problem by simply

measuring and noting its vibration characteristics. The techniques of identifying

specific defects and problems are presented in the section on VIBRATION

ANALYSIS.

4.4 Characteristics of Vibration

Whenever vibration occurs, there are actually four forces involved that

determine the characteristics of the vibration. These forces are:

The exciting force, such as unbalance or misalignment.

The mass of the vibrating system, denoted by M.

The stiffness of the vibrating system, denoted by the symbol K.

The damping characteristics of the vibrating system, denoted by the symbol C.

The exiting force is trying to cause vibration, where as the stiffness, mass and damping

forces are trying to oppose the exiting force and control or minimize the vibration.

The characteristics needed to define the vibration include:

Frequency

Displacement

Velocity

Acceleration

Spike energy

Phase

4.4.1 Vibration Frequency

The amount of time required to complete one full cycle of the vibration is called

the period of the vibration. If, for example, the machine completes one full cycle of

vibration in 1/60th of a second, the period of vibration is said to be 1/60th of a second.

Although the period of the vibration is a simple and meaningful characteristic, a

characteristic of equal simplicity but more meaningful is the vibration frequency.

Vibration frequency is simply a measure of the number of complete cycles that occur in a

specified period of time such as "cycles-per-second" (CPS) or "cycles-per-minute"

23

(CPM). Frequency is related to the period of vibration by this simple formula:

Frequency = 1/Period

In other words, the frequency of a vibration is simply the "inverse" of the period of the

vibration. Thus, at the period or time required to complete once cycle is 1 / 60th of a

second, then the frequency of the vibration would be 60 cycles-per-second or 60 CPS.

Given a frequency expressed in Hz, you can convert it to CPM:

CPM = Hertz x 60 Seconds/Minute

Given a frequency expressed in CPM, you can convert it to Hz:

Hertz = CPM/60 Seconds/Minute

Significance of Vibration Frequency

There are literally hundreds of specific mechanical and operational problems that

can cause a machine to exhibit excessive vibration. Obviously, when a vibration problem

exists, a detailed analysis of the vibration should be performed to identify or pinpoint the

specific cause. This is where knowing the frequency of vibration is most important.

Vibration frequency is an analysis or diagnostic tool.

The forces that cause vibration are usually generated through the rotating motion

of the machine’s parts. Because these forces change in direction or amplitude according

to the rotational speed (RPM) of the machine components, it follows that most vibration

problems will have frequencies that are directly related to the rotational speeds.

To illustrate the importance of vibration frequency, assume that a machine,

consisting of a fan operating at 2400 RPM and belt driven by a motor operating at 3600

RPM, is vibrating excessively at a measured frequency of 2400 CPM (1 x fan RPM), this

clearly indicates that the fan is the source of the vibration and not the motor or belts.

Knowing this simple fact has eliminated literally hundreds of other possible causes of

vibration.

Predominant Frequency: Predominant frequency is the frequency of vibration having

the highest amplitude or magnitude.

Synchronous Frequency: Synchronous frequency is the vibration frequency that occurs

at 1 x RPM.

Sub synchronous Frequency: Sub synchronous frequency is vibration occurring at a

frequency below 1 x RPM. A vibration that occurs at 1/2 x RPM would be called a Sub

24

synchronous frequency.

Fundamental Frequency: Fundamental frequency is the lowest or first frequency

normally associated with a particular problem or cause. For example, the product of the

number of teeth on a gear times the RPM of the gear would be the fundamental gear-

mesh frequency. On the other hand, coupling misalignment can generate vibration at

frequencies of 1 x, 2x and sometimes 3 x RPM. In this case, 1 x RPM would be called the

fundamental frequency.

Harmonic Frequency: A harmonic is a frequency that is an exact, whole number

multiple of a fundamental frequency. For example, a vibration that occurs at a frequency

of two times the fundamental gear mesh frequency would be called the second harmonic

of gear mesh frequency. A vibration at 2 x RPM due to, say, misalignment, would be

referred to as the second harmonic of the running speed frequency (1 x RPM).

Order Frequency: An order frequency is the same as a harmonic frequency.

Sub harmonic Frequency: A sub harmonic frequency is an exact submultiples (1/ 2, 1/3,

1/4, etc.) of a fundamental frequency. For example, a vibration with a frequency of

exactly 1/2 the fundamental gear-mesh frequency would be called a sub harmonic of the

gear mesh frequency. Vibration at frequencies of exactly 1/2, 1/3 or 1/4 of the rotating

speed (1 x RPM} frequency would also be called . Sub harmonic frequencies; and these

can also be called Sub synchronous frequencies. However, not all Sub synchronous

frequencies are sub harmonics. For example, a vibration with a frequency of 43% of the

running speed (1 x RPM) frequency is a Sub synchronous frequency but it is not a sub

harmonic.

4.4.2 Vibration Amplitude

As mentioned earlier, vibration frequency is a diagnostic tool, needed to help

identify or pinpoint specific mechanical or operational problems. Whether or not a

vibration frequency analysis is necessary, depends on how "rough" the machine is

shaking. If the machine is operating smoothly, knowing the frequency or frequencies of

vibration present is not important. The magnitude of vibration or how rough or smooth

the machine vibration is, is expressed by its vibration amplitude. Vibration amplitude can

be measured and expressed as:

Displacement

25

Velocity

Acceleration

SPIKE ENERGY

Vibration Displacement

The vibration displacement is simply the total distance traveled by the vibrating

part from one extreme limit of travel to the other extreme limit of travel. This distance is

also called the "peak-to-peak displacement". Peak-to-peak vibration displacement is

normally measured in units called mils, where one mil equals one-thousandth of an inch

(1 mil = 0.001 inch). Measured vibration amplitude of 10 mils simply-means that the

machine is vibrating a total distance of 0.010 inches peak-to-peak.

In Metric units, the peak-to-peak vibration displacement is expressed in micrometers

(sometimes called microns), where one micrometer equals one-thousandth of a millimeter

(1 micrometer = 0.001 millimeter).

Vibration Velocity

The vast majority of machine failures caused by vibration problems are fatigue

failures, & the time required to fatigue failure is determined by both how far an object is

deflected.(displacement) and the rate at which the object is deflected (frequency), of

course, displacement is simply a measure of distance traveled and frequency is a measure

of the number of times that “trip” is taken in a given period of time such as a minute or

second, if it is known how far one must travel in a given period of time, it is a simple

matter to calculate the speed or velocity required. Thus, a measure of vibration velocity is

direct measure of fatigue in short

Fatigue=displacement * frequency

Velocity=displacement *frequency

Thus: velocity=fatigue

Vibration velocity is measurement of the speed at which a machine or machine

component is moving as it undergoes oscillating motion.

Vibration velocity is expressed in inches-per-second peak (in/sec-pk) for English

units in metric units, vibration velocity is expressed in millimeters-per-second peak.

Vibration Acceleration

26

VIBRATION ACCELERATION is another important characteristic of vibration

that can be used to express the amplitude or magnitude of vibration. Technically,

acceleration is simply the rate of change of velocity. The acceleration of the weight is

maximum or at its peak value at the upper limit of travel where the velocity is zero (0).

As the velocity of the weight increases, the rate of change of velocity or acceleration

decreases. At the neutral position, the weight has reached its maximum or peak velocity

and at this point, the acceleration is zero (0). After the weight passes through the neutral

position, it must begin to slow down or "decelerate" as it approaches the lower limit of

travel. At the lower limit of travel the rate of change of velocity (acceleration) is, again, at

its peak value.

Expressed in in/sec/sec-peak or mm/sec/sec-peak.

This can also be written as;

in/sec/sec = in/sec2

Or

mm/sec/sec = mm/sec2

4.4.3 Spike Energy

When flaws or defects appear in a bearing, the resulting vibration will appear as a

series of short duration spikes or pulses such .The duration or "period" of each pulse

generated by an impact depends on the physical size of the flaw; the smaller the flaw, the

shorter the pulse period will be. As the size of the defect increases, the period of the pulse

becomes longer. A short-term (40 millisecond sec) time waveform that was taken on a

ball bearing with a small nick purposefully ground on the bearing inner race way. It can

be seen that the pulse period lasts only a few microseconds (1 microsecond = 1 millionth

of a second). Of course, if the period of a vibration signals is-known, the frequency of the

vibration can be found by simply taking the inverse of the period. For example, if it takes

1/3600 minute to complete one cycle of a vibration, then the vibration frequency is 3600

cycles per minute (CPM) or the inverse of the period.

In the case of the pulses generated by the bearing defects, since the pulse periods

are so short, the period inverses (frequencies) are typically very high. To illustrate, a

MICRO-FLAW is generally defined as a defect that is so small that it is essentially

invisible to the naked eye. The pulses generated by a micro-flaw are typically less than 10

27

micro-seconds (i.e. 10 millionths of a second). By taking the inverse of a 10 micro-

second pulse, the fundamental frequency becomes 100,000 Hz (TOOK Hz) or 6,000,000

CPM. As bearing deterioration progresses, the flaw gets larger. The next stage is a

MACRO-FLAW or one that is detectable with the naked eye. Since the macro-flaw is

larger, the duration or period of the pulse generated is longer and, thus, the fundamental

pulse frequency is lower. Typically, a macro-flaw will generate a pulse with a period

exceeding 20 microseconds, resulting in a fundamental pulse frequency of 50K Hz

(3,000,000 CPM) or less. Of course, as the bearing defects continue to increase in size,

the resultant pulse periods become even longer resulting in a decrease in fundamental

pulse frequency. Experimentation has revealed that by the time the fundamental pulse

frequency has reduced to approximately 5k Hz (300,000 CPM), bearing deterioration has

generally reached severe levels.

With the above facts in mind, the following outlines the basic features of the

SPIKE ENERGY (abbreviated gSE) approach developed by 1RD Mechanalysis

1. Since the frequencies of bearing vibration are very high, utilize a vibration acceleration

signal from an accelerometer transducer. Vibration acceleration tends to emphasize higher

frequencies as shown by the comparison in Figure.

2. Incorporate a "band-pass" frequency filter that will electronically filter out frequencies

above 50K Hz (3,000,000-GPM) -and below 5K Hz (300,000 CPM). By eliminating

frequencies above 50K Hz/, micro-flaws, defects that are undetectable with the naked

eye, will not affect the measurement. In other words, when the SPIKE ENERGY (gSE)

measurements reveal a significant increase, a visual inspection of the bearing should

provide confirmation with a visible flaw. For most predictive maintenance programs,

detecting micro-flaws is of little concern since deterioration to the macro-flaw stage may

take several months.

The lower cut-off frequency of 5K Hz (300,000 CPM) filters out or ignores most

other inherent sources of vibration including unbalance, misalignment, aerodynamic and

hydraulic pulsations, electrical frequencies, etc., that tend to dominate or "hide" the

vibration from bearing defects.

3. Since the spike-pulse signals generated by bearing defects have very low RMS values,

incorporate a true peak-to-peak detecting circuit instead of an RMS detecting circuit.

28

4.4.4 Phase

Phase, with regards to machinery vibration, is often defined as "the position of a

vibrating part at a given instant with reference to a fixed point or another vibrating part.

Another definition of phase is: "that part of a vibration cycle through which one part or

object has moved relative to another part".

The concept of "phase" is often the most confusing to newcomers to the field of vibration

detection and analysis; however, from a practical standpoint, phase is simply a convenient

mean of determining the "relative motion" of two or parts of a machine or vibrating

system. The units of phase are degrees, where one complete cycle of vibration equals

360 degrees.

4.5. INSTRUMENTS FOR VIBRATION DETECTION AND

ANALYSIS

4.5.1 Introduction

Instruments for measuring and analyzing machinery vibration are available in a

wide array of features and capabilities, but are generally categorized as:

1. Vibration meters.

2. Vibration frequency analyzers

4.5.2 The Vibration Transducer

Regardless of the vibration instrument being used, the "heart" of every instrument

is the vibration transducer. This is the device that is held or attached to the machine to

convert the machine's mechanical vibration into an electrical signal that can be processed

by the associated instrument into measurable characteristics of vibration amplitude,

frequency and phase. Many different varieties of vibration transducers have been used

over the years. However, with few exceptions, the transducer provided as standard with

nearly all present-day vibration meters, analyzers and data collectors is the vibration

accelerometer.

An accelerometer is a self-generating device that produces a voltage output

proportional to vibration acceleration (G's). The amount of voltage generated per unit of

vibration acceleration (G) is called the sensitivity of the accelerometer and is normally

expressed in milli volts-per-G (mv/G), where 1 milli volt equals one-thousandth of a volt

29

(1 mv = 0.001 volt). Accelerometers are available with sensitivities ranging from less

than 1 mv/G to 10,000 mv/G; however, most accelerometers for general purpose

vibration detection and analysis applications will have sensitivities ranging from 10 to

100 mv/G.

Fig: 4.3 Basic construction of an accelerometer

Theory of Operation

Figure 4.1 shows a simplified diagram of typical accelerometer construction. The

component of the accelerometer that generates the electrical signal is called a

"piezoelectric" element. A piezoelectric material is a non-conducting crystal that

generates an electrical charge when mechanically stressed or "squeezed". The greater the

applied stress or force, the greater the generated electrical charge.

Many natural and man-made crystals have piezoelectric properties. There are also

a number of ceramic (polycrystalline) materials which can be given piezoelectric

properties by the addition of certain impurities and by suitable processing. These are

called "Ferro-electric" materials. Most commercially available accelerometers used today

incorporate Ferro-electric materials because they can be fabricated in a variety of shapes

and their piezoelectric properties can be controlled more easily than crystals to suit many

applications.

Referring to the diagram in Figure 4-1 the accelerometer consists of a mass

(usually a stainless steel disk) compressed against a "stack" of piezoelectric disks. The

size and number of piezoelectric disks used in an accelerometer determines not only its

sensitivity (mv/G), but its usable frequency range as well. When the accelerometer is held

or attached lo a vibrating object, the piezoelectric elements will be subjected to resultant

30

"inertia" forces of the mass. Thus, a forces proportional to the vibration acceleration is

applied to the piezoelectric elements, resulting in an electrical charge signal proportional

to vibration acceleration.

The operation of an accelerometer used for measuring and analyzing machinery

vibration is exactly the same as that of a ceramic cartridge used on phonographs and

record players, where the vibration of a phonograph needle riding in the grooves of a

record is converted to an equivalent electrical signal.

The amount of electrical signal generated by the piezoelectric element is

relatively small and many times must be transmitted by an interconnecting cable to the

vibration instrument or analyzer which may be some distance away. For this reason, a

common practice is to incorporate an electronic amplifier directly inside the

accelerometer to amplify the signal so it can be transmitted through long cables without

worrying about signal loss or interference Horn radio frequencies (RF interference) or

high voltage electro-static interference or high voltage transformers, electrical fields

around motors, etc. Accelerometers built-in amplifiers can normally be used with

interconnecting cables up to 1000 feet (330 meters) in length without appreciable signal

loss or interference.

Where to Take the Readings

Fig: 4.4 Direction for placing the sensor

Since vibratory forces generated by the rotating components of a machine are

passed through the bearings, vibration readings for both detection and analysis should be

taken directly on the bearings whenever possible.

FFT means:

31

The term "FFT" stands for "Fast Fourier Transform". Nearly 200 years ago,

French mathematician, Baron Jean Baptist Joseph Fourier established that any periodic

function (which includes machinery vibration signals) can be represented mathematically

as a series of sines and cosines. In other words, it is possible to take a vibration time

waveform, whether simple or complex, and mathematically calculate the vibration

frequencies present along with their amplitudes. The process is called a "Fourier

Transform". Although a Fourier Transform can be done manually, the process is

extremely time consuming. However, with the introduction of digital technology, the

process can be carried out very fast. Hence the term: Fast Fourier Transform or FFT.

Digital vibration analyzers and data collectors actually include a computer chip

programmed to perform the FFT function.

Analog Signal

The FFT process begins with an analog signal from a vibration transducer.

Normally, the transducer will be a vibration accelerometer; however, signals from other

types of transducers can be processed as well such as microphones, pressure transducers,

current transformers, etc.

Input

Since a vibration accelerometer is normally used for vibration detection and

Analysis, it may be necessary to convert the acceleration signal to velocity by "single

integration" or to displacement by "double integration". These functions are carried out at

the input section. Calibration of the analog signal, based on transducer sensitivity, is also

performed at the input.

4.5.3 DATA PAC 1500

Instrument Details:

32

ENTEK IRD (company)Data Pac 1500Portable data collector \ analyzer.

Data Pac 1500 is part of Entek IRD is complete range of monitoring products

and services to all industry segments world wide .the data pac 1500 is a fully featured

portable data collector \ analyzer designed in a small lightweight package that monitors

the conduction of the equipment found in many process industries such as power

generators petrochemical pulp and paper and primary metals. This easy-to use instrument

features high frequency range and true zoom capabilities normally only found in high

priced, bulky real-time analyzers .The data Pac 1500 collects field data, including

vibration information and process variables with a frequency range of 10cpm -

4518000cpm (.18hz)-75.3khz .it also includes true zoom capability ,screen capture and

print utilities.

Fig: 4.5 DATA PAC 1500

The data Pac 1500 utilizes the latest advances in analog and digital electronics

including digital signal processing (DSP) and industry highest resolution A\D converter

to provide both speed and accuracy in the data collection process. The instrument

incorporates a large VGA resolution screen for easy reading and comprehensive data

presentation online context sensitive help is building to all applications so they are easy

to use and require minimum training . The data Pac 1500 accepts industry standard

type 1 or type 2 PC memory cards to provide both unlimited and reliable data storage and

is powered by long life, rechargeable, easily removable Ni-cad battery cells.

33

Features:

Inputs/outputs:

Single data channel, constant current interface standard +/- 10volts engineering

units (EU), providing for vibration inputs and process inputs (temperature prop is

optional). Reference input channel, supports a variety of externally powered TTL

compatible inputs. Including photocells, electromagnetic transducers or ENTEK IRD lace

tach.

Frequency:

Frequency response: 10CPM to 4518000CPM (0.18Hz to 75.3 kHz) non integrated

21CPM to 4518000CPM (0.36Hz to 75.3 kHz) integrated

Frequency ranges: 42 ranges between 600CPM and4518000CPM (10Hz and 75300Hz)

Frequency resolution: upto12800 lines

GSE corner frequencies: 100, 200, 500, 1000, 2000, 5000Hz

Amplitude range /resolution:

18 bit A\D converter is incorporated for a solid 96db dynamic range

Auto ranging capability sets full scale in 1,2and5 increments

Last hardware range is stored for each measurement to improve measurement speed

Supported measurement:

Acceleration

Velocity

Displacement

Spike energy

Temperature

Thrust or axial position

DC voltage

AC voltage

Adb, Vdb

Phase (1x-99x)

Speed

34

Time synchronous FFT’s

Time synchronous wave form

Amplitude vs. RPM (optional)

Start up (coast down FFT waterfall plots (optional)), NY quist plots

(Optional), speed

Profiling plots (optional).

Signal processing:

A wide range of options are available and controllable by the host software including

RMS, peak, peak to peak, and DC meter types

Linear, exponential, RMS and peak hold averaging

FFT processing (hamming, hanning, Kaiser-bessel flat top and rectangular window)

12.5 KHz real time data collection and processing rate

Time domain data collection

Automatic amplitude ranging

CHAPTER-V

35

VIBRATION ANALYSIS

5.1 INTRODUCTION

There are literally hundreds of specific mechanical and operational problems that

can result in excessive machinery vibration. However, since each type of problem

generates vibration in a unique way, a thorough study of the resultant vibration

characteristics can go a long way in reducing the number of possibilities—hopefully to a

single cause. A simple, logical and systematic approach that has been proven successful

in pinpointing the vast majority of the most common day-to-day machinery problems.

5.2 DEFINE THE PROBLEM

The following lists some of the reasons for performing a vibration analysis:

1. Establish "baseline data" for future analysis needs. At the beginning of a

predictive maintenance program, even machines in good operating condition should be

thoroughly analyzed to establish their normal vibration characteristics. Later, when

problems do develop, this baseline information can be - extremely useful in performing

a follow-up analysis to show precisely the vibration characteristics that have changed.

2. Identify the cause of excessive vibration. Referring to the vibration severity

guidelines machines in service that have vibration levels in the "rough" regions or greater

should be thoroughly. Analyzed to identify existing problems for immediate correction.

Once corrections have been made, a follow-up analysis should be performed to insure

that problems have been solved and the machine returned to satisfactory condition. If all

significant problems have been solved, the follow-up analysis data will serve as the

baseline data for future analysis as outlined in (1) above.

3. Identify the cause of a significant vibration increase. Once a developing problem

has been detected by routine, periodic checks, the obvious next step is to perform a

detailed vibration analysis to identify the problem for correction. Here also, a follow-up

analysis will verify that the problems have been corrected and provide a baseline for

future comparison

36

4. Identify the cause of frequent component failures such as bearings, couplings,

seals, shafts, etc.

5. Identify the cause of structural failures such as the structure or foundation, piping

etc.

6. Identify the source of a noise problem.

5.3 DETERMINE MACHINE DETAILS

Some of the important detailed features of the machine that need to be known for

Accurate analyses include:

1. The rotating speed (RPM) of each machine component: Of course, direct-coupled

machines have only one rotating speed (RPM) that needs to be known. However,

machines that include gear drives will have more than one.' For single gear increasers or

reducers, both the input and output speeds are needed. For multiple gear increasers or

decreases, the rotating speeds of the various intermediate gears must be known along

with the input and output speeds.

2. Types of bearings: Of course worn or defective sleeve or plain bearings will have

different vibration characteristics than defective rolling-element bearings. Therefore, it is

most important to know whether the machine has plain or rolling element bearings. If the

machine has rolling-element bearings, it is also beneficial to know the number of rolling

elements and other details of bearing geometry; with this information, the vibration

analyst can actually calculate the frequencies of vibration caused by specific bearing

defects such as flaws on the outer and inner raceways, rolling elements, etc. Details on

determining specific bearing defect frequencies are presented in the ANALYSIS OF

ROLLING ELEMENT BEARINGS section of this chapter.

3. Number of fan blades: Knowing the machine RPM and number of blades on a fan

will enable the analyst to easily calculate the "blade-passing" frequency. This is simply

the product of the number of fan blades times fan RPM. This frequency of vibration is

also called the "aerodynamic pulsation frequency.

4. Number of impeller vanes: Similar to fans and blowers, knowing the number of

vanes on a pump impeller allows the analyst to calculate the vane-passing frequency, also

called the "hydraulic-pulsation" frequency.

37

5. Number of gear teeth: The rotating speed and number of teeth on each gear must be

known in order to determine the possible "gear-mesh" frequencies.

6. Type of coupling: Gear and other lubricated types of couplings can generate some

unique vibration characteristics whenever their lubrication breaks down or if lubrication

is inadequate.

7. Machine critical speeds: Some machines such as high speed, multi-stage centrifugal

pumps, compressors and turbines are designed to operate at speeds above the natural or

"resonant" frequency of the shaft. The resonant frequency of the shaft or rotor is called its

"critical" speed, and operating a near this speed can result in extremely high vibration

amplitudes. Therefore, knowing the rotor critical speed relative to machine RPM and

other potential exciting force frequencies are very important.

8. Background vibration sources: Many times the vibration being measured on a

machine is actually coming from another machine in the immediate area. This is

particularly true for machines mounted on the same foundation or that are interconnected

by piping or other structural means. Therefore, it is important to be aware of potential

"background" contributions. This is especially true with machine tools, due to the low

levels of vibration required! If possible, the machine under analysis should be shut down

and readings taken to directly determine the amount and significance of background

vibration.

5.4 VISUAL INSPECTION

Before collecting data, the vibration analyst should first make a visual check of

the machine to determine if there are any obvious faults or defects that could contribute

to the machines condition. Some obvious things to look for include;

1. Loose or missing mounting bolts

2. Cracks in the base, foundation or structural welds

3. Leaking seals

4. Worn or broken parts

5. Wear, corrosion or build-up of deposits on rotating elements such as fans.

Slow Motion Studies

38

Another test that is helpful in a visual inspection of the machine is slow motion

observation of the various rotating elements of the machine with a high-intensity

stroboscopic light. The strobe light must be one that has an adjustable flash rate. Simply

adjust the strobe to flash at a rate which is slightly faster or slightly slower than the

rotating speed (1 x RPM) of the machine. This will make the rotating components appear

to rotate slowly.

Slowing down the rotating motion of the machine makes it possible to visually

detect problems that may be difficult to detect any other way. Visual run out of a shaft

may pinpoint or verity a bent shaft condition. Eccentricity of "V" belt sheaves and pulleys

can be easily detected in slow motion. Slow motion studies are especially useful in

evaluating problems with belt drives. Worn grooves in pulleys or belts with variations in

thickness can easily be seen by observing the action of the belt riding up and down in the

pulley grooves. On multiple-belt drives, belt slippage can be determined by observing the

belts in slow motion.

5.5 PROBING STUDIES

The tendency in vibration analysis is to concentrate on analyzing vibration data

taken at the bearings of the machine. While this data is definitely an important part of any

vibration analysis, in many cases the vibration that is occurring at the machine's bearings

is actually the result of problems elsewhere in the "system. For example, in one case a

vertical pump had a vibration of 0.7 in/sec measured at the top bearing of the pump

motor. However, overall vibration readings taken on the pump base, foundation and

piping revealed that the discharge piping was vibrating at a level of 3.0 in/sec or over four

times higher than the pump motor itself. The problem turned out to be resonance of the

discharge piping and not a problem with the pump itself. The pump and drive motor in

this case were simply responding to the piping problem.

The only way other problems in the system can be detected, such as the piping

resonance described above, is to go looking for them. Depending on the anticipated

vibration frequencies, select overall displacement, velocity or acceleration for

measurement. Some of the areas that should be checked include:

1. Suction and discharge piping on pumps: Take overall measurements in three directions.

39

On long piping runs, take readings at several locations along the piping.

2. Externally mounted components such as exciters, lube-oil pumps, surge bottles, etc.

Here also, take overall measurements in three directions

3. Take overall measurements on nearby machines that may contribute background

vibration. If a nearby machine has higher vibration amplitudes than the one being

analyzed, it is very likely some of the vibration is coming from the background source.

4. Compare overall vibration readings across all mounting interfaces to detect obvious

signs of looseness or weakness.

5. In addition to taking comparative overall readings across the mounting interfaces

To detect Obvious looseness problems, the vibration, amplitudes taken vertically

at The mounting points of a machine, such as the four feet of a motor, can be compared to

reveal the possibility distortion or "soft-foot or distortion conditions caused by uneven

mounting or foot will usually be indicated if one or more of the feet reveals a

significantly higher amplitude than the other feet. If this is defected, the condition should

be verified and Corrected before further analysis is carried out. Soft-foot conditions can

be checked by placing a dial indicator directly on the foot and carefully loosening the

mounting bolt while observing the indicator reading. Any movement or "spring" in

excess of 0.002 - 0.003 inch is generally considered excessive and should be corrected.

5.6 OBTAIN HORIZONTAL, VERTICAL AND AXIAL SPECTRUMS (FFTS) AT

EACH BEARING OF THE MACHINE TRAIN

In many cases, the analysis steps carried out thus far may be sufficient to pinpoint

the specific problem causing excessive vibration. If not, the next step is to obtain a

complete set of amplitude-versus-frequency spectrums or FFTs at each bearing of the

machine train. For a proper analysis, the machine should be operating under normal

conditions of load, speed, temperature, etc.

In order to insure that the analysis data taken includes all the problem-related vibration

characteristics and, yet, is easy to evaluate and interpret, the following recommendations

are offered;

Interpreting the Data

40

Once horizontal, vertical and axial FFTs have been obtained for each bearing of

the machine train, the obvious next question is: "What is this data telling me?"

Essentially, amplitude-versus-frequency spectrums or FFTs serve two very important

purposes in vibration analysis:

1. Identify the machine component (motor, pump, gear box, etc.) of the machine train

that has the problem And

2. Reduce the number of possible problems from several hundred to only a limited few.

Identifying the Problem Component Based On Frequency

Figure 5-1 shows a fan operating at 2200 RPM, belt driven by an 1800 RPM

motor. The rotating speed of the belts is 500 RPM. Assume that a vibration analysis was

performed on this machine and the only significant vibration detected had a frequency of

2200 CPM or 1 x RPM of the fan. Since the vibration frequency is exactly related to fan

speed, this clearly indicates that the fan is the component with the problem. This simple

fact eliminates the drive motor, belts and possible background sources as possible causes.

Most problems generate vibration with frequencies that are exactly related to the

rotating speed of trip in trouble. These frequencies may be exactly 1 x RPM or multiples

(harmonics) of 1 x RPM such as 2x, 3x, 4x, etc. In addition, some problem's may cause

vibration frequencies that are exact sub harmonics of 1 x RPM such as 1/2x, l/3x or 1/4 x

RPM. In any event, the FFT analysis data can identify the machine component with the

problem based on the direct relationship between the measured vibration frequency and

the rotating speed of the various machine elements.

Identifying the Problem Component Based On Amplitude

Identifying the fan as the source of vibration based on vibration frequency was

quite easy in the above example because of the notable differences in the rotating speeds

of the various machine components. The obvious question, of course is: What about

direct-coupled machines that is operating at exactly the same speed?" In this case, the

component with the problem is normally identified as the one with the highest amplitude.

For example, consider a motor direct coupled to a pump. Examining the analysis data, it

is noted that the highest vibration amplitude on the motor is 1.0 in/sec compared to 0.12

in/sec on the pump. In this case, the motor is clearly the problem component since its

41

vibration amplitude is nearly 8 times higher than that measured on the pump.

In general, the machine component that has the problem is usually the one with

the highest amplitude of vibration. The forces that cause vibration tend to dissipate in

strength at increased distances from the source. However, there are exceptions to this rule

such as the example given earlier where a vertical pump was vibrating excessively due to

a resonance problem with the discharge piping. In this case, the exciting force was

actually generated by the motor/pump but was being amplified by the resonant condition

of the piping.

Another exception to this rule involves misalignment of direct coupled machines.

Sir Isaac Newton’s third law of physics slates that "whenever one body exerts a force on

another, the second always exerts on the first a force which is equal in magnitude but

oppositely directed." In other words, "for every action, there is an equal but opposite

reaction." In the case of coupling misalignment, the vibratory force (action) is generated

at the coupling between the driver a driven components. As a result, the "reaction" forces

on the driver and driven unit; will be essentially equal, resulting in reasonably

comparable vibration amplitudes. The only reason one component may have a slightly

higher or lower amplitude than the other is because of differences in the mass and

stiffness characteristics of the two components. But, in most cases with the coupling

misalignment, the vibration is fairly uniformly "shared" by the driver and driven units.

Fig 5.1 Different components generate different vibration frequencies

Reducing the List of Possible Problems Based On Frequency

In addition to identifying the problem machine component based on frequency

and/or amplitude characteristics, the second purpose of FFT analysis data is to limit or

42

reduce the list of possible problems based on the measured vibration frequencies.

As stated earlier, each mechanical and operational problem generates its own

unique vibration frequency characteristics. Therefore, by knowing the vibration

frequency, a list of the problems that cause or generate that particular frequency can be

made, which greatly reduces the long list of possibilities.

The chart lists the most common vibration frequencies is they relate to machine

rotating speed (RPM), along with the common causes for each frequency. To illustrate

how to use the chart, assume that the belt-driven fan pictured in Figure 4-1 has excessive

vibration at 2200 CPM which is 1 x RPM of the fan. Of course, this clearly indicates that

the fan is the component with the problem and not the drive motor or belts. In addition,

since the vibration frequency is 1 x RPM of the fan, the possible causes listed on the chart

are:

1. Unbalance

2. Eccentric pulley

3. Misalignment—this could be misalignment of the fan bearings or misalignment of the

fan and motor pulleys.

4. Bent shaft

5. Looseness

6. Distortion—from soft foot or piping strain conditions

7. Bad belts—if belt RPM

8. Resonance

9. Reciprocating forces

10. Electrical problems

Using this simple chart, along with the fact that the vibration frequency is 1 x

RPM of the fan has reduced the number of possible causes from literally hundreds to only

ten (10) likely causes, A little common sense can reduce this list even further. First, since

the vibration frequency is not related to the rotating speed (RPM) of the drive belts,

possible belt problems can be eliminated as a possible cause. Secondly, since this is a

reciprocating machine such as a reciprocating compressor or engine, the possibility of

reciprocating forces can be eliminated from the remaining list. Finally, since the

frequency is not related to the drive motor or AC line frequency. In any way, the

43

possibility of electrical problems can be eliminated. Now, the number of possible causes

of excessive vibration has been reduced to only seven (7) by simply knowing that the

vibration frequency in this case is 1 x RF of the fan.

Table 5.1: VIBRATION FREQUENCIES AND THE LIKELY CAUSES

Frequency in Terms Of RPM

Most Likely causes Other possible causes & Remarks

1x RPM Unbalance 1) Eccentric journals, gears or pulleys 2) Misalignment or bent shaft if high axial vibration3) bad belts if RPM of belt4} Resonance5) Reciprocating forces 6) Electrical problems

2 x RPM Mechanical looseness 1) Misalignment if high axial vibration 2) Reciprocating forces 3) Resonance 4) bad belt if 2 x RPM of belt

3 x RPM Misalignment Usually a combination of misalignment and excessive axial clearance (looseness).

Less than 1x RPM

Oil Whirl {Less than 1/2 x RPM

1) Bad drive belts2) Background vibration3) Sub-harmonic resonance4) "Seat" Vibration

Synchronous (A.C line frequency)

Electrical Problems Common electrical problems include broken rotor bars, eccentric rotor, and unbalanced phases in poly-phase systems, unequal air gap.

2xSynch. Frequency

Torque Pulses Rare as a problem unless resonance is excited

Many Times RPM (Harmonically Related Freq.)

Bad Gears Aerodynamic Forces Hydraulic forces Mechanical LoosenessReciprocating Forces

Gear teeth times RPM of bad gear Number of fan blade times RPMNumber of impeller vane times RPM May occur at 2, 3, 4 and sometimes higher harmonics if severe looseness

High Frequency (Not Harmoni-cally Related)

Bad Anti-Friction bearing

1) Bearing vibration may be unsteady amplitude and frequency 2) Capitation, recirculation and flow turbulence causes random high frequency vibration3)Improper lubrication of journal bearings 4)rubbing

Comparing Tri-Axial (Horizontal, Vertical and Axial) Data

44

Not only can specific vibration problems be recognized by their specific frequency

characteristics, but in many cases by the direction in which the vibration occurs. This is

why it is necessary to take analysis data in the horizontal, vertical and axial directions - to

further the process of elimination.

Table 5.1 shows a typical "set" of tri-axial data taken on one bearing of a belt

driven fan operating at 2200 RPM. Of course similar data would be taken on the, other

fan bearing as well as the motor bearings. "Stacking" the horizontal, vertical and axial

data for a particular bearing on the same sheet as shown, greatly simplifies the

comparison. Note

That the same full-scale amplitude range (0 to 0.3 in/sec) was used for all the data

to further simplify the comparison.

There are basically two comparisons that need to be made from the data in Figure 5-2.

First, how do the horizontal and vertical readings part; and secondly, how do the radial

readings (horizontal and vertical) compare1 to the axial readings.

Fig 5.2: Typical tri-axial data taken on a belt-driven fan

Comparing Horizontal and Vertical Readings

45

When comparing the horizontal and vertical data, it is important to take note of how

and where the machine is mounted and also, how the bearings are mounted to the

machine. Basically, the vibration analyst needs to develop a "feel" for the relative

stiffness between the horizontal and vertical directions in order to see whether the

comparative horizontal and vertical readings indicate a normal or abnormal situation.

Machines mounted on a solid or rigid base may be evaluated differently than machines

mounted on elevated structures or resilient vibration isolators such as rubber pads or

springs.

To explain the significance of machine stiffness, assume that the fan in Figure 5-1

is mounted on a rigid, solid concrete base which, in turn, is mounted on a solid

foundation located at ground level. This would be regarded as a "rigid" installation and

under normal conditions the vertical stiffness would be greater than the horizontal

stiffness. If such is the case/one would expect that normal problems, such as unbalance,

would cause higher amplitude of vibration in th2 horizontal direction than the vertical

direction, if a rigidly mounted machine has higher vibration in the vertical direction than

the horizontal direction, this would generally be considered as 'abnormal', and may

indicate a looseness or weakness condition. On the other hand, if this same machine was

mounted on springs or rubber pads, a higher amplitude in. the vertical direction may not

be considered unusual or an indication of structural problems.

Another factor that needs to be considered is the "ratio" between the horizontal and

vertical Amplitudes. As explained, it is not unusual for rigidly mounted machines to have

higher amplitudes of vibration in the horizontal direction, compared to the vertical

direction. However, the ratio between the horizontal and vertical amplitudes should be

checked to see if it is normal or indicative of some unusual problem. As a normal

unbalance response, it is not unusual for machines to exhibit ratios between the horizontal

and vertical amplitudes of 1:1, 2:1, 3:1 or 4:1, depending on the particular installation. In

other words, it would not be unusual for a rigidly mounted fan, motor or pump to have a

vibration amplitude at 1 x RPM as much as 4 times higher in the horizontal direction than

the vertical direction due to unbalance. Ratios beyond 4:1 somewhat unusual and

typically indicate an abnormal condition such as looseness or resonance.

Comparing Radial (Horizontal & Vertical) Data to Axial Data

46

The second important comparison that needs to be made to tri-axial analysis data is

how the radial (horizontal and vertical) readings compare to the axial readings. Relatively

high amplitudes of axial vibration are normally the result of:

1. Misalignment of couplings

2. Misalignment of bearings

3. Misalignment of pulleys or sheaves on belt drives

4. Bent shafts

5. Unbalance of "overhung" rotors such as the fan in Figure 5.1

A general rule, any time the amplitude of axial vibration exceeds 50% of the

highest radial (horizontal or vertical) amplitude, the possibility of a misalignment or bent

shaft condition should be considered.) CM course, extremely high amplitudes of axial

vibration may also be due to resonance or unbalance of an overhung rotor. Verifying the

cause of a high axial vibration using "phase analysis" techniques will be covered in the

sections to follow.

Examining the axial vibration in the examples given in Figures, it can be seen that in

neither instance is the amplitude of axial vibration greater than 50% of the highest radial

amplitude. As a result, misalignment or bent shaft Conditions are not indicated examples.

'Where Do Multiple Harmonic Vibration Frequencies Come From?

Something that often worries or confuses the beginning vibration analyst is the

appearance of numerous "harmonic" frequencies that sometimes appear in their FFT

analysis data. A good example is the frequency analysis data presented in Figure -5-3.

Although the predominant vibration is clearly 2200 CPM (1 x RPM of the fan), vibration

frequencies can also be seen at 4400 CPM (2 x RPM), 6600 CPM (3 x RPM) and 8800

CPM (4"x RPM). Although their amplitudes are considerably lower than that at 1 x RPM,

these "harmonic" frequencies are very important and should not be ignored, as will be

explained in the following Paragraphs.

The presence of multiple or "harmonically" related vibration frequencies is not

uncommon, and their presence in the FFT data can be easily explained by examining the

frequency characteristics of various vibration waveforms. Figure 5.3 illustrates four (4)

different types of vibration waveforms — a sinusoidal is a sine wave, a square wave, s

triangular or "saw-tooth" wave and a spike pulse. These waveforms can be readily

47

generated by various machinery problems, depending on the nature of the problem and

the extent of the exciting forces. The '1 Linda -mental" frequency of each of the

waveforms in Figure 5-3 is the same; however, the frequencies presented in the FFTs will

be considerably different.

Fig 5.3: Different wave forms result in different frequency characteristics

A sinusoidal or "sine" wave could be the result, of a simple unbalance or

misalignment problem. If a frequency analysis (FFT) is performed on a true sinusoidal

waveform, the result will be a single frequency of vibration with certain amplitude and

NO multiple frequencies.

By comparison, a frequency analysts (FFT) of & square waveform will not only

display the fundamental frequency (1x), but the odd multiple or harmonic frequencies as

well (i.e. 3x, 5x, 7x, etc.). The number of odd multiple frequencies present in the FFT

data will depend on how close the waveform is to a true square wave, the intensity or

amplitude of the vibration and the response characteristics (peak or RMS) of the

instrument as well as its dynamic range. Figure 4-8 shows a 6000 CPM (1 00 Hz) square

waveform signal obtained from an electronic signal generator along with the FFT

frequency analysis. Note that the frequency analysis not only includes the fundamental

frequency of 6000 CPM, but the odd multiples as well (i.e. 18,000 CPM, 30,000 CPM,

48

42,000 CPM, etc.). One possible explanation (or a square wave vibration would be an

unbalance condition combined with system looseness. If the unbalance force was great

enough, the machine could literally be lifted off the foundation and held to the limit of

looseness until the unbalance force has rotated to a position where the upward force is

reduced, allowing the machine to drop. Another possibility is a mild rubbing condition

that might "flatten" the unbalance sine wave whenever the rub occurs.

The fundamental (1x) frequency accompanied by the odd multiple or harmonic

frequencies, similar to a square wave. However, the amplitudes of the odd harmonics of a

triangular waveform decrease more quickly at higher frequency than do those of a square

waveform as shown in Figure 5-3. Triangular or saw tooth waveforms can also be

generated by conditions such as looseness or excessive bearing clearance that result in

"distortion" of an unbalance sine we Here also, the number of odd multiple frequencies

that accompany the fundamental frequency will depend not only on the amplitude of the

fundamental frequency, but the dynamic range and circuit response characteristics (peak

RMS) of the analysis instrument.

Some problems such as a cracked or broken tooth on a gear, or a flaw on a

bearing raceway or rolling element, will generate vibration in the form of impact or

spike-pulses. A frequency analysis or FFT of a spike-pulse signal will reveal the

fundamental impact frequency, followed by the entire multiple or harmonic frequencies

(i.e. 2x, 3x, 4x, 5x, 6x, etc.) as shown in Figure 4-3. As before, the number of harmonic

frequencies evident in the FFT will depend on the amplitude of the fundamental

component and the dynamic range and circuit response characteristics (peak or RMS) of

the analysis instrument.

The presence of multiple, harmonic frequencies in an FFT are definitely important

and should not be ignored, even though their amplitudes may be considerably less than

that of the fundamental frequency. Their mere existence indicates that the vibration is not

a true sine wave, and may provide clues to other significant problems such as looseness

conditions, gear tooth problems, bearing problems, etc. In the case of the belt driven fan

in Figure 5-1, the harmonic frequencies only appeared at the drive-end bearing (bearing

C). Ultimately, the problem was found to be a loose pulley on the fan shaft, which was

allowing the pulley to "rattle" on the shaft during rotation. This caused a spike-pulse

49

distortion of the unbalance sine wave, resulting in the harmonic vibration frequencies.

Once the set-screws were tightened securing the pulley to the shaft, the multiple

harmonic frequencies totally disappeared, leaving only the 1 x RPM unbalance vibration

frequency.

Distortion of a sinusoidal vibration waveform, resulting in multiple vibration

frequencies, may not only be the result of mechanical problems such as looseness,

bearing defects, rubbing or gear defects as described above. (Waveform distortion can

also result from the setup and operation of the vibration analysis equipment. For

example, if a magnetic holder is being used to mount the vibration accelerometer to the

machine, any looseness or rocking of the magnet on the surface of the machine can result

in the appearance of multiple frequencies in the analysis data. In addition, if the

amplitude of machine vibration exceeds the full-scale amplitude range selected on the

analyzer instrument, the true vibration signal may be "chopped", resulting in multiple

frequency components in the FFT data that do not physically exist. For example, if the

actual level of machine vibration was 1.0 in/sec but the analyzer was set for a 0.3 in/sec

full-scale range, the vibration signal would be chopped off, creating an approximate

square waveform. The result, of course, would be odd multiple frequencies in the analysis

data that do not actually exist.

Side-Band Frequencies

"Side-band" frequencies are an additional vibration frequency that often appears

FFT data that can be confusing to the beginning vibration analyst. Side band vibration

frequencies are the result of a variation in the amplitude of given vibration frequency

signal as a function of time. This variation in amplitude with time is also called

"amplitude modulation". For example, consider a Rolling element bearing with a

significant flaw or defect on the rotating inner raceway.)

50

Fig: 5.4 spike pulses due to flaw on the inner race of the bearing

As the inner raceway rotates, spike pulses will be generated each time a rolling

element impacts the flaw. However, the amplitude or intensity of the pulses generated

will vary as the defect rotates into and out of the load zone of the bearing. This is shown

in Figure.

Impacts that occur when the defect is within the load zone will obviously be mw

intense than those that occur out of the load zone. The result is a modulation the

fundamental bearing defect frequency. The fundamental bearing defect frequency in this

case is the frequency at which rolling elements impact the inner raceway flaw and is

called the "ball passing frequency of the inner raceway" or simply BPFI. When

discussing side-band frequencies, the fundamental bearing frequency in this case would

be called the "carrier" frequency. The frequency at which the amplitude of the carrier

frequency varies is called the "modulating" frequency. The modulating frequency in the

case of a defect on the inner raceway will be 1 x RPM, since the defect is rotating into

and out of the bearing load zone at the rotating speed of the shaft.

5.7 DETERMINE IF THE VIBRATION IS DIRECTIONAL OR NON-

DIRECTIONAL

In addition to a comparison of tri-axial (horizontal, vertical and axial data) other analysis

techniques such as simple probing studies has been discussed to show how the list of

possible problems can be reduced. A vibration frequency of 1 x RPM is probably the

most common "predominant" vibration encountered during analysis because so many

different yet common day-to-day problems can cause it. These problems include.

1. Unbalance

2. Bent shafts

3. Misalignment— of couplings, bearings and pulleys.

4. Looseness

51

5. Resonance

6. Distortion—from soft foot or piping strain conditions

7. Eccentricity---of pulleys and gears

8. Reciprocating forces

Of all the problems listed above, the only ones that generate uniform radial forces

and resultant vibration are unbalance and bent shafts. All of the remaining problems

typically generate forces and resultant vibration which is very highly directional in

nature. Therefore, determining whether or not the radial vibration directional or non-

directional can be an extremely valuable analysis tool in reducing the list of possible

problems.

To explain the difference between directional and uniform or non-directional vibration,

consider the response of a machine to a simple unbalance problem. An unbalance

condition generates a certain amount of radial force which is governed by the amount of

unbalance weight (ounces, grams, etc.), the radius of the weight or its distance from the

shaft centerline and the rotating speed (RPM) of the machine.

In any case, an unbalance generates a fixed amount of force that is simply

changing in direction with shaft rotation. If the stiffness of the machine was the same in

the horizontal and vertical directions, the machine would literally move in a circular path,

and the radial vibration amplitudes would be the same in all radial directions. Of course,

the horizontal and vertical stiff nesses will probably not be exactly the same, so the radial

motion will probably be somewhat elliptical, resulting in slightly different amplitudes

measured in various radial directions. In any case, a simple unbalance, uncomplicated by

other problems, generates a fairly uniform, non-directional radial vibration. In terms of

radial vibration, a bent shaft reacts in much the same way as simple unbalance. However,

remember ' from our earlier discussion that a bent shaft will also be characterized by rela-

tively high axial vibration amplitudes as well.

Compared to unbalance and bent shafts, the other listed causes of 1 X RPM

Vibration DOES NOT generate uniform radial vibration. Instead, they create radial

vibration which is very highly directional. For example, consider the radial vibration

generated by coupling misalignment. When a coupling is misaligned, obviously it is

misaligned in a certain direction. As a result, the radial forces and, hence, the radial

52

vibration will be most pronounced in the direction of misalignment.

Similar to coupling misalignment, a distortion problem from a soft foot or

piping strain problem creates misalignment. Of the machine's bearings in a certain

direction with the result being highly directional radial vibration.

An eccentric pulley used in a "V" belt drive produces variations in belt tension with each

revolution, causing a highly directional vibration measured in the direction of belt

tension. An eccentric gear creates directional forces due to the "cam-like" action with the

mating gear, similar to an eccentric pulley. Unbalanced reciprocating forces due to

misfiring, valve leakage and other operational problems with engines and reciprocating

compressors generate vibration in the direction of reciprocation which are, of course,

highly directional. Structural looseness or weakness problems such as loose mounting

bolts or deterioration in grouting, simply allow the machine more freedom to move in the

direction of the looseness. Although some other exciting force must be present, such as

unbalance, structural looseness usually results in highly directional vibration.

Detecting Directional versus Non-Directional Vibration

There are basically three ways to determine whether the vibration of a machine

reasonably uniform or highly directional in nature. These include:

1. A comparison or horizontal, vertical and axial FFT data

2. Comparing the horizontal and vertical phase measurements

3. Multiple radial amplitude measurements

Comparing Horizontal and Vertical Phase Readings

Figure 5-5 illustrates two types of radial vibration—uniform and highly directional. Of

course, uniform or reasonably circular radial vibration is typically the result of a simple

unbalance problem. Phase measurements, which were discussed, are obtained by either

triggering a stroboscopic (strobe) light with the vibration signal or by comparing the

vibration signal with a refer pulse such as that obtained with a photo-electric pickup

(photocell) or laser In any case, phase was described as the "relative" motion of two or

more parts of a machine.

53

Fig: 5.5 Comparative horizontal and vertical phase readings are used to distinguish

between uniform and highly directional radial vibration

However, phase can also describe how a single element of a machine is vibrating, such as

a bearing. In other words, comparative phase measurements taken in the horizontal and

vertical directions of a particular bearing can reveal whether the bearing is vibrating in a

highly directional or a reason uniform manner.

In the case of a normal unbalance, it is the "heavy spot" of unbalance that; dually

causes the vibration. And, since it is the vibration signal that triggers the strobe light or is

compared to the reference pulse, it can be said that, indirectly, the heavy spot is

responsible for the ultimate phase angle measurement. With this in mind then, it should

be apparent that if the machine bearing is vibrating in a reasonably uniform or circular

pattern, from the time that the heavy spot rotated to a position to cause the machine to

move horizontally, the heavy spot had to rotate an additional 1 /4 revolution or 90 degrees

to cause it to move vertically. Therefore, if the machine is, intact, vibrating radially in a

reasonably uniform or circular manner, a comparison of phase readings taken in the

horizontal & vertical directions should show a difference of approximately 90 degrees.

Of course, even with simple unbalance, the stiffness in the horizontal and vertical

directions will probably not be exactly the same and, as a result, the radial motion will

probably not be a perfect circle. Therefore, when comparing phase readings taken in the

horizontal and vertical directions, the phase difference may not be exactly 90 degrees.

Because the radial motion may not be a perfect circle, a tolerance or plus or minus 30

degrees is normally allowed. In other words, comparative horizontal and vertical phase

readings between 60 degrees and 120 degrees indicate a fairly uniform radial vibration or

one that is NOT highly directional.

In the case of highly directional radial vibration, comparative horizontal and

vertical phase readings will either be nearly the same (0 degrees difference) or 180

54

degrees out-of-phase, depending on which side of the machine bearing the readings are

taken. Referring to Figure 4-5, if the vibration was occurring virtually along the straight

line designated "A", the machine would reach its maximum motion toward the horizontal

measurement location at exactly the same instant it reached its maximum motion toward

the vertical measurement location. In this case, comparative horizontal and vertical phase

measurements would be the same (i.e. differ by 0 degrees). However, if the directional

vibrate was occurring along the straight line designated as "B", then at the exact instant

the machine reached its maximum motion towards the horizontal measurement location,

it would have reached its maximum location away from the vertical measurement

location. In this case, comparative horizontal and vertical phase readings would differ by

180 degrees.

In summary, a simple comparison of horizontal and vertical phase readings can

quickly tell whether the radial vibration is fairly uniform or highly directional. In

addition, it should be pointed out that it does not make any difference how the machine is

vibrating radially relative to the directions of vibration measurement. Any time the ratio

between the maximum and minimum radial vibration amplitude exceeds much beyond

5:1, comparative horizontal and vertical phases readings will indicate a highly directional

vibration by virtue of a 0 degree or 180 degrees phase comparison.

5.8 IDENTIFYING THE MOST COMMON MACHINERY

PROBLEMS

5.8.1 Vibration due to Unbalance

Unbalance of rotating machine components is, perhaps, the easiest problem lo

pinpoint with confidence. Simple unbalance, uncomplicated by other problems, can be

readily identified by the following characteristics:

1. The vibration occurs at a frequency of 1 x RPM of the unbalanced component. The

presence of multiple, harmonic frequencies (i.e. 2x, 3x, 4x, times RPM) usually indicates

additional problems such as looseness, rubbing, etc

2. The radial vibration is reasonably uniform and not highly directional. A comparison of

horizontal and vertical phase readings will normally show a difference between 60

55

degrees and 120 degrees. If comparative horizontal and vertical phase readings cannot be

taken, multiple radial amplitude readings should not show a discrepancy in excess of 5:1.

3. If a specific machine component such as a motor or fan is the source of unbalance, that

component will! Have significantly higher amplitudes of vibration at the 1 x RPM

frequency. Unbalance of couplings will likely reveal comparable amplitudes on both the

driver and driven machine components.

Unbalance conditions can often be affected by other operating conditions such as

load or temperature. For example, machines operating at elevated temperatures can

physically distort or change shape due to thermal changes, resulting!! a change rotor

balance. Large, fabricated boiler draft fans must often be balanced at operating

temperature due to thermal distortion. They may run smoothly when cold but vibrate

excessively when hot.

In addition, due to minor variations in the track and pitch-angle of the fan blades.

Large fabricated fans may show significant changes in the unbalance vibration

characteristics with changes in flow conditions. In other words, a change in the damper

setting may result in a significant change in the unbalance amplitude & phase

characteristics. Such affects are referred to as "aerodynamic unbalance', and [joint out

the importance of balancing a rotor under its normal operating conditions of temperature

and flow conditions.

5.8.2 Bent Shaft Problems

Bent shafts are a common problem encountered on machinery, and are often the

result of manufacturing errors or mishandling and damage during transportation or

machine installation. In addition, a rotor may "bow" as the result of thermal distortion at

elevated temperatures or due to excessive unbalance forces.

56

Fig: 5.6 uneven rotor and bent shaft problems

Regardless of the cause, bent shafts will usually generate a predominant vibration at 1 x

RPM, very similar to simple unbalance. And, like unbalance, the radial vibration caused

by a, bent shaft will be fairly uniform and not highly directional. However, unlike

unbalance, bent shaft conditions will normally cause a relatively significant vibration in

the axial direction as well. As staled earlier, any time the amplitude of vibration measured

in the axial direction exceeds 1/2 (50%) o! the highest measured radial vibration, a bent

shaft is a very possible cause.

Because bent shafts cause significant vibration in the axial direction, a bent shaft

problem can normally be verified using a phase analysis of the axial vibration. However,

there are actually two different types of bent shaft conditions:

1. Rotors that have a simple "bow and:

2. Shafts that have a bend or "kink", but only near a particular bearing.

Each type of bend will result in significant axial vibration, but each type will

cause the various bearings of the machine to vibrate in the axial direction in a notice-ably

different manner. Therefore, an axial phase analysis cans not only verity a bent shaft

condition, but can also help in identifying the nature and location of the bend as well.

57

5.8.3 Shaft with a Kink or Bend Close To the Bearing

The axial vibration caused by a bent shaft can actually occur in two different

ways. Normally, if the bend is fairly close to a particular bearing, such as a "kink" in the

stub shaft of a motor or pump caused by bumping the shaft during transportation or

installation, the bearing will tend to vibrate axially in a "twisting", motion This twisting

motion can be easily recognized by taking comparative axial phase measurements at

multiple axial positions as shown in Figure 4.7. Four axial phase readings at each bearing

of the machine are recommended; however, physical constraints may make it impossible

to take all the readings desired. In any case, more than one axial phase reading is needed,

so try to take &s many as possible.

If the bearing is, in fact, "twisting" due to a kink in the shaft that is very close or

actually through the bearing itself, the result will be a drastic difference in the phase

readings obtained at the four axial positions, as shown in Figure 5-7. In Figure 5-8, it can

be seen that the upper and lower measurement points {1 and 3) are actually 180 degrees

out-of-phase, as are the measurement points on opposite sides of the shaft (2 and 4). This

clearly indicates that the bearing is vibrating axially in a twisting fashion. Further

verification of a bend or "kink" in the shaft can be carried out using a dial indicator.

Fig 5.7: four axial phase readings at each bearing are needed to see how each bearing is vibrating axially

Fig 5.8: These axial phase readings show a twisting axial motion.

58

Bearings that are "cocked" in the machine housing may also cause significant

vibration amplitudes in the axial direction, and may reveal the same "twisting" action as

that caused by a kinked shaft. However, a cocked or misaligned bearing can usually be

distinguished from a kinked shaft by comparing the amplitudes of vibration measured at

the four axial positions. Normally, if a bearing is cocked in the housing, it will be cocked

in a specific direction and show a significant difference in the amplitudes measured at the

four axial positions. On the other hand, a shaft that has a simple bend or "kink" will

reveal fairly uniform amplitudes in the four axial positions.

5.8.4 Identifying a Simple Shaft Bow

A shaft that has a simple bow may not cause the supporting bearings to vibrate

axially in a "twisting" type of motion. Instead, a simple bow may cause the supporting

bearings to vibrate axially in a "planer" fashion

In order to identify a simple bow as the cause of high axial vibration, it will be

necessary to compare the "relative" axial motion of the support bearings. If the shaft is

simply bowed, the supporting bearings of the rotor will reveal a substantial "out-of-

phase" condition. Although a pronounced bow may reveal as much as a 180 degrees

difference in the axial phase of the rotor supporting bearings, an out-of-phase condition

of only 90 degrees or more is significant enough to indicate a possible bow in the shaft.

Run out checks with a dial indicator should be performed to verify the bent shaft

condition—especially if the amplitudes of axial vibration far exceed 50% of the highest

radial amplitudes.

When comparing the axial phase readings at the supporting bearings of a rotor, it is

most important to keep in mind the direction of the transducer. To illustrate, when taking

axial phase- readings on the left side bearing of the rotor, the vibration transducer may

have been pointing to the right. However, when axial phase readings were taken on the

right side bearing, it may have been necessary to point the vibration transducer to the left.

If this was the case, it will be necessary to correct the phase readings for one of the

bearings by 180 degrees to compensate for the necessary 180 degree change in transducer

direction. Of course, if the direction of the pickup axis can be kept the same at all bearing

locations, then no correction factor is necessary.

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5.8.5 Vibration Due to Misalignment

Surveys have shown that at the beginning stages of most predictive maintenance

programs, misalignment of direct coupled machines is by far the most common cause of

machinery vibration. In spite of self-aligning bearings and flexible couplings, it is

difficult to align two shafts and their bearings so that no forces exist which will cause

vibration. Although machines may be well aligned initially, several factors can affect

alignment, including:

Fig: 5.9 parallel misalignment and angular misalignment

1. Operating temperature: Machines aligned when cold may "grow" out of alignment due

to variations in thermal conditions,

2. Settling of the base or foundation

3. Deterioration or shrinkage of grouting

The following are general characteristics to look for:

1. The radial vibration caused by coupling misalignment is typically highly directional on

both the driver and driven units. Misalignment occurs in a certain direction and, as a

result, the radial forces are not uniformly applied in all radial directions like that from

unbalance.

2. The vibration frequencies due to misalignment are usually 1 x, 2x and 3x RPM, and

may appear in any combination depending on the type and extent of misalignment.

Angular misalignment normally causes vibration at 1 x RPM, whereas offset or parallel

misalignment causes vibration predominantly at 2 x RPM. In fact, offset misalignment is

probably the most likely cause of a predominate 2 x RPM vibration. Combinations of

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angular and offset misalignment may show combinations of 1x and 2 x RPM and in some

cases even 1x, 2x and 3 x RPM.

3. Whenever misalignment is suspected, an axial phase analysis comparing the relative

axial motion of the driver and driven units can be most helpful. As stated earlier, "for

every action there is an equal but opposite reaction". As a. result, misalignment

problems will normally reveal a significant phase difference \ up to 180 degrees.

However, phase differences as little as 60 degrees Tin relative axial motion is

sufficient to suggest misalignment.

5.8.6 Vibration Due To Looseness

Excessive vibration may exist due to looseness conditions; however, looseness is

not the actual cause of the vibration. Some other exciting force such as unbalance or

misalignment must be present to actually cause the vibration.

Fig: 5.10 vibrations due to looseness (excessive clearance in bearings and loose bolts)

Looseness is simply a loss or reduction in the normal stiffness of the machine or

system, perhaps due to loose mounting bolts, cracks in the base or foundation,

deterioration in grouting, cracked welds, loose lags or anchors or rotors loose on the

shaft. Looseness conditions simply allow whatever exciting forces that exist in the

machine to exhibit or generate higher amplitudes of vibration than they would if no

looseness problems existed. If the predominate exciting force is an unbalance at 1 x

RPM, then the predominate vibration due to looseness would be 1 x RPM in this case.

However, if the predominate exciting force is occurring at 2 x RPM due to an offset

misalignment, then the looseness would occur at a frequency of 2 x RPM. Looseness

does not have to occur at a frequency of 2 x RPM as many published vibration diagnostic

charts would lead one to believe.

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Two general types of looseness are:

1. Looseness associated with the rotating system, including rotors loose on the shaft,

bearings loose on the shaft or in the machine housing and excessive sleeve bearing

clearance.

2. Looseness of the support system of a machine such as loose mounting bolls, grouting

deterioration or cracks in the structure.

Mechanical Looseness and "Sub harmonic" Frequencies

On occasion, certain looseness conditions can also result in "sub harmonic"

Frequencies of vibration (i.e. 1/2, 1/3, or 1/4 x RPM) with frequencies at 1/2 x RPM

being the most common. For example, there have been many reported cases of excessive

wear and clearance in sleeve bearings of large motors that have resulted in vibration

frequencies of 1/2x, 1x, 1-1/2x, 2x, 2-1/2x, 3x, 3-1/2x and Higher orders of 1/2 x RPM.

Why and how vibration frequencies at multiples of ' half-order (1/2 x RPM) are generated

has never been fully explained. However, when detected, possible looseness conditions

including bearing clearance Problems should be suspected.

5.8.7 Vibration Due To Eccentricity

Of course, no rotor or shaft can be made perfectly round. Some eccentricity or

"out-of-roundness" will be present on nearly every rotating assembly. Eccentricity is a

common cause of unbalance, and for common machines such as fans, blowers, pumps,

etc., normal balancing procedures can be carried out to minimize the effects of

eccentricity. However, in certain situations, eccentricity can result in "reaction" forces

that cannot be totally compensated by simply balancing the rotor. Probably the most

common examples are eccentric belt pulleys and chain sprockets, eccentric gears and

eccentric motor armatures.

In the case of an eccentric belt pulley or chain sprocket, each revolution of the

eccentric pulley or sprocket will cause a variation in belt or chain tension. The result will

be a vibration frequency at 1 x RPM of the eccentric element, with a directional force on

a line between the centers of the driver and driven pulleys or sprockets. Although this

could be easily mistaken as an unbalance problem, a simple test for- the directionality of

the radial vibration by taking comparative horizontal and vertical phase readings or by

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taking multiple radial amplitude readings will quickly reveal the highly directional nature

of the vibration. Slow motion studies with a stroboscopic light or run out checks with a

dial indicator will confirm the eccentricity problem.

Fig: 5.11 Vibrations Due To Eccentricity

Eccentric gears will cause highly directional vibration at 1 x RPM of the eccentric

gear in a manner similar to that of eccentric belt pulleys and chain sprockets, and can be

identified by taking comparative horizontal and vertical phase readings or by taking

multiple radial amplitude readings as described earlier.

5.8.8 Vibration Due To Resonance

Resonance is a very common cause of excessive vibration on machines because

1. Machines consist of many individual elements or components such as suction and

discharge piping, bearing pedestals, bases, and accessory items such as exciters and lube

oil pumps, etc... Of course, each component has its own mass and stiffness characteristics

and, hence, its own unique natural frequency.

2. The stiffness of each machine component is different in different directions. As a

result, each machine component will likely have several different natural frequencies.

For example, consider a fan bearing. Most likely, the stiffness of the bearing will be

different in the horizontal, vertical and axial directions. As a result, the natural

frequencies of this particular machine component will also be different in the horizontal,

vertical and axial directions.

When one considers all of the various machine components, along with the

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multiple natural frequencies possible for each component, the reason that resonance is

such a common problem is quite understandable. All that is required is that the natural

frequency of one machine component, in one of its directions of vibration, be the same as

one exciting force frequency inherent to the machine, when this happens, resonance and

high levels of vibration will result.

Although machines that are installed and brought into service may not exhibit

resonance problems initially, resonance may become a problem in the future if changes in

machine stiffness occur as the result of bearing wear, grouting deterioration, loosening of

mounting bolts or other problems.

5.8.9 Vibration due to defective rolling element bearings

When a rolling element bearing develops flaws on the raceways and/or rolling

elements, there are actually a number of vibration frequency characteristics that can result

depending on the extent of deterioration.

5.12 vibrations due to worn rollers, worn gear teeth and worn belts

Thus, identifying these characteristic frequencies cannot only help to verify that a

bearing is definitely failing, but can also give some indication of the extent of

deterioration. The following is a discussion of the four stages that a bearing will typically

go through from the earliest stage of deterioration to that approaching catastrophic

failure. Catastrophic failure id defined here as simply the total in ability of the bearing to

perform its intended functions of minimizing the friction generated through rotating

motion and keeping rotating and non-rotating parts from coming into contact with one

another. In other words, failure will occur when either the bearing literally comes apart or

seizes due to excessive heat buildup.

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5.9 VIBRATION ANALYSIS

5.9.1 Introduction

Interpreting vibration characteristics carries out diagnostics studies based on

vibration analysis. The following vibration characteristics are utilized to interpret the

machinery health condition.

1. Vibration displacement

2. Vibration velocity

3. Vibration acceleration will include the health condition.

4. Vibration frequency will indicate the defect

5. Vibration base will help to indicate the defective location

5.9.2 Dominant Frequency

It is sometimes useful to know the dominant frequency of vibration of a machine

that has several rotating parts. Consider for example a belt driven blower. The motor and

fan run at different speeds. The dominant frequency will reveal which part of the machine

is causing the most vibration. The measurements taken on the motor bearings would

include vibration of the motor plus vibrations from the fan transmitted through the drive

belt and mounting structure. Conversely, measurement taken on the fan bearings would

include vibrations of the fan plus vibrations transmitted from the motors as shown in the

figure. In many cases the point with the most vibration would pin point which part has

the trouble, but not always. Measurements taken on the fan contains vibrations of the fan

plus transmitted vibrations from the motor.

The following sequence is used to find the dominant frequency:

1. Measure and record the displacement (D) at a given point.

2. In same manner and at the same point, measure and record the velocity (V).

3. The dominant frequency can be found by dividing the velocity measurement (V) by the

displacement measurement (D) and multiplying by the constant 19100. The answer will

be the dominant frequency of vibration in cycles per minute.

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Dominant frequency (CPM) =

velocity (V) millimeters/second x 19100 (metric units)

Displacement (D) micrometers

For example, if the motor runs at 1750 RPM and the fan at 2600 RPM.

Measurements taken on the motor are displacement (D) = 47 micrometers and velocity

(V) = 6.5 millimeters / seconds.

The dominant frequency then becomes:

(6.5/47) XI 9, 120 =2,644 cpm

2644 CPM is nearest the fan speed. The fan is the dominant part and is causing

vibration.

Generally the dominant frequency will be equal to the rotating speed of the part

cause the vibration, assuming that the trouble is unbalance. In any event the dominant

vibration frequency will normally be some multiple of RPM of the part. After

determining the dominant frequency, the type of the trouble present may be assumed

from the following table.

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CHAPTER-VI

ARTIFICIAL NEURAL NETWORKS

6.1 INTRODUCTION

An artificial neural network (ANN), usually called "neural network" (NN), is a

mathematical model or computational model that tries to simulate the structure and/or

functional aspects of biological neural networks. It consists of an interconnected group of

artificial neurons and processes information using a connectionist approach to

computation. In most cases an ANN is an adaptive system that changes its structure based

on external or internal information that flows through the network during the learning

phase. Neural networks are non-linear statistical data modeling tools. They can be used to

model complex relationships between inputs and outputs or to find patterns in data.

A neural network is an interconnected group of nodes, akin to the vast network of

neurons in the human brain.

Fig: 6.1 a simple neural network

6.1.1 Background

Component based representation of a neural network. This kind of more general

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representation is used by some neural network software.

There is no precise agreed-upon definition among researchers as to what a neural network

is, but most would agree that it involves a network of simple processing elements

(neurons), which can exhibit complex global behavior, determined by the connections

between the processing elements and element parameters. The original inspiration for the

technique came from examination of the central nervous system and the neurons (and

their axons, dendrites and synapses) which constitute one of its most significant

information processing elements (see Neuroscience). In a neural network model, simple

nodes (called variously "neurons", "neurodes", "PEs" ("processing elements") or "units")

are connected together to form a network of nodes — hence the term "neural network."

While a neural network does not have to be adaptive per se, its practical use comes with

algorithms designed to alter the strength (weights) of the connections in the network to

produce a desired signal flow.

These networks are also similar to the biological neural networks in the sense that

functions are performed collectively and in parallel by the units, rather than there being a

clear delineation of subtasks to which various units are assigned (see also

connectionism). Currently, the term Artificial Neural Network (ANN) tends to refer

mostly to neural network models employed in statistics, cognitive psychology and

artificial intelligence. Neural network models designed with emulation of the central

nervous system (CNS) in mind are a subject of theoretical neuroscience (computational

neuroscience).

In modern software implementations of artificial neural networks the approach

inspired by biology has for the most part been abandoned for a more practical approach

based on statistics and signal processing. In some of these systems, neural networks or

parts of neural networks (such as artificial neurons) are used as components in larger

systems that combine both adaptive and non-adaptive elements. While the more general

approach of such adaptive systems is more suitable for real-world problem solving, it has

far less to do with the traditional artificial intelligence connectionist models. What they

do have in common, however, is the principle of non-linear, distributed, parallel and local

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processing and adaptation.

6.1.2 Models

Neural network models in artificial intelligence are usually referred to as artificial

neural networks (ANNs); these are essentially simple mathematical models defining a

function. Each type of ANN model corresponds to a class of such functions.

6.1.3 The Network in Artificial Neural Network

The word network in the term 'artificial neural network' arises because the function f(x)

is defined as a composition of other functions gi(x), which can further be defined as a

composition of other functions. This can be conveniently represented as a network

structure, with arrows depicting the dependencies between variables. A widely used type

of composition is the nonlinear weighted sum, where, where K (commonly referred to as

the activation function) is some predefined function, such as the hyperbolic tangent. It

will be convenient for the following to refer to a collection of functions gi as simply a

vector.

Fig:6.2 ANN dependency graph

This figure depicts such a decomposition of f, with dependencies between variables

indicated by arrows. These can be interpreted in two ways.

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The first view is the functional view: the input x is transformed into a 3-dimensional

vector h, which is then transformed into a 2-dimensional vector g, which is finally

transformed into f. This view is most commonly encountered in the context of

optimization.

The second view is the probabilistic view: the random variable F = f(G) depends upon

the random variable G = g(H), which depends upon H = h(X), which depends upon

the random variable X. This view is most commonly encountered in the context of

graphical models.

The two views are largely equivalent. In either case, for this particular network

architecture, the components of individual layers are independent of each other (e.g., the

components of g are independent of each other given their input h). This naturally

enables a degree of parallelism in the implementation.

6.1.4 Learning

What has attracted the most interest in neural networks is the possibility of

learning. Given a specific task to solve, and a class of functions F, learning means using

a set of observations to find which solves the task in some optimal sense. This entails

defining a cost function such that, for the optimal solution f *, (i.e., no solution has a cost

less than the cost of the optimal solution).

The cost function C is an important concept in learning, as it is a measure of how

far away a particular solution is from an optimal solution to the problem to be solved.

Learning algorithms search through the solution space to find a function that has the

smallest possible cost.

For applications where the solution is dependent on some data, the cost must

necessarily be a function of the observations; otherwise we would not be modeling

anything related to the data. It is frequently defined as a statistic to which only

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approximations can be made. As a simple example consider the problem of finding the

model f which minimizes, for data pairs (x,y) drawn from some distribution . In practical

situations we would only have N samples from and thus, for the above example, we

would only minimize. Thus, the cost is minimized over a sample of the data rather than

the entire data set.

When some form of online learning must be used, where the cost is partially

minimized as each new example is seen. While online learning is often used when is

fixed, it is most useful in the case where the distribution changes slowly over time. In

neural network methods, some form of online learning is frequently used for finite

datasets.

6.1.5 Employing artificial neural networks

Perhaps the greatest advantage of ANNs is their ability to be used as an arbitrary

function approximation mechanism which 'learns' from observed data. However, using

them is not so straightforward and a relatively good understanding of the underlying

theory is essential.

Choice of model: This will depend on the data representation and the application. Overly

complex models tend to lead to problems with learning.

Learning algorithm: There are numerous tradeoffs between learning algorithms. Almost

any algorithm will work well with the correct hyper parameters for training on a

particular fixed dataset. However selecting and tuning an algorithm for training on

unseen data requires a significant amount of experimentation.

Robustness: If the model, cost function and learning algorithm are selected appropriately

the resulting ANN can be extremely robust.

With the correct implementation ANNs can be used naturally in online learning

and large dataset applications. Their simple implementation and the existence of mostly

local dependencies exhibited in the structure allows for fast, parallel implementations in

hardware.

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6.1.6 Applications

The utility of artificial neural network models lies in the fact that they can be used

to infer a function from observations. This is particularly useful in applications where the

complexity of the data or task makes the design of such a function by hand impractical.

6.1.7 Real life applications The tasks to which artificial neural networks are applied tend to fall within the

following broad categories: Function approximation , or regression analysis, including time series prediction,

fitness approximation and modeling.

Classification , including pattern and sequence recognition, novelty detection and

sequential decision making.

Data processing , including filtering, clustering, blind source separation and

compression.

Robotics , including directing manipulators, Computer numerical control.

Application areas include system identification and control (vehicle control, process

control), quantum chemistry, game-playing and decision making (backgammon, chess,

racing), pattern recognition (radar systems, face identification, object recognition and

more), sequence recognition (gesture, speech, handwritten text recognition), medical

diagnosis, financial applications (automated trading systems), data mining (or knowledge

discovery in databases, "KDD"), visualization and e-mail spam filtering.

6.2 PATTERN CLASSIFICATION NETWORK:

A two layer feed-forward network with non linear output functions for the units in

the output layer can be used for the task o f pattern classification. The number of units in

the input layer corresponds to the dimensionality of input pattern vectors. The units in the

input layer are all linear, as the input layer merely contributes to fan out the input to each

of the output units. The number of output units depends on the number of distinct classes

in the pattern classification task. We assume for this discussion that the output units are

binary. Each output unit is concerned to all the input units, and a weight is associated

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with each connection. Since the output function of a unit is a hard limiting threshold

function, for a given set of input-output patterns, the weighted sum of the input values

compared with the threshold for the unit to determine whether the sum is greater or less

than the threshold. Thus, in this case a set of in equalities are generated with the given

data. Thus there is no unique solution for the weights in this case. Typically, if the

weighted sum of the input values to the input values to the output values exceeds the

threshold, the output signal is labeled as 1, otherwise as 0. Multiple binary output units

are needed of the number of pattern classes exceeds 2.

6.3 BACK PROPOGATION ALGORITHM (generalized delta rule)

Given a set of input-output patterns (al,bl),l=1,2,…….L,

Where the lth input vector and the al = (al1,al2…..all)T and the lth output vector

bl=(al1,al2……alk)T.

Assume only one hidden layer and initial setting of weights to be arbitrary.

Assume input layer with only linear units.

Then the output signal is equal to the input activation value for each of these units. Let η

be the learning rate parameter.

Let a =a (m) =a and b=b (m) =bl.

Activation of unit I in the input layer, xi= ai(m)

Activation unit j in the hidden layer,

Output signal from the jth unit in the hidden layer,

Activation of unit k in the output layer,

Output signal from unit k in the output layer,

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Error term for the kth output layer,

Calculate the error for the lth pattern,

Total error for all patterns,

Apply the given patterns one by one, may be several limits, in some random order and

update the weights until the total error reduces to an acceptable value.

6.4 APPLICATION OF ANN TO VIBRATION ANALYSIS

6.4.1 Reasons for Applying Ann

Process upsets and abnormal situations often entail a certain degree of

unpredictability

Unknowns and unpredictable behavior of processes operating in combination with

one another call for artificial intelligence

Artificial neural networks are widely preferred due to their pattern recognition

capabilities

6.4.2 Developing an ANN system

In order to overcome the ever present restriction in the development of expert

systems based on neural networks a four phased data production analysis procedure for

training has been developed. The four interleaved approaches for data collection are

simple fault simulation, finite element method(FEM) simulation, test rig simulation and

real data gathering using this technique the amount of data can be extended to fulfill the

strictest requirements of a neural network capable of handling almost all rotating

machinery at the user sites. The adopted approach makes it possible to vary such

parameters as type and structure of the machinery in question, together with the

operational parameters such as running speed, load and environmental factors. The data

flow scheme during the development process is shown in figure. In this approach data

from the simple fault simulator FEM model test rig and real world can be combined and

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analyzed in one module and then treated in the same way when training the neural

network. Basically this approach overcomes the problem of gathering sufficient amount

of data from faulty machinery in the field which for the defined fault and machinery

scenarios would take hundreds of years to be adequate for training.

Fig 6.3 the data flow chart

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Simulated fault simulation

Simulated data

FEM simulation Simulated data

Vibration parameters statistical FFT spectrum ceptrum auto correlation

Test measurement

Test data Data conversion

Test data

Simulated test, vibration parameters

Plant measurement

Test data Data conversion

Test data

Data optimization

Optimized dataANN

6.4.3 Test rig simulation

A test rig has been built to enable the generation of fault data for training the

neural networks and neuro fuzzy system in addition; the test data is used to refine the

simulation model. The test rig consists of a motor, brake and a shaft with two bearings.

The test rig has been used for data collection for different fault types such as unbalance,

misalignment and different types of bearing faults. All these fault types have been studied

at different stages of fault severity. The data from the test rig gives the basic information

for the development of the hybrid expert system. As work on the project developed, the

test rig was modified to represent a more complicated item of plant.

6.4.4 Simple fault simulator

A simple PC based fault simulator (SFS) has been developed. The SFS can be

used to predict the characteristic features of vibration acceleration signals for different

fault types such as unbalance, misalignment and different types of bearing faults. The

SFS can also introduce noise to the signals due to various sources, i.e the effects of other

machinery and amplifier/transducer performance. Linked to the SFS there is a module for

the calculation of different measuring parameters, which have been programmed the

background for this is simply that there are a great no of different measurement

parameters used in practice.

6.4.5 FEM simulation

A finite element model simulation FEM was developed to provide a more

sophisticated degree of control over the synthesized data. The complexity of the FEM

model is much greater than the SFS and allows a variety of changes to be made to the

model for generating different fault situations. The great advantage of the fem simulation

is the possibility of making structural changes to the machine with minimum effort,

especially if the model has been built for this purpose. In this case the model has been

parameterized using super element techniques in order to keep the no of degrees freedom

of the model at a reasonable level for calculation purposes. The model basically

represents the test rig but offers the capability of making dimensional changes such as

shaft diameter variation and bearing distance variation thus introducing to the response

the effect of transfer functions due to the variation of natural frequencies

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6.4.6 Problems developing diagnostic expert systems

Rules are a common form of knowledge representation and are present in most AI

applications such as expert systems and decision support systems. Such rules are

normally obtained from human experts as a result of a lengthy knowledge engineering

process other systems may obtain their knowledge from machine learning programs. Rule

based systems are widely used because they allow the incorporation of multiple clauses,

enable the use of confidence measures, can be subjected to mathematical rigor i.e formal

logic enable modular systems to be built and most important of all a lot of human

reasoning can be expressed as rules. Rule based systems have some serious disadvantages

1. The process of acquiring knowledge from human experts is very time consuming,

prone to errors and is quite an expensive process to carry out.

2. Rules are brittle when presented with nosy, incomplete or non linear data.

3. Rules do not scale up very well, inconsistencies and errors start to creep in as the

knowledge based grows.

The main cause of brittleness with in rule based systems is a requirement that every

possible combination of antecedents and their values must be explicitly provided for.

Thus in order to cope with the complexities of real world data a practical rule based

system must have a large number of rules to account for the most common cases that

should occur. Except for smaller, restricted applications it is most unlikely that any given

rule based system will be robust or complete enough (i.e have sufficient rules) to provide

reasonably correct answers when presented with deviant input. Most expert systems

experience a sharp drop of in-operational capability when confronted with novel

situations for which no specific rules exist. However, vibration data has a great deal of

variability in the amplitude, frequency and phase of the measured data points. This

variability of data input is the main cause of diagnostic failure within rule based system.

Vibration data often stresses the pattern matching ability of rule based to breaking point.

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6.4.7 Advantages of applying ANN’s for fault detection

One of the tools used for fault detection is the application of artificial neural

networks for the analysis of vibrations generated by a piece of equipment.

Although there are numerous efficient methods for modeling of mechanical

systems, they all suffer the disadvantage that they are only valid for a particular machine.

Changes within the design or the operational mode of the machine normally require a

manual adaptation. Using neural networks to model technical systems eliminates this

major disadvantage. The basis for a successful model is an adequate so called knowledge

base on which the network is “trained”. Without prior knowledge of the machines

systematic behavior or its history, training of a neural network is possible.

A second advantage of neural network is that the trained network is not only valid

for a small section of the complete operational range of the machine. A neural network

that has been trained and there by possessing a tolerable residual is valid for all

conditions included in the knowledge base.

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CHAPTER VII

CASE STUDY

BOILER FEED PUMP 4B

7.1 Description of the Equipment

Boiler Feed Pump (BFP) is used to pump the feed water (chemically treated water)

in to the boiler. The FK6D30 type BFP consists of FAiB56 Booster Pump (BP) directly

driven from one end of the shaft of an electric motor. BFP is driven from the opposite end

of Motor shaft through a spacer type flexible coupling.

Fig: 7.1 Boiler feed pump train

The BP is a single stage, horizontal, axial split casing type, having the suction and

discharge branches on the casing bottom half, thus allowing the pump internals to be

removed without disturbing the suction and discharge pipe work or the alignment

between the pump and the driving motor. The rotating assembly consists of the shaft,

Impeller, nuts, keys, seal sleeves, thrust collar, the rotating parts of the mechanical seals,

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pump coupling. The rotating assembly is supported at each end of the shaft by a white

metal lined journal bearing. The residual axial thrust is taken up by a tilting double thrust

bearing mounted at the non drive end of the pump. The present work deals with the main

pump which is connected to the motor by flexible hydraulic coupling. The boiler feed

pump is supported by the journal bearings. The line diagram of the entire unit is shown in

figure 7.1.

7.2 Specifications:

No of stages……………………………...6

Design flow rate…………………………448.5 m3/sec.

Speed ……………………………………5178 rpm.

No of impeller vanes of main pump…….7no’s

No of impeller vanes of booster pump….5no’s

Booster pump speed…………………….1485 rpm

Variable speed geared coupling

Motor speed……………………………..Ne=1482 rpm

Gear ratio………………………………..u1=Ze/Zi=143/41

Primary speed N1………………………..N1 = 5289 rpm

Full load slip…………………….………..S = 2.1%

Max output speed………………………..Ne =5178 rpm.

Regulating range………………………...4:1 down loads.

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7.3 Experimentation

The measurements are recorded using “Data PAC 1500”, dual channel seismic

pick-up, with a frequency range of 10cpm to 4518000cpm(0.18hz to 75.3 Hz), with A/D

converter, VGA resolution screen data collector of Entek IRD,USA make, over a period

of 6 months at regular monthly intervals. The instrument is mounted on the bearing

supports along horizontal (H), vertical (V), and axial (A) directions, the axial direction

being in line with the axis of the shaft. The measurements are made in displacement and

velocity modes. Accelerations have been computed. Regular logging of the data has

provided on the basis for performance trend monitoring of the rotating structure and

prediction of faults to apply reasoning to trace the root cause.

7.4 Data collected before rectification

Vibration readings before rectification:

DATE SUPPORT POINT

DISPLACEMENT(um)H V A

VELOCITY(mm/sec)H V A

11th NOVEMBER 2008

BPNDEBPDE

MMDEMMNDE

MPDEMPNDE

12.0 2.5 4.58.2 3.2 5.07.2 4.3 5.85.3 2.8 1.818.4 11.2 14.528 38 25

1.6 1.5 1.31.5 0.6 1.50.9 0.8 1.00.8 0.4 0.44.0 3.3 3.29.2 5.0 8.3

25th November 2008

BPNDEBPDE

MMDEMMNDE

MPDEMPNDE

17.2 12.3 13.514.5 5.3 6.89.8 3.6 6.40.8 0.4 0.44.0 3.3 3.29.2 5.0 8.3

2.5 1.8 1.41.8 0.8 1.60.9 1.0 1.20.9 0.6 0.67.8 3.8 5.212 12.2 9.2

10th December 2008

BPNDEBPDE

MMDEMMNDE

MPDEMPNDE

13 5.2 149.5 2.2 5.29.8 3.6 6.45.8 2.6 2.213 14 12.526 25 18

1.8 1.5 1.41.2 0.6 1.40.9 0.8 1.20.8 0.5 0.53.6 4 3.28.1 5.5 7.0

23rd December 2008

BPNDEBPDE

MMDEMMNDE

MPDEMPNDE

12 16.5 5.88.5 3.4 4.66.6 4.5 5.85.6 2.2 217 16.5 1328 45 42

2.3 1.4 1.01.5 0.7 0.90.8 0.7 1.30.8 0.5 0.64.8 5.1 4.010 7.2 6.6

81

06th January 2009 BPNDEBPDE

MMDEMMNDE

MPDEMPNDE

29 11 13.421 6 19.510.5 9 13.513.5 4.5 5.527.5 21.5 2154 46 22

6.8 4.7 3.44.7 2.2 2.92.1 2.1 3.11.8 1.6 1.610.8 10.5 11.516.5 16.3 14.5

20th January 2009 BPNDEBPDE

MMDEMMNDE

MPDEMPNDE

10.5 12 8.57.5 2.8 4.56.2 4.5 5.35.8 2.1 2.215 45 13.528 29 25

1.8 1.4 1.11.2 0.6 1.40.8 0.6 1.00.7 0.6 0.54.8 4.5 4.29.2 6.2 10

O3rd January 2009 BPNDEBPDE

MMDEMMNDE

MPDEMPNDE

10 4.8 8.58 8.2 56.5 4 5.55.8 3 2.113.5 17 621 40 25

1.6 1.3 1.21.3 0.7 0.80.8 0.6 1.00.8 0.5 0.62.8 3.0 2.46.5 3.0 7.0

17th January 2009 BPNDEBPDE

MMDEMMNDE

MPDEMPNDE

22 10 1217 5.0 1012 10 1110 6.0 5.0170 14 1536 22 48

5.1 4.6 3.13.9 2.4 2.92.4 1.7 2.82 1.3 1.56.2 8.4 6.46.4 8.5 13.7

17th FEBRUARY 2009

BPNDEBPDE

MMDEMMNDE

MPDEMPNDE

24.0 12.0 13.819.0 7.00 16.013.0 9.00 13.010.0 7.00 6.0024.0 170 4.0038.0 28.0 12.0

4.70 3.90 3.104.30 2.50 3.702.70 2.10 3.101.90 1.20 1.409.10 9.40 7.809.80 9.70 16.2

30th MARCH 2009 BPNDEBPDE

MMDEMMNDE

MPDEMPNDE

17.0 6.42 8.8812.9 3.56 9.5610.3 7.35 8.558.95 5.51 3.6311.3 11.0 9.0531.8 18.1 9.19

2.95 2.34 1.491.85 1.21 1.601.47 1.13 1.181.48 1.04 1.154.97 5.74 5.4011.3 4.40 20.7

14th APRIL 2009 BPNDEBPDE

MMDEMMNDE

MPDEMPNDE

26.8 8.60 10.016.6 5.20 10.512.4 8.20 11.412.6 6.40 5.7068.6 29.6 26.468.4 98.0 27.2

5.10 3.90 3.003.70 2.10 3.202.30 2.20 3.002.50 1.80 2.3015.2 17.1 18.123.6 27.7 18.1

17th APRIL 2009 BPNDEBPDE

MMDEMMNDE

26.8 8.60 10.016.6 5.20 10.512.4 8.20 11.412.6 6.40 5.70

5.10 3.90 3.003.70 2.10 3.202.30 2.20 3.002.50 1.80 2.30

82

MPDEMPNDE

35.8 21.1 20.262.89 87.9 20.7

9.50 6.60 11.716.6 21.5 10.0

7.5 ANALYSIS OF DATA

Observing the readings from 11-11-2008 to 17-04-2009 the vibration velocity on

14-04-2009 at the main pump non driving end was tending towards abnormality. Also On

17-04-2009 the vibration velocity was intolerable. Added to these the reading at the main

pump drive end on 17-04-2009 was high.

Dominant frequency = V/D * 19100

= 21.5/87.9*19100=4671.786cpm

Thus, X=4671.786/5178=0.98=1 approximately,

Where X=the ratio of the dominant frequency to the speed

Since X is more than one times the speed of the main pump, the defect was found

to be unbalance or looseness.

The main pump vane passing frequency

= number of impeller vanes X main pump running speed.

= 7 X 5178 =36,248 cpm.

In the frequency vs. velocity spectrums the vane passing frequency harmonics of

main pump were present and 2x is having higher value. So, due to the 1x of main pump

running speed and 2x of the main pump vane passing frequency are the dominant

frequencies the cause for the frequent vibration increase was the looseness of the main

pump.

83

7.6 Spectrum Analysis before Rectification

Fig 7.1 Velocity spectrum of MPDE bearing in horizontal direction

Fig 7.2 Velocity spectrum of MPDE bearing in vertical direction

84

Fig 7.3 Velocity spectrum of MPDE bearing in axial direction

Fig 7.4 Velocity spectrum of MPNDE bearing in horizontal direction

85

Fig 7.5 Velocity spectrum of MPNDE bearing in vertical direction

Fig 7.6 Velocity spectrum of MPNDE bearing in axial direction

86

7.7 Observations from the Spectrums:

In all the spectrums of Main Pump Drive End and Main Pump Non Drive End 1x

running speed harmonic are present.

In the vertical spectrum of Main Pump Non Drive End 1x running speed

frequency peak is predominant and having higher value 19.9 mm /see

In all the spectrums of Main Pump Drive End & Main Pump Non Drive End main

pump vane passing frequency and its harmonics are found and 2x of vane passing

frequency peak is predominant having value 7.9 mm /see

In all the spectrums of Main Pump Non Drive End side bands to vane passing

frequency peak harmonics are found.

In all the spectrums of Main Pump Drive End both the booster pump and main

pump vane passing frequency peaks are found.

7.8 Conclusions:

All the vibration values of booster pump non drive end, booster pump drive end,

main motor booster pump end, and main motor non drive end are in the good

zone. But Main Pump Drive End & Main Pump Non Drive End is in alarm level.

Here 1x is predominant frequency peak in the Main Pump Drive End & Main

Pump Non Drive End spectrums Misalignment/ Looseness of the main pump

were suspected.

A harmonic with vane passing frequency peak of the main pump are found and is

having predominant peak value. So the looseness/misalignment of the pump

impeller was suspected.

The main pump foundation bed bolts are checked for looseness and must be

tightened.

87

7.9 Action taken

Due to high vibration on pump side (at NDE vertical) pump stopped on 18-04-

2009 and attend for the rectification. Pump NDE side bed bolts were tightened and thrust

bearing top cover is lifted by 0.01mm. After attending the work pump taken into the

service on 21-04-2009 and vibration readings were taken and observed that vibration

readings were reduced to normal value i.e. in the good zone.

7.10 Data collection after rectification

DATE SUPPORT POINT

DISPLACEMENT(um)H V A

VELOCITY(mm/sec)H V A

21st APRIL 2009

BPNDEBPDE

MMDEMMNDE

MPDEMPNDE

16.3 6.65 9.0513.4 3.84 9.4012.4 7.99 9.1710.9 5.94 4.7116.4 19.7 12.633.1 23.2 8.35

3.21 2.53 2.022.26 1.10 1.551.63 1.61 1.591.50 1.14 1.525.27 5.61 6.198.44 6.20 6.34

28th APRIL 2009

BPNDEBPDE

MMDEMMNDE

MPDEMPNDE

19.0 9.08 11.015.5 3.60 9.6811.4 7.08 9.189.24 5.29 4.2920.4 15.2 6.2530.0 19.3 6.38

3.19 3.19 2.302.26 1.26 1.511.48 1.27 1.981.92 1.34 1.115.52 6.54 5.828.10 5.29 14.2

12th MAY 2009 BPNDEBPDE

MMDEMMNDE

MPDEMPNDE

25.0 10.8 12.018.4 4.60 10.812.6 9.00 10.812.2 6.00 5.2022.0 20.8 15.036.4 28.0 18.2

5.40 4.10 3.103.20 2.50 3.002.50 2.10 2.903.40 1.80 2.409.30 11.6 11.413.9 9.70 10.1

ISO standards iso-10816

Good : 0 to 5.4mm / sec

Satisfactory : 5.4 to 10.6mm / sec

Alarm : 10.6 to 16.mm / sec

Not permitted : >16. mm / sec

88

7.11 Spectrums after rectification

Fig 7.7 Velocity spectrum of BPNDE bearing in horizontal direction

Fig7.8 Velocity spectrum of BPNDE bearing in horizontal direction (Booster pump vane

passing frequency peak)

89

Fig 7.9 Velocity spectrum of BPNDE bearing in horizontal direction (Booster pump vpf

& harmonics)

Fig 7.10 Velocity spectrum of MPDE bearing in horizontal direction (1x main pump

harmonics &vane passing frequency and its harmonics)

90

Fig 7.11 Velocity spectrum of MPDE bearing in vertical direction (1x harmonics)

Fig 7.12 Velocity spectrum of MPDE bearing in axial direction

91

Fig 7.13 Velocity spectrum of MPNDE bearing in horizontal direction

Fig 7.14 Velocity spectrum of MPNDE bearing in vertical direction

92

Fig 7.15 Velocity spectrum of MPNDE bearing in horizontal direction (side bands of

main pump vpf)

Fig 7.16 Velocity spectrum of MPDE bearing in vertical direction (main pump vpf &

harmonics)

93

Fig 7.17 Velocity spectrum of MPNDE bearing in vertical direction (1x harmonics)

Fig 7.18 Velocity spectrum of MPDE bearing in axial direction (main pump vpf &

harmonics)

94

CHAPTER VIII

APPLICATION OF ANN TO FAULT RECOGNITION

ON BFP

8.1 NETWORK SPECIFICATIONS:

For the purpose of recognizing the faults present in the given boiler feed pump

from the vibration patterns, the ANN was developed and trained using actual data

pertaining to the boiler feed pump and applying the back propagation algorithm. The final

network architecture is shown below:

The parameters pertaining to the ANN and the training process are

Network architecture:

Input layer: 3 units

Hidden layers: 2

Number of neurons in each hidden layer: 2

Model of neuron: perceptron model.

Output function: hyperbolic tangent

8.2 Training of the network:

A ‘c’ program was used for back propagation training of the ANN based on the

back propagation algorithm documented above. The data collected was used for training

the network. In addition to this, past data pertaining to the same boiler feed pump was

also used.

Once the network was trained, 10 new sets of data were used for testing the network in

addition to the 58 training sets.

95

8.3 Results From ANN Program:

The back propagation learning law depends upon random initialization of

weights, and hence yields different results with each execution of the program. The

results of one such execution are documented below:

Inputs to the program are:

Learning Rate =0.1

Momentum Rate=0.1

Number of Iterations: 500

Results after training ANN are:

Row Target Output Match

TRN 1 unbalance unbalance Ok

TRN 2 unbalance unbalance Ok

TRN 3 misalignment misalignment Ok

TRN 4 unbalance unbalance Ok

TRN 5 misalignment misalignment Ok

TRN 6 misalignment misalignment Ok

TRN 7 misalignment misalignment Ok

TRN 8 misalignment misalignment Ok

TRN 9 misalignment misalignment Ok

TRN 10 misalignment misalignment Ok

TRN 11 looseness looseness Ok

TRN 12 looseness looseness Ok

TRN 13 looseness looseness Ok

TRN 14 looseness looseness Ok

TRN 15 looseness looseness Ok

TRN 16 looseness looseness Ok

TRN 17 misalignment misalignment Ok

TRN 18 misalignment misalignment Ok

TRN 19 misalignment misalignment Ok

TRN 20 unbalance unbalance Ok

96

TRN 21 looseness looseness Ok

TRN 22 looseness looseness Ok

TRN 23 misalignment misalignment Ok

TRN 24 looseness looseness Ok

TRN 25 unbalance unbalance Ok

TRN 26 unbalance unbalance Ok

TRN 27 unbalance unbalance Ok

TRN 28 unbalance unbalance Ok

TRN 29 unbalance unbalance Ok

TRN 30 unbalance unbalance Ok

TRN 31 unbalance unbalance Ok

TRN 32 unbalance unbalance Ok

TRN 33 unbalance unbalance Ok

TRN 34 unbalance unbalance Ok

TRN 35 unbalance unbalance Ok

TRN 36 unbalance unbalance Ok

TRN 37 unbalance unbalance Ok

TRN 38 unbalance unbalance Ok

TRN 39 unbalance unbalance Ok

TRN 40 unbalance unbalance Ok

TRN 41 unbalance unbalance Ok

TRN 42 unbalance unbalance Ok

TRN 43 unbalance unbalance Ok

TRN 44 unbalance unbalance Ok

TRN 45 unbalance unbalance Ok

TRN 46 unbalance unbalance Ok

TRN 47 unbalance unbalance Ok

TRN 48 unbalance unbalance Ok

TRN 49 unbalance unbalance Ok

TRN 50 unbalance unbalance Ok

TRN 51 unbalance unbalance Ok

97

TRN 52 unbalance unbalance Ok

TRN 53 looseness looseness Ok

TRN 54 looseness unbalance Wrong

TRN 55 unbalance unbalance Ok

TRN 56 unbalance unbalance Ok

TRN 57 unbalance unbalance Ok

TRN 58 unbalance unbalance Ok

TST 59 misalignment misalignment Ok

TST 60 misalignment misalignment Ok

TST 61 misalignment misalignment Ok

TST 62 misalignment misalignment Ok

TST 63 misalignment misalignment Ok

TST 64 unbalance unbalance Ok

TST 65 looseness looseness Ok

TST 66 unbalance unbalance Ok

TST 67 misalignment misalignment Ok

TST 68 looseness looseness Ok

98

CHAPTER IX

RESULTS AND DISCUSSIONS

9.1 VIBRATION SPECTRUM ANALYSIS

All the vibration values of booster pump non drive end, booster pump drive end,

main motor booster pump end, and main motor non drive end are in the good

zone. But Main Pump Drive End & Main Pump Non Drive End is in alarm level.

Here 1x is predominant frequency peak in the Main Pump Drive End & Main

Pump Non Drive End spectrums Misalignment/ Looseness of the main pump

were suspected.

A harmonic with vane passing frequency peak of the main pump are found and is

having predominant peak value. So the looseness/misalignment of the pump

impeller was suspected.

The main pump foundation bed bolts are checked for looseness and must be

tightened

99

9.2 SUMMARY OF ANN RESULTS:

The results obtained from ANN application may be summarized as below: For

Testing Data Sets:

Network Output

Target Unbalance Misalignment Looseness

Unbalance 2 0 0

Misalignment 0 6 0

Looseness 0 0 2

Table 9.1

For All Data Sets:

Network Output

Target Unbalance Misalignment Looseness

Unbalance 38 0 1

Misalignment 0 16 0

Looseness 0 0 13

Table 9.2

Matrix represents the number of times a fault has been diagnosed correctly or

incorrectly.

100

For example: In Table 9.2.,

Looseness has been diagnosed correctly 13 times and has been incorrectly

diagnosed 1 time as unbalance.

9.3 CORRELATION OF THE MATHEMATICAL AND ANN

ANALYSIS;

SET1 SET 2 SET 3

SPEED (N) 5178 5178 5178

VELOCITY (V) 16.6 21.5 10

DISPLACEMENT (D) 62.89 87.9 20.75

MATHEMATICAL

ANALYSIS

LOOSENESS LOOSENESS UNBALANCE

ANN ANALYSIS LOOSENESS LOOSENESS LOOSENESS

Table: 9.3

Results obtained by conventional methods and by application of the Artificial

Neural Network show a high degree of correlation. Thus, it may be concluded that the

pattern recognition and pattern classification properties of Artificial Neural Networks

make it highly feasible to apply them on a regular basis in industries.

101

CHAPTER-X

CONCLUSIONS

10.1 FROM VIBRATION SPECTRUM ANALYSIS

The reason for the frequent increase in vibration was found to be due to looseness

problem in the main pump bed bolts and it is also the fact that, the unbalance is caused

due to the flow related unbalance in the main pump. This problem was conformed using

the spectrum analysis. The spectrums were collected using DATAPAC 1500.

In order to rectify this problem various operations were performed. It was found

that the main pump bed bolts are not properly tightened and having some looseness. To

rectify this, the main pump bed bolts were tightened and the thrust bearing top cover is

lifted by 0.01mm to overcome the misalignment. So that the vibration must be reduced.

After the operations were performed the vibration readings and spectrums were

taken using the analyzer. The readings were found to be feasible to satisfy ISO standards.

Results obtained by conventional methods and by application of the Artificial

Neural Network show a high degree of correlation. Thus, it may be concluded that the

pattern recognition and pattern classification properties of Artificial Neural Networks

make it highly feasible to apply them on a regular basis in industries.

102

REFERENCES

1. R.K.Biswas “vibration based condition monitoring of rotating machines” national

conference on condition monitoring [NCCM-2006] December 2006 pg no 34-40.

2. M.Todd, S.D.J.McArthur, G.M.West, J.R.McDonald, S.J.Shaw. J.A.Hart paper

on “the design of a decision support system for the vibration monitoring of

turbine generators”

3. David Clifton, research article on “Condition Monitoring of Gas-Turbine

Engines”

4. T.W. Verbruggen a book on “Wind Turbine Operation & Maintenance based on

Condition Monitoring”

5. A Ramachandra, S B Kandagal, paper on “Prediction of Defects in Antifriction

Bearings using Vibration Signal Analysis”

6. Sadettin Orhan, Nizami Aktu¨rk, Veli C¸ elik, “Vibration monitoring for defect

diagnosis of rolling element bearings as a predictive maintenance tool:

Comprehensive case studies”

7. Peter W. Hills, Mechanalysis (India) Limited, India, “A more intelligent approach

to rotating equipment monitoring”

8. Cornelius, Scheffer, the paper on “Pump Condition Monitoring through Vibration

Analysis”.

9. Sheng Zhang, Joseph Mathew, Lin Ma, Yong Sun and Avin Mathew, a paper on

“Statistical condition monitoring based on vibration signals”.

10. P. Caselitz, J. Giebhardt,[10], presented a paper on “Condition Monitoring and

Fault Prediction for Marine Current Turbines”.

11. Steven M. Schultheis,[11], Charles A. Lickteig, presented a paper on

“Reciprocating Compressor Condition Monitoring”.

12. Peter W. Hills, Mechanalysis (India) Limited, India presented a paper on “A more

intelligent approach to rotating equipment monitoring”

13. L. B. Jack, A. K. Nandi, presented a paper on “Feature Selection for ANNs using

Genetic Algorithms in Condition Monitoring”.

103

14. Ms S Wadhwani, Dr S P Gupta, Dr V Kumar, “Wavelet Based Vibration

Monitoring for Detection of Faults in Ball Bearings of Rotating Machines”

15. Zhigang TIAN, “An Artificial Neural Network Approach for Remaining Useful

Life Prediction of Equipments Subject to Condition Monitoring”.

16. N.M. ROEHL C.E. PEDREIRA" H.R. TELES DE AZEVEDO presented a paper

on “Fuzzy art neural network approach for incipient Fault detection and isolation

in rotating machines”.

17. P.A.L. Ham, B.Sc.C.Eng..F.I.E.E. “Trends and future scope in the monitoring of

large steam turbine generators”

18. Dukkipati.S.Rao vibration technology published by Narosa publishers, 2004

19. G.K.Groover “mechanical vibrations” published by Nem Chand and pros 1996

20. R.A Collacat condition monitoring published by M c Graw Hill

21. G.D Rai an introduction to power plant engineering khanna publishers

22. R.S Khurmi theory of machines

23. Dr.NTTPS Vibration Analysis Material

24. Dr.NTTPS Vibration Basics Material

25. NBC bearing journals

26. http://www.skf.com

27. http://www.nbc.com

28. A.V.Barkov, N.A.Barkova, and A.Yu. Azovtsev, "Condition Monitoring and

Diagnostics of Rotating Machines Using Vibration", VAST, Inc., St. Petersburg,

Russia, 1997.

29. Eshleman R I“Some recent advances in roto dynamics” 3rd International

conference on vibrations of rotating machinery .University of York 1984.

30. A collection of condition diagnostics papers on the Internet site:

http://www.vibrotek.com/ref.htm

104

APPENDIXTHE CODE USED TO DETECT THE FAULTS:

#include<stdio .h>

#include<math. h>

#include<ctype.h>

#ifndef VAX

#include<string.h>

#include<process.h>

#include<conio.h>

#include<stdlib.h>

/*for declaration of calloc() on PC or compatible*/

#include<malloc.h>

#endif

/*define constants used throughout functions*/

#define NMXUNIT 10 /*MAXIMUM NUMBER OF UNITS IN A LAYER*/

#define NMXHLR 5 /*MAXIMUM NUMBER OF HIDDEN LAYERS*/ #define

NMXOATTR 5 /*MAXIMUM NUMBER OF OUTPUT FEATURES*/ #define

NMXINP 30 /*MAXIMUM NUMBER OF INPUT SAMPLES*/

#define NMXIATTR 7 /*MAXIMUM NUMBER OF INPUT FEATURES*/

#define SEXIT 3 /*EXIT SUCCESSFULLY*/

#define RESTRT 2 /*RESTART*/

#define FEXIT 1 /*EXIT IN FAILURE*/

#define CONTNE 0 /*CONTINUE CALCULATION*/

/*Data base: declaration of variables*/

float eta; /**learning rate**/

float alpha; /**momentum rate**/

float err_curr; /**normalized system error**/

float maxe; /* *maximum allowed system error* */

105

float maxep; /* *maximum allowed pattern error* */

float *wtptr[NMXHLR+l];

float *outptr[NMXHLR+2];

float *errptr[NMXHLR+2];

float *delw[NMXHLR+l];

float target[NMXINP][NMXOATTR];

float input[NMXINP][NMXIATTR], ep[NMXINP];

float outpt[NMXINP][NMXOATTR];

int nunit[NMXHLR+2], nhlayer, ninput, ninattr, noutattr;

int result, cnt, cnt_num;

int nsnew, nsold;

char task_name[20];

FILE *fpl, *fp2, *fp3,*fl,*f2,*f3,*f4,*f5,*fopen();

int fplotl10;

double x[15][5],y[15][5],P[15][5];

float a,al,a2;

int i, j,number=10;

*random number generator(computer independent*/

long randseed = 568731L;

int random()

{

randseed = 156251 * randseed + 22221L;

return((randseed>> 16) & 0x7FFF);

}

/*allocate dynamic storage for the net*/

void initQ

{

106

int lenl, len2, i, k;

float *pl,*p2,*p3,*p4;

lenl=len2 = 0;

nunit[nhlayer+2] = 0;

for (i=0;i<(nhlayer + 2);i++) {

lenl += (nunit[i] + 1) * nunit[i+l];

len2 += nunit[i] + 1;

}

pl=(float *) calloc(lenl+l,sizeof(float)); /*weights*/

p2=(float *) calloc(len2+l,sizeof(float)); /*outputs*/

p3=(float *) calloc(len2+l,sizeof(float)); /*error*/

p4=(float *) calloc(lenl+l,sizeof(float)); /*delw*/

/*set up initial pointers*/

wtptr[0] = pl;

outptr[0] = p2;

errptr[0] = p3;

delw[0] = p4;

/*set up the rest of pointers*/

for(r=l;i<(nhlayer+l);i++) {

wtptr[i]=wtptr[i- 1 ]+nunit[i] *(nunit[i- 1 ]+ 1 );

delw[i]=delw[i-1]+nunit[i]*(nunit[i-1]+1);

}

for(i=1;i<(nhlayer+2);i++)

{

outptr[i]=outptr[i-1]+nunit[i-1]+1;

errptr[i]=errptr[i- 1 ]+nunit[i- 1 ]+ 1 ;

}

/*set up threshold outputs*/

for(i=0;i<nhlayer+l ;i++)

{

*outptr[i]+nunit[i])=1.0;

107

}

// getch();

}

/* Initialize weights with random numbers between -0.5and+0.5*/

void initwt()

{

int i , j;

for(j=0;j<nhlayer+l ;j++)

for(i=0;i<(nunit[j]+l)*nunit|j+l];i++)

{

*(wtptr[j]+i)=random()/pow(2.0,15.0)-0.5;

*(delw[j]+i)=0;

}

// getch();

}

/*specify architecture of net and values of learning

parameters*/

set_up()

{ int i;

eta=0.9;

printf(“\nmomentum rate eta (default=0.9)?: ");

scanf("%f”,&eta);

alpha=0.7;

printf("\n learning rate alpha (default=0.7)?:");

scanf("%f”,&alpha);

maxe=0.01;

maxep=0.001;

printf("\n maximum total error (default=0.0l)?: ");

scanf("%f”,&maxe);

printf("\n Max individual error (default=0.001)?:");

scanf("%f”,&maxep);

108

cnt_num=1000;

printf("\n Max number of iterations(default=1000`)?: ");

scanf("%d",&cnt_num);

printf("\nNo. of hidden layers?: ");

scanf("%d",&nhlayer);

for(i=0;i<nhlayer;i++){

printf("\n\t no.of units for hidden layer %d?: ",i+l);

scanf("%d",&nunit[i+l]);

printf("\ncreate error file? If so typel, or type 0: " );

printf("\nExecution starts");

nunit[nhlayer+1 ]=noutattr;

nunit[0]=ninattr;

}

*read file for net architechture and learning parameters. File name has suffix_v.dat*/

dread(taskname)

char *taskname;

{

int i , j,c;

char var_file_name[20];

strcpy(var_file_name,taskname);

strcat(var_file_name,"_v.dat");

if((fp 1 =fopen(var_file_name,"r"))==NULL)

{

perror("\nCannot open datafile");

exit(0);

}

fscanf(fpl,

“%d%d%d%f%f%d%d”,&ninput,&noutattr,&ninattr,&eta,&alpha,&nhlayer,&cnt_num);

for(i=0;i<nhlayer+2;i++)

fscanf(fpl,''%d",&nunit[i]);

if((c=fclose(fpl))!=0)

109

printf("\nfile cannot be closed %d", c);

}

/*Read file containing weights and thresholds, filename has suffix _w.dat*/

wtread(taskname)

char *taskname;

{

int i , j,c;

char wt_file_name[20];

strcpy(wt_file_name,taskname);

strcat(wt_file_name,"_w.dat");

if(( fp2 = fopen(wt_file_name, "r")) == NULL)

{

perror("\nCannot open data file");

exit (0);

}

for (i=0;i<nhlayer +1 ;i++)

{

for(=0;j<(nunit[i]+l)*nunit[i+l];j++)

{

fscanf(fp2,"%f “, (wtptr[i]+j));

}

}

if((c=fclose(fp2)) !=0)

printf("\nFile cannot be closed %d”, c);

}

/*Create file for net architecture and learning parameters. File name has suffix _v.dat*/

dwrite(taskname)

char *taskname;

{

int i, j, c;

char var_file_name[20];

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strcpy(var_file_name,taskname);

strcat(var_file_name,"_v.dat");

if (( fpl=fopen(var_file_name,"w+")) == NULL)

{

perror("Cannot open data file");

exit(0);

}

fprintf(fpl,”%u%u%u%f%f%u%u\n”ninput,noutattr,ninattr,eta,alpha,nhlayer,cnt_num);

for(i=0;i<nhlayer+2;i++)

{

fprintf(fpl, "%d",nunit[i]);

}

fprintf(fpl,"\n%d%f”,cnt,err__curr);

fprintf(fpl,"\n");

for(i=0;i<ninput;i++)

{

for(j =0 ;j <noutattr ;j++)

fprintf(fpl,"%f “,outpt[i][j]);

fprintf(fpl,"\n");

}

if((c=fclose(fpl))!=0)

printf("\nFile cannot be closed %d",c);

}

/*Create for file for saving weights and threshold values learned for training. File name

has suffix __w.dat* /

wtwritte(taskname)

char *taskname;

{

int i, j,c,k;

char wt_file_name[20];

strcpy(wt_file_name,taskname);

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strcat(wt_file_name, "_w.dat");

if((fp2=fopen(wt_file_name,”w+”)) = NULL)

{

perror("Cannot open data file");

exit(0);

}

k=0;

for(i=0;i<nhlayer+l ;i++)

for(=0;j<(nunit[i]+l) * nunit[i+l]; j++)

{

if(k==8)

{

k=0;

fprintf(fp2,"\n”);

}

fprintf(fp2,"%f” , *(wtptr[i]=j));

k++;

}

if((c=fclose(fp2))!=0)

printf(“\nFile cannot be closed %d", c);

}

/*Bottom_up calculation of net for input pattern i*/

void forward(i)

{

int m,n,p,offset;

float net;

/*input level output calculation*/

for(m=0;m<ninattr;m++)

*(outptr[0]+m) = input[i][m];

/*hidden and output layer output calculation*/

for(m=l ;m<nhlayer+2;m++)

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{

for (n=0;n<nunit[m];n++)

{

net=0.0;

for(p=0;p<nunit[m-l]+lp++)

{

offset = (nunit[m-l]+l)*n+p;

net += *(wtptr[m-l]+offset)

*(*(outptr[m-l]+p));

}

*(outptr[m]+n)=l/(l+exp(-net));

}

}

for (n=0;n<nunh[nhlayer+l];n++)

outpt[i][n] = *(outptr[nhlayer+l]+n);

}

/* Several conditions are checked to see whether learning should terminate*/

int introspective (nfrom,nto)

int nfrom;

int nto;

{

int i,flag;

/*reached maximum iteration?*/

if (cnt>=cnt_num) return(FEXIT);

/*error for each pattern small enough?*/

nsnew=0;

flag-1;

for (i=nfrom; (i<nto) && (flag = 1); i++)

{

if (ep[i] <=maxep) nsnew++;

else flag =0;

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}

if (flag = 1) return (SEXIT);

/*System total error small enough?*/

if(err_curr<=maxe) return (SEXIT);

return(CONTNE);

}

/*Threshold is treated as weight of link from

a virtual node whose output value is unity*/

int rumelhart(rrom_snum,to_snum)

int from_snum;

int to_snum;

{

int i,j,k,m,n,p,offset, index;

float out;

char *err_file = "criter.dat";

nsold =0;

cnt = 0;

result=CONTNE;

if(fplotl10==l)

if((fp3=fopen(err_file,"w")) == NULL)

{

I

perror("Cannot open error file");

exit(0);

}

do{

err_curr =0.0;

/*for each pattern*/

for(i=from_snum; i<to_snum;i++)

{

/*bottom_up calculation*/

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forward(i);

/*top_down error propagation*/

/*output_level error process*/

for(m=0;m<nunit[nhlayer+1];m++) {

out= *(outptr[nhlayer+1] +m);

*(errptr[nhlayer+1]+m) = (target[i][m]-out)*(l-out)*out;

/*Hidden and output layer errors*/

for(m=nhlayer+1;m>=1;m--) {

for(n=0);n<nunit[m-1]+l;n++) {

*(errptr[m-1]+n)=0.0;

for(p=0;p<nunit[m];p++) {

offset = (nunit[m-1]+l) * p+n;

*(delw[m-1]+offset)=eta * (*(errptr[m]+p))*(*(outptr[m-1]+n)) +alpha *(*(delw[m-

1]+offset));

*(errptr[m-1]+n)+-=*(errptr[m]+p)* (*(wtptr[m-1]+offset));

}

*(errptr[m-1]+n)= *(errptr[m-1]+n)*(l-*(outptr[m-1]+n)) * ( *(outptr[m-1]+n));

}

}

/*Weight changes*/

for(m=l;m<nhlayer+2;rn++) {

for(n=0;n<nunit[m];n++) {

for(p=0;p<nunit[m-l]+l;p++) {

offset = (nunit[m-l]+l) * n+p;

*(wtptr[m-l]+offset) += *(delw[m-l]+offset);

}

}

}

ep[i] = 0.0;

for (m=0;m<nunit[nhlayer+l];m++){

ep[i] += fabs((target[i][m]-*(outptr[nhlayer+l]+m)));

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}

err_curr+=ep[i]*ep[i];

}

/*Normalised system error*/

err_curr = 0.5*err_curr/ninput;

/**Save errors in file to draw the system error with plot 10**/

if(fplotl10==l)

fprintf(fp3,"%ld,%2.9f\n",cnt,err_curr);

cnt++;

/*Check condition for terminating learing*/

result = introspective(from_snum,to_snum);

} while (result = CONTNE);

/*Update output with changed weights*/

FILE *r;

r=fopen("c:\\output\\reporttxt","w");

for (i=from_snum; i<to_snum;i++) forward(i);

for(i=0;i<nhlayer+l ;i++)

{

index = 0;

for(j=0;j<nunit[i+l];j++)

{

fprintf(r," \n\nweights between unit %d of layer %d", j,i+l);

fprintf(r,"and units of layer %d\n", i);

for(k=0;k<nunit[i] ;k++)

fprintf(r,"%f\n",*(wtptr[i]+index++));

fprintf(r,"\n Threshold of unit %d of layer %d is %f “, j, i+1, *(wtptr[i] + index++));

}

}

fprintf(r,"\n\nTotal number of iteration is %d", cnt);

fprintf(r,"\nNormalized system error is %f\n\n\n", err_curr);

116

return(result);

}

/*Read in the input data file specified by user during the interactive session*/

user_session()

{

inti,j,showdata;

char fnam[20],dtype[20];

FILE *fp;

printf("\n Start of learning session");

/*For task with name task_name, input data file of the task

is automatically said to be task_jiame.dat by the program*/

//printf("\n\t Enter the task name: ");

//scanf("%s", task_name);

printf("\nHow many features in input pattern?: ")

scanf("%d",&ninattr);

printf("\nhow many output units?: ");

scanf("%d",&noutattr);

printf("\nTotal number of input samples?:");

scanf("%d",&ninput);

strcpy (fnam,task_name);

strcat(fnam,".dat");

printf("\nlnput file name is %s ", fnam);

if(( fp=fopen(fnam, "r")) == NULL)

{

printf("\nFile %s does not exist", fnam);

exit(0);

}

printf("\nDo you want to look at data just read?");

printf("\n Answer yes or no: ");

scanf("%s",dtype);

showdata = ((dtype[0] == ‘y’) || (dtype[0] =='y'));

117

for (i=0;i<ninput;i++) {

for(j=0;j<ninattr;j++) {

fscanf(fp, "%f ',&input[i][j]);

if (showdata) printf("%f ',input[i][j]);

}

for(j=0;j<noutattr;j++) {

fscanf(fp,"%f”,&target[i][j]);

if(showdata)printf("%f\n",target[i][j]);

}

}

if((i=fclose(fp)) !=0)

printf("\nFile cannot be closed %d",i);

exit(0);

}

}

/*Main body of learning*/

Leaming()

{

int result;

user_session();

set_up();

init();

do{

initwt();

result = rumelhart(0,ninput); }

while (result = RESTRT);

if (result = FEXIT)

printf("\nMax number of iterations reached,");

printf("\n but failed to decrease system");

printf("\n error sufficiently");

}

118

dwrite(task_name);

dwrite(task_name);

}

/*Main body of output generation*/

output_generation()

{

int i,m,nsample;

charans[10];

chardfile[50];

FILE*fl;

/* If task is already in the memory, data files for task donot

need to be readin. But, if it is a new task, data files

should be read into reconstruct the net*/

printf("\nGeneration of outputs for a new pattern");

printf("\n\t Present task name is %s",task_name);

printf("\n\t Work on a different task? ");

printf("\n\t Answer yes or no: ");

scanf("%s", ans);

if ((ans[0]=’y’) || (ans[0]='Y'))

{

printf("\n\t Type the task name: ");

scanf("%s", task_name);

dread(task_name);

init();

wtread(task_name) ;

/*Input data for output generation are created*/

printf("\nEnter file name for patterns to”);

printf(" be processed;");

scanf("%s",dfile);

if ((fpl=fopen(dfile,"r")) = NULL)

{

119

perror("Cannot open dfile");

exit(0);

}

printf("\nEnter number of patterns for processing: ")

scanf("%d",&nsample);

for(i=0;i<nsample;i—)

for(m=0;m<ninattr;m—)

fscanf(fp1,”%f”&input[i][m]);

/*0utput generation calculation starts*

fl=fopen("c:\\output\\output.txt"."w");

for(i=0;i<nsample;i++)

{

forward(i);

for(m=0;m<noutattr;m++)

{

fprintf(fl,"%f\n",outpt[i][m]*8.43472);

}

printf("\n");

}

printf("\nOutputs have been generated");

if((i=fclose(fpl))!=0)

printf("\nFile cannot be closed %d",i);

}

void main()

{

char select[20],cont[10];

//FILE *f5;

clrscr();

strcpy(task_name, "train" );

do

{

120

printf("\n** Select L(earning) or 0(utput generation)**\n");

do

{

scanf("%s",select);

switch(select[0])

{

case 'o':

case 'O’:

output_generation();break;

case T:

case 'L':

learning();

break;

default:

printf("\nanswer learning or output generation");

break;

}

}while((select[0]!=’o’)&&(select[0]!=’O’&&(select[0]!=T)&&(select[0]!='L1));

printf("\nDo you want to continue? ");

scanf("%s",cont);

}while ((cont[0]=’y’) 11 (cont[0]='Y'));

}

121