Caledonian Journal of
Engineering
Volume 04, Number 01
January - June 2008
Published by Caledonian College of Engineering, Post Box 2322,
CPO Seeb, Postal Code 111, Sultanate of Oman.
General Information
Caledonian Journal of Engineering is published bi-annually by Caledonian College of
Engineering. The journal endeavors to publish high quality, peer reviewed research
papers in the field of Science and Technology to encourage research and scholarly
activities in Oman, and also in the Gulf.
All correspondence and contributions may be sent to:
Associate Editor,
Caledonian Journal of Engineering
Caledonian College of Engineering
Post Box 2322
CPO Seeb 111
Sultanate of Oman
Email: kaleel@caledonian.edu.om.
Information for Authors
The topics covered by the journal include:
•
Research / Technical papers in the filed of Mathematics, Civil Engineering,
Mechanical Engineering, Chemical Engineering, Process Operation and
Maintenance Engineering, Electrical Engineering, Electronic Engineering,
Communication Engineering and Computer Engineering
Responsibilities of Authors
The authors are responsible for the originality of their papers and their scientific
correctness.
Guidelines for paper submission
All papers must be the author’s original work. It is essential that each manuscript should
be accompanied by an abstract of maximum of 200 words. All authors’ contact addresses,
emails, telephone numbers and fax numbers should be included in the paper. The title of
a paper must be restricted to 50 words. Please refer to the template for other information
regarding the submission of papers. (The template is available in the inner back cover
page).
The Editorial Board has the right to accept or reject a paper, and to make necessary
modifications. The board’s decision shall be held final.
Caledonian Journal of Engineering
Editorial Board
Editor-in-Chief
Dr.Syed Anisuddin
Editors
Dr.Feroz Shaik
Dr.Syed Mohammed Rizwan
Associate Editor
Dr.K.P.Ramachandran
Caledonian College of
Engineering, Oman
Dr.K.V.Gangadharan
National Institute of Technology,
Surathkal, India
Dr.Gulshan Taneja
M D University, Rohtak, Haryana,
India
Prof.James Sommerville
Glasgow Caledonian University,
Scotland, United Kingdom
H.Kalilur Rahman
Prof.Mehmet A. Hastaoglu
Department of Energy Systems,
GYTE, Kocaeli, Turkey
Members
Dr.Faris Salman
K.P. Mansoor Ali
Prof.Gautam Datt
Dr.G.Prabhakaran
Advisory Committee
Dr.A.Arunagiri
Multimedia University, Malaysia
Dr.Brian Stewart
Glasgow Caledonian University,
Scotland, United Kingdom
Prof.Mohsen Morad Sherif
College of Engineering, Al Ain,
UAE
Dr.S.R.R.Senthil Kumar
Higher College of Technology,
Oman
Prof.VSRK.Prasad
Andhra University,
Visakhapatanam, India
Dr.Xavier Fernando
Ryerson University, Canada
From the Editor-in-Chief’s desk………..
It is with great pleasure that we release Volume 04,
Number 01 edition of “Caledonian Journal of Engineering”.
Six research papers encompassing various fields of engineering and science are
included, and it is particularly gratifying to note that one paper is co authored by
faculty of GCU, UK. Papers from AITM Aurangabad and PSG Coimbatore, India
are highly appreciated.
It is also worth mentioning that the future issues of this journal will bear the
International Standard Serial Number as ISSN1999:9496.
My thanks go to all the contributors and the editorial team for their consistent
hard work.
We also welcome contributors from leading higher educational institutions, so
that the ideas can be freely exchanged and knowledge is disseminated to all.
Dr Syed Anisuddin
Editor – in - Chief
Caledonian Journal of Engineering
Volume04, Number 12, January- June 2008
PAPERS
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
VIRTUAL CELLS FOR MANUFACTURING SYSTEMS UNDER
TURBULENT ENVIRONMENT – A REVIEW OF THRUST AREAS
R.V.Murali
Department of Mechanical & Industrial Engineering, Caledonian College of Engineering, Sultanate of
Oman
ABSTRACT
Cellular manufacturing systems (CMS), since its conceptual introduction about two decades ago, have
proved to be more efficient than traditional job shop functional layout systems for a certain range of
parameters and datasets. The concept of CMS is based on the philosophy of Group Technology (GT) where
the parts, to be machined, are grouped on the basis of similarity in terms of resources requirements. In
CMS, existing resources are separated into machine groups or cells that would encircle machineries to
process a family of parts. Thus, each cell is responsible for production of a particular family of parts and
every time new cells are physically reformed as and when demand for new products or new planning period
arrives or product mix is introduced. This poses a difficulty in physical reorganization of the facilities and it
will be even worse when the frequency of reformation of cells is high i.e. turbulent environment. In the
recent past, a concept called Virtual Cellular Manufacturing Systems (VCMS) which does not demand
physical relocation of machines every time to reform a cell, it is rather a conceptual & logical (virtual)
grouping of machines from within current departments in order to produce a family of parts. This paper
brings out various thrust research areas and opportunities in terms of design, operations and practical
applicability (empirical nature) of virtual cell based manufacturing systems in order to meet turbulent
environment.
to be rearranged and a new set of cells is to be
reformed in order to produce new product variety
1.0 INTRODUCTION
or new product mix. So much so, classical
cellular manufacturing may not be appropriate if
While designing of a manufacturing system for a
frequent introduction of new variety of products,
particular type of industry, it is essential to look
or high product mix variability or frequent
into various aspects such as product volume
change of operational sequence or dynamic
variability, product mix variability, physical
routing schedule.
shape and size of various parts to be produced,
processing times, types of machinery required
and availability of human workforce, methods of
arranging machineries & materials handling
systems (layouts) and a strong market
competition.
In a typical job shop layout (figure 1),
machineries are laid out on the basis of their
functionality and the raw materials are flowing
from one machine to another in order to get
transformed into useable products with complete
routing flexibility. On the other hand, in a
traditional CMS, machine groups (cells) are
physically formed and dedicated to a particular
family of parts (figure 2). Each cell is engaged in
producing a particular family of parts (Greene
TJ, Sadowski PR, 1984 & Molleman E, Slomp J,
Rolefes S, 2002). In many occasions, more than
one cell is required for a job to completely
change into a product even though inter-cell
movements are kept to a minimal. When a new
product arrives or a different variety of product
is to be introduced, currently formulated cells are
Di – Departments on the basis of type of machine tool
Xi, Yi, Zi – Workforce attached with respective department
Figure. 1: Job Shop Layout
Very recently, a concept called Virtual Cellular
Manufacturing Systems (VCMS) is introduced in
which there is no need of physical reorganization
of machineries every time to form a cell, it is
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Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
team work, enhanced responsibility &
accountability and increased operator expertise .
rather a conceptual (virtual & logical) grouping
of machines within the machining area in order
to produce a family of parts (figure 3).
The major research areas where much of the
research so far has been focused on are the
design part of VCMS and comparison of
performance of VCMS with that of traditional
cellular manufacturing systems & functional
layouts. Design phase of a VCMS clearly refers
to formation of machine cells & part families and
eventual dedication of particular cells to a
particular family of parts so that all/few
objectives such as total materials handling
cost/time, reduced exceptional elements,
effective manpower utilization and increased
productive processing time and reduced number
of set ups, setup time and tooling are met with.
Typical benefits resulting from VCMS include
reduced setup and lead times, reduced work in
process inventories, reduced materials handling
times, proper organization of tooling, accessories
VC1 (F1)
Figure. 2: Cellular Layout
LOOK
VC3 (F3)
D1
and jigs and fixtures, improved worker
responsibility and satisfaction, improvised team
work, enhanced productivity and quality and so
on.
2.0 VCMS- A
LITERATURE
VC2 (F3)
D2
D3
INTO
VIRTUAL CELLS
(FOR PLANNING PERIOD ’T1’)
Virtual cell concept was first proposed in 1980s
when McLean defined it as an imaginary group
of machineries which is no longer identifiable
explicitly as cells. This virtual concept of cells is
present in the minds of people and controlling
elements and systems in a shop floor.
VC1 (F1)
VC2 (F3)
VC3 (F3)
D1
D2
Although many researchers have defined
VCMSs based on their understanding and
experience gained over the years, the simplest
definition could be forming a pool of
machineries virtually and dedicating them to
produce a particular family of products / parts
so that total set up time, material handling time
and part make-span time are minimized to a
greater extent. Frequent reformation of cells
owing to (i) dynamic topography of products and
product mix, (ii) strong competition in the
markets, (iii) inability of traditional cellular
layouts and functional layouts (Vakharia AJ,
Moily JP, Huang Y, 1999) to meet the varied
requirements have resulted in virtual cells
concept (Rheault M, Drolet JR, Abdulnour
G,1995 & 1996). Other perceived benefits of
VCMS include improved human relations &
D3
VIRTUAL CELLS
(FOR PLANNING PERIOD ’T2’)
VCx- Virtual Cell Number
Figure. 3: Virtual Cells
As mentioned earlier, current research works on
Virtual Cellular Manufacturing Systems have
been towards design and operational sectors.
However, there is a little work done in empirical
research and hence large potential is identified in
this sector. Inputs from empirical research can
significantly improve the realism of search
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Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
introduction of virtual cellular manufacturing
systems in 1978 is explained in the graph (Figure
4) and the nature of work done in Table 1.
settings, particularly in the area of design and
operations.
Further, combining multiple types of research
i.e. design and/or operation and/or empirical
investigative works could undoubtedly enhance
the power of virtual cell concepts in terms of
quality and applicability (Kanan VR, Ghosh S,
1996).
This graph (figure 4) shows various research
themes and solution methodology adopted in
each theme. It is evident from the graph that the
research thrust for VCMS concept appears to be
on the rise and still a lot of scope is identified to
further explore in the field.
3.0 OPTIMIZATION PARAMETERS
IN VCMS
4.0 SIMULATION PHASE FOR THE
RESEARCH OUTCOMES
In all VCMS research works, key parameters that
are to be optimized are identified along with
appropriate resource constraints. Accordingly
one or more objective functions are formulated.
The outcomes of the optimization could well be
pertaining to total materials handling costs,
productive machining hours to minimize setup
and handling time/costs, inter-cell and intra cell
movements of parts, cell independence, labor
cross training and cell load balancing and so on.
A quick review of such parameters would be
really helpful here in order to find the impact
directions of research yet to be carried out.
Although, adequate magnitude of research was
done and is being underway on design and
operational sectors of VCMS, empirical research
on VCMS has not been given much attention.
Therefore, a lot of potential is perceived in
pressing the outcomes of the research on design
and operation into real time implementation.
Also, more analytical and simulation phases for
the above areas still remain unexplored.
5.0 SUMMARY
From the graph (figure 4) and eventual
explanation in Table 1, there are some interesting
observations that could be noticed. The current
research focused on either design aspects or
operational aspects or empirical point of view.
There is a scope perceived when these three
areas are integrated in terms of parameter ranges,
data sets and resource types. Ironically, this
would enhance the quality and impact of the
research to realize the power of VCMS.
In papers (Gert Nomden, Jannes Slomp Nallan
C. Suresh, 2006), (Irani SA, Cavalier TM, Cohen
PH, 1993), (Kannan VR, Ghosh S, 1996)
(Vakharia AJ, Moily JP, Huang Y., 1999),
(Suresh NC, Meredith JR., 1994), (Slomp J,
1998), various objectives that were formulated
for optimization include maximization of
productive output [in terms of machining hours],
minimization of total number of additional
machines of type m needed for creating
independent virtual cells, minimization of
number of additional cells to which each worker
is assigned, maximization of machine coverage
of machines and finally maximization of multifunctionality of workers.
6.0 CONCLUSIONS
The extensive efforts, investigation and hard
work put in by the researchers in the area of
VCMS have given us an ample of opportunities
to look into to further our research work. The
mathematical models developed so far have
undoubtedly led us towards a generalized range
of parameters in which VMCs may be effectively
and efficiently utilized. However, there is a
major need to understand the real industrial
scenario and therefore we focus our research
efforts into more of empirical nature.
In paper (R.V.Murali, D.Ragavesh & G.
Prabhakaran, 2007), the objective of minimizing
the total materials transfer costs (both inter and
intra cellular movements of parts) is considered
leading to reduced total manufacturing costs.
Solution methodologies employed in various
research works in order to solve these objective
functions
include
Goal
and
Integer
Programming, LINGO formulation and Tabu and
evolutionary search algorithms.
The concise version of the detailed research
work done in each year right from the conceptual
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Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
REFERENCES
[1] Gert Nomden, Jannes Slomp and Nallan
Suresh (2006) Virtual manufacturing cells:
taxonomy of past research and identification
future research issues, International Journal
Flexible Manufacturing Systems 17, p.71-92.
[11] Suresh NC and Meredith JR (1994) Coping
with the loss of pooling synergy in cellular
manufacturing systems, Management Science,
40(4), p.466–483.
C.
A
of
of
[12] Vakharia AJ and Moily JP, Huang Y (1999)
Evaluating virtual cells and multistage flow
shops: an analytical approach, International
Journal of Flexible Manufacturing Systems,11,
p.291–314.
[2] Greene TJ and Sadowski PR.(1984) A
review of cellular manufacturing assumptions,
advantages and design techniques, Journal of
Operation Management 4, p.65–97.
[3] Irani SA, Cavalier TM and Cohen PH (1993)
Virtual manufacturing cells: exploiting layout
design and intercell flows for the machine
sharing problem, International Journal of
Production Research 31(4), p.791–810.
[4] Kannan VR and Ghosh S (1996) A virtual
cellular manufacturing approach to batch
production, Decision Science 27(3), p.519–539.
[5] Kanan VR and Ghosh S (1996) Cellular
manufacturing using virtual cells, International
Journal of Operation, Prodcution Management
16 (5), p.99-112.
[6] Molleman E, Slomp J and Rolefes S. (2002)
The evolution of a cellular manufacturing
system—a longitudinal case study, Int J Prod
Econ, 75, p.305–322.
[7] Rheault M, Drolet JR and Abdulnour G.
(1995) Physically reconfigurable virtual cells: a
dynamic model for a highly dynamic
environment, Comput Ind Eng, 29(1-4), p.221–
225.
[8] Rheault M, Drolet JR and Abdulnour G
(1996) Dynamic cellular manufacturing systems
(DCMS), Comput Ind Eng, 31, p.143–146.
[9] R.V.Murali, D.Ragavesh and Dr.G.
Prabhakaran (2007) A Study, design and
optimization virtual cellular manufacturing
systems, proceedings of Computer Aided
Production Engineering (CAPE) international
conference, Glasgow Caledonian University,
Glasgow, UK.
[10] Slomp J (1998) Design of manufacturing
cells: PFA applications in Dutch industry. In:
Suresh NC, Kay JM, editors. Group technology
and cellular manufacturing. Boston, Dordrecht,
London: Kluwer Academic Publishers. p.153–
168.
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Caledonian Journal of Engineering
NO
YEAR
PUBLISHED
1
1978
2
1982
3
1989
4
1991
5
1992
6
1993
7
1994
8
9
1995
10
1996
11
12
1998
13
14
15
1999
16
17
2000
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Volume04, Number 01, January - June 2008
Table 1: Nature of work done during evolution of VCMS
NATURE OF WORK / REMARKS
An informal existence of Virtual Manufacturing Cells reported by Altom. In this
effort, an attempt is made to analyze the costs and savings associated wile
implementing Group Technology (GT).
Formal definition of VCMS was given as a cell no longer identified as a fixed
physical group of machines and rather dynamically changing.
A survey was taken from user and non-users of cellular manufacturing system.
It revealed that most of the firms used a hybrid layout (dedicate equipment and
manufacturing cells) due to high relocation cost and high product-demand
variability.
An analytical model was developed for partitioning work centers in order to
create cells (as opposed to traditional job-shop and functional layouts.)
The analytical model developed in 1991 was carefully looked into in terms of
advantages of it over functional layouts. This paper superseded the long time
controversy such as doubts on performance and limited adoption of cellular
manufacturing in industries.
An attempt is made to redefine the term VMCS exploiting the layout design and
intercellular flows when machine sharing is imminent. This has resulted in
using a pool of resources rather than dedicating a cell to a particular type of part
family. In this work, several similar machines are clustered into process
department and several dissimilar machines constitute flow lines.
Part scheduling problem is formulated and solved by linear programming with
an objective of minimizing total travel distance and lateness of the jobs.
This effort addressed various issues such as a loss of pooling synergy associated
with introduction of cellular manufacturing. Alternatively, this effort
recommended the use of part family oriented scheduling (FLP) in the
conventional job shop layouts. This has paved the way later to focus more
attention on Virtual Cellular Manufacturing Systems (VCMS).
This year has seen a detailed survey of US manufacturing practices being
adopted among all make-to-order industries. This has ferreted out an indicator
of limited applicability of CMS in US industry.
FLP was analyzed and renamed as virtual cells using the family based
scheduling to realize the scheduling and setup efficiencies while retaining the
job-shop layouts.
An attempt to propose cellular manufacturing using virtual cells (FLP oriented
job-shop layouts) was made.
Since the limited applicability of CMS was envisaged from the US survey, a
concept of an adaptable cellular manufacturing system was perceived in
principle.
Firstly in the VCMS history, dedicating workers to part families and cells is
initiated by Khuling.
Study of VCMS in a multistage flow shops environment was analyzed using
queuing theory by Vakharia.
This effort brings out the significance of human beings in VCMS environment
and insists the importance of information structure that enables the operation
between the people and Virtual Manufacturing Cell
A framework was proposed here for classification of manufacturing cells where
in virtual cells consists of people and equipment that are dedicated to a
part/product family and workflow is dependent on time and information flow.
A prototype design of VCMS applicable to Small-to-Medium Scale industries
was proposed in this year which has increased the attention formally to the
possible use of VCMS in industries.
An effort was made to explain how cell design is done in real practice and
investigated the need and objectives of implementing manufacturing cells and
5
Caledonian Journal of Engineering
19
2001
20
2002
21
22
2003
23
2004
25
2005
26
2006
methods and organization employed to do so. It elaborated the various
constrains of implementations.
Part scheduling problem is formulated and solved by Lagrangian relaxation
approach with an objective of minimizing tardiness
A Genetic Algorithm was developed to solve part scheduling problem with an
objective of minimizing total travel distances.
An integrated framework for production planning and cell formation was
carried out through a 3 step approach. A mathematical model was developed to
minimize intercellular flows, tardiness, utilization and throughput and solved
using tabu search method.
Enhanced version of PFA was analyzed and presented. It resulted in formation
of virtual cells which can be both either process oriented or product oriented.
Algorithms were written to create VMCs considering the routing data and
frequently used machines.
An attempt is made to present a frame work for the design of VMCs including
labor skills and team accountability. This is intended for maximizing the
capacity as efficiently as possible and making VMCs as independently as
possible using goal programming approach.
This work is an extended research to previously done (2004) to include the
labor dimension in addition to machines and workers (called as Dual Resource
Constrained (DRC) systems)
A complete run-through on Virtual manufacturing cells to bring about various
research undertaken and identification of future research directions in order to
completely realize the power of VCMS
Nature of work index
24
Volume04, Number 01, January - June 2008
Published Year
Figure.4: VCMS literature published vs Year
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Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
REMOVAL OF COPPER IONS FROM EFFLUENTS USING
COCONUT SHELL COKE IN A FIXED BED ADSORBER
S Feroz and Shah Jahan
Department of Mechanical and Industrial Engineering, Caledonian College of Engineering,
Sultanate of Oman
ABSTRACT
The removal of copper metal ions from effluents using charcoal coke in fixed bed adsorption column is
investigated. The effects of various parameters like flow rate, particle size and initial concentration are
studied. It was observed that an increase in flow rate, initial concentration decreases the time required for
saturation of bed whereas with an increase in particle size of the adsorbent the time of saturation of the bed
increased.
KEYWORDS: Coconut Shell Coke, Fixed Bed Adsorber, Saturation Curve, Adsorbent.
coagulation, reverse osmosis, electro dialysis,
ion exchange, and adsorption have been
employed for removal of metal ions from
effluents.
1.0 INTRODUCTION
Water, a universal solvent is in true sense “the
elixir of life”. With diminishing sources of clean
water, its management has become a vital issue.
The constituents in natural water exhibit
properties that may be classified as either
conservative or non- conservative. The former
relates to concentration of species that remains at
relatively constant ratio to each other throughout
the system. This applies mostly to more
abundant lighter elements such as sodium,
potassium and calcium. The non-conservative
behavior is shown by other metals such as Fe,
Cu, Zn, Pb, Hg which varies in concentration
depending on variables such as position, time,
temperature and most importantly, biological
activity.
The present work is aimed at removing the
copper ions from effluent water using the
technique of adsorption. Adsorption involves
contact of solids with either liquids or gases and
the mass transfers in the direction of fluid to
solid. The adsorption operation involves the
property of certain solids, which selectively
adsorb specific substances from solution on to
their surfaces. All adsorption processes are
exothermic and adsorption on solid surfaces may
be classified on the basis of magnitude of the
energy of adsorption. Adsorption depends on
temperature, pressure, surface structure, size and
porosity. With rise in pressure or decrease in
temperature, the adsorption capacity increases.
As the particle size decreases, the interfacial area
increases thereby enhancing adsorption but it is
often restricted due to clogging, if the adsorbent
particle size is the lowest.
Modern industries require large quantities of
fresh water. A substantial quantity of this water
is discharged as waste water or effluent, which
contain large amount of pollutants. Pollutants
from industries involves proteins, fats,
carbohydrates, inorganic chemicals, salts of
metals like Ag, Cd, Cu, Fe, Ni, Zn etc. Copper is
found in effluents from some major industries
like chlor alkali, electroplating, paints and dyes,
petroleum refining, fertilizers etc.
The adsorption operations can be batch, semibatch or continuous. Batch operations are
generally conducted when small amounts are to
be treated and the equilibrium distribution
depends on the time of contact. The semi-batch
operations are generally conducted in fixed bed
towers and in such towers the solid is stagnant
while the fluids are continuous. In continuous
counter current operations both solid and fluid
are continuously brought into contact with each
other in the opposite direction with a continuous
flow of two streams. This operation is used when
Pollutants cause direct toxicity both to human
and other living beings due to their presence
beyond specific limits. The trust of
environmental research is to adopt suitable
techniques either to prevent the metal pollution
or to reduce it to very low levels. Various
techniques such as chemical precipitation,
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Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
obtained on all the metal ions except copper
followed Fruendlich isotherms.
the cost of adsorbent is cheap (McCabe W.L.,
Smith J.C., Peter Harriot). Bauxite, molecular
sieves, alumina, silica gel, peat, coconut shell
coke, bagasse, flyash, etc., are commonly used
adsorbents (Treybal R.E.). This investigation is
confined to fixed bed adsorber, where the copper
metal ions present in the effluents are adsorbed
on to coconut shell coke adsorbent and the effect
of flow rate, initial concentration and particle
size are studied.
Seco et al., (Seco Aurrora, Marzal Paula,
Gabaldon Carmen and Ferror Jose, 1999)
conducted studies for adsorption of cadmium and
zinc on activated carbon, influence of pH, cation
concentration and adsorbent concentration. The
single adsorption of cadmium and zinc from
aqueous solutions were investigated on granular
activated carbon in a wide range of experimental
conditions, pH, metal and carbon concentration.
Activated carbon is efficient as sorbent for both
metals. Metal removal increased with pH and
carbon concentration, and decreased with the
initial metal concentration. The adsorption
processes were modeled using the surface
complex formation triple layer model (TLM) and
its parameters were determined. Modelling was
performed
assuming
a
single
surface
stiochiometry, which successfully predicted
cadmium and zinc removal in all the
experimental conditions.
2.0 LITERATURE REVIEW
Gupta et al., (Gupta Vinod K, Ali and Imran,
2000) studied the utilization of bagasse, fly ash
for the removal of zinc from waste water.
Bagasse, fly ash, a waste product in sugar
industries, has been converted into an
inexpensive and effective adsorbent. The product
was characterized by different chemical and
physical methods and has been used for the
removal of zinc from waste waters. Various
parameters such as pH, adsorbent dosage, initial
metal ion concentration, temperature, particle
size etc., were optimized. Zinc was adsorbed by
the adsorbent up to 90 to 95% in batch and
column experiments.
3.0 EXPERIMENTAL SET-UP
The experimental set-up shown in the schematic
diagram (Figure.1) consists of a storage tank of
mild steel with dimensions 24x10x12 inches. A
submerged pump of capacity 0-400 lph is used to
pump the feed solution into the column. A 60 cm
long & 6.5 cm inner dia acrylic cylinder is used
as adsorption column. The use of acrylic limits
the use of column for organic solutions to low
and moderate concentrations while it is suitable
for most inorganic solutions up to a wide range
of concentrations. The constant flow of liquid
from the storage tank to the column is
maintained using a rotameter 0-5 lt/h capacity.
In the adsorption studies on phosphate treated
sawdust, separation of Zn 2+, Cu 2+, and Ni+2,
their removal and recovery from electroplating
wastes was done by Siddiqui et al.,(Siddique,
Bilquees Ara, Sharma P.P. and Sultan
Mohammad, 1998). Phosphate treated sawdust
was found to exhibit remarkable adsorption
capacity for Cu+2, Zn+2 and Ni+2. The effect of
initial concentration in electroplating wastes
waters; pH and adsorption doses were
extensively studied. It was reported that the data
Figure.1: Experimental set-up
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Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
4.0 EXPERIMENTAL PROCEDURE
4.4 Sample Analysis
The steps involved in experimentation are:
Solutions Required:
• Preparation of coconut shell coke
1.
• Preparation of feed solution
2.
3.
4.
5.
6.
7.
• Experimentation
• Sample analysis
4.1 Preparation of Coconut Shell Coke
Coconut shells are made up of stone cells and are
hard, porous and impregnated with lignin,
tannins and contain a small amount of oil. The
coconut shells were surface treated to remove all
the fibers on its surface and then subjected to
partial oxidation. Partial oxidation is necessary
in order to prevent the formation of ash. The
final material i.e. the black and brittle activated
carbon is crushed in ball mill. The material is
sieved and segregated according to the desired
sizes (2.855 mm, 1.85 mm, and 1.55 mm). The
adsorbent is then subjected to continuous
washing for about 3 hours to remove the intense
black color.
0.01N EDTA (Ethylene diamine tetra
acetic acid) solution.
0.01N Zinc sulphate solution.
Indicators.
EBT (Erichrome Black – T )
FSBF (Fast Sulphon Black – F )
Concentrated Ammonia Solution.
Buffer solution :- It was prepared by
dissolving 17.5 gms of ammonium
chloride in 142 ml of concentrated
ammonia solution and the solution was
made upto the mark in 250 ml
volumetric flask.
Copper ions present in solution can be
determined by titrating with a solution of EDTA
which was standardized against a standard
solution of zinc sulphate. The desired pH for the
titration was maintained by using concentrated
ammonia solution. Fast Sulphon Black – F
(FSBF) is used as indicator, gives wine red
coloured complex with copper ions. After all the
Cu+2 is complexed the indicator will set free and
the end point will be indicated by colour change
from wine red to dark green. The reactions are as
follows:-
4.2 Preparation of Feed Solution
Copper sulphate feed solution ‘A’ (70 ppm), ‘B’
(100 ppm) and ‘C’ (150 ppm) are prepared by
dissolving 5.498 grms, 7.8552 grams and 11.78
grms respectively in 20 lts of distilled water. The
solution was constantly stirred for about half an
hour to obtain uniform concentration.
Cu +2 + FSBF
→ Cu-FSBF (complex)
Cu +2 +EDTA
→ Cu- EDTA (wine red)
Cu-FSBF +EDTA → Cu-EDTA +FSBF (dark
green)
4.3 Experimentation
5.0 RESULT & DISCUSSION
The column is filled with the adsorbent and the
storage tank with copper sulphate solution of
desired concentration. The pump is switched on
and the rotameter is adjusted to a desired flow
rate. The solution is allowed to pass through the
bed and sample coming out through the bed is
collected. The same procedure is repeated for
different initial concentrations, flow rates and for
different adsorbent sizes.
5.1 Break through Curve
The experiments are carried out for known
values of initial concentration of metal ion,
adsorbent size, and flow rate. The data on
adsorption is plotted in Figure.2. The sudden rise
in outlet concentration is observed immediately
at a time of about 10 min, which may be
considered as break through point. There after
concentration in the effluent increased
continuously with time up to t = 150 min and
then remained constant. This indicates the
saturation state of the bed. The portion of
effluent concentration curve between t= 5 min to
t = 150 min was termed the break through curve.
Initial concentrations – 150ppm, 100ppm and 70
ppm
Flow rate – 5 lph, 10 lph and 15 lph.
Adsorbent sizes – 2.85 mm, 1.85 mm and
1.55mm.
9
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
90
80
Cout(ppm)
70
60
50
5 LPH
40
30
20
10
0
0
100
200
300
400
tim e (m in)
Figure.2: Outlet concentration versus time (Initial Concentration = 100 ppm; Flow Rate = 5 LPH; and
Size of Adsorbent = 1.85 mm).
1.85 mm and 140 min in case of 1.55 mm and
thereafter the percentage of solute adsorbed
remained nearly constant when the bed
approached a state of equilibrium. With
increase in particle size, the time taken for
saturation of bed increases enormously which
indicates that larger the size of the adsorbent
particle, greater will be the interfacial area
available for adsorption and the bed slowly
approaches saturation.
5.2 Effect of Flow Rate
To study the effect of flow rate on removal of
copper ion by adsorption, other variables such
as initial concentration of metal ion, and
adsorbent size are kept constant during the
period of experimentation.
The data on adsorption are plotted in Figures 3
and 4. It was observed that the percent
removal of metal ion decreased continuously
with increase in time up to 180 min for 5 LPH,
90 min in the case of 10 LPH and 25 min in
the case of 15 LPH and thereafter the
percentage of solute adsorbed remained nearly
constant when the bed approached a state of
equilibrium. With increase in flow rate, the
time taken for saturation of bed decreases
enormously which indicates that more the
mass of metal ions entering the bed, faster will
be the saturation of bed.
5.4 Effect of Initial Concentration
To study the effect of initial concentration on
removal of copper ion by adsorption, other
variables such as particle size, height of the
adsorbent bed and flow rate are kept constant
during the period of experimentation.
The data on adsorption are plotted in Figure 7
and 8. It was observed that the percent
removal of metal ion decreased continuously
with increase in time up to 130 in case of 150
ppm, 180 min in case of 100 ppm and 260 min
in case of 70 ppm and thereafter the
percentage of solute adsorbed remained nearly
constant when the bed approached a state of
equilibrium. With increase in initial
concentration, the time taken for saturation of
bed decreases enormously which indicates that
higher the initial concentration larger will be
the driving forces. With increase in driving
force the bed adsorbs much more quantity of
metal ions and thus the time taken for
saturation of bed decreases.
5.3 Effect of Particle Size
To study the effect of particle size on removal
of copper ion by adsorption, other variables
such as initial concentration of metal ion, and
flow rate are kept constant during the period of
experimentation. The data on adsorption are
plotted as shown in Figures 5 and 6. It was
observed that the percent removal of metal ion
decreased continuously with increase in time
up to 180 min in case of 2.85 mm, 150 min in
case of
10
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
120
Cout(ppm)
100
80
5 LPH
10 LPH
60
15 LPH
40
20
0
0
100
200
300
400
tim e (m in)
Figure.3: Outlet concentration versus time for different flow rates
(Initial Concentration = 100 ppm and Size of Adsorbent = 2.85 mm).
60
% Adsorption
50
40
5 LPH
30
10 LPH
15 LPH
20
10
0
0
100
200
300
400
tim e(m in)
Figure.4: Percentage of Adsorption versus time for different Flow rates
(Initial Concentration = 100 ppm and Size of Adsorbent = 2.85 mm).
11
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
100
Cout (ppm)
90
80
70
2.85 mm
60
50
40
1.85 mm
1.55 mm
30
20
10
0
0
100
200
300
400
time(min)
Figure.5: Outlet concentration versus time for different particle sizes
(Initial concentration = 100 ppm and Flow Rate = 5 LPH).
% Adsorption
90
80
70
60
1.55 mm
50
1.85 mm
40
30
20
2.85 mm
10
0
0
100
200
300
400
time(min)
Figure.6: Percentage of adsorption versus time for different particle sizes
(Initial Concentration = 100 ppm and Flow Rate = 5 LPH).
12
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
140
120
Cout(ppm)
100
70 ppm
80
100 ppm
60
150 ppm
40
20
0
0
100
200
300
400
time(min)
Figure.7: Outlet concentration versus time for different initial concentrations
(Flow Rate = 5 LPH and Size of Adsorbent = 2.85mm).
70
% Adsorption
60
50
70 ppm
40
100 ppm
30
150 ppm
20
10
0
0
100
200
300
400
time(min)
Figure.8: Percentage of adsorption versus time for different initial concentrations
(Flow rate = 5 LPH and Size of Adsorbent = 2.85mm).
13
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
6.0 CONCLUSIONS
The effects of various parameters like flow rate,
particle size and initial concentration are studied
and the following conclusions were drawn.
•
•
the increase in flow rate and initial
concentration decreases saturation time of
the bed.
the increase in particle size results in an
increase in saturation time of bed.
REFERENCES
[1] Gupta., Vinod K., Ali., and Imran. (2000)
Utilization of bagasse fly ash for the removal of
copper and zinc from waste water, Sep Purif
Technol 18(2), 130 – 140
[2] McCabe W.L., Smith J.C. and Peter Harriot,
Unit Operations of Chemical Engineering, 5th
Edition, McGraw Hill.
[3] Perry and Chilton, Perrys Chemical
Engineers Hand book, 7th Edition , McGraw Hill.
[4] Siddique., Bilquees Ara., Sharma, P.P.;
Sultan Mohammad., (1998) Adsorption studies
on phosphate treated sawdust ; separation of Cr
(vi), Zn+2,Ni+2 , Cu+2 and their removal and
recovery from electroplating waste, Aurelia. Sci.
Technol Environ. Prot, 3 (2), 103 – 110.
[5] Seco Aurrora., Marzal Paula., Gabaldon
Carmen., Ferrer Jose., (1999) Study of
adsorption of cadmium and zinc on to an
activated carbon. Influence of pH , cation
concentration and adsorbent concentration, Sep.
Sci. Technol.
[6] Treybal R.E., Mass –Transfer Operations, 3rd
Edition, McGraw Hill.
14
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
COAST DOWN FACTOR TO INVESTIGATE THE TRIBOLOGICAL
BEHAVIOUR OF LUBRICANTS IN JOURNAL BEARING.
R. Edwin Browne1, Dr. K. P. Ramachandran2, Dr. A.K.M. De Silva3, Prof. D.K. Harrison4
1&2 Department of Mechanical and Industrial engineering, Caledonian College of Engineering, Sultanate of Oman.
1. Corresponding Author, edwinbrowne@caledonian.edu.om, 2.ramkp@caledonian.edu.om.
3&4 School of Engineering and Computing, Glasgow Caledonian University, Cowcaddens Road, Glasgow, G4 0BA,
Scotland, UK .3.A .DeSilva@gcal.ac.uk,4.D.K.Harrison@gcal.ac.uk
ABSTRACT
The run down time condition of any rotating system when analysed will lead to useful information for condition
based maintenance. When the power supply is cut off to any rotor system, the total momentum gained during the
sustained operation will dissipate and the system will come to rest. The time elapsed between the power supply cutoff and the system to stop is defined as Coast Down Time (CDT). The graphical representation of the speed with
respect to CDT is known as Coast Down Time- Profile (CDT-P).This paper presents an experimental investigation
conducted on the horizontal rotor system with full journal bearing at different cut-off speeds and tribological
conditions. Investigation indicates that CDT is a dependant parameter upon inertia forces on the system components,
mechanical and environmental conditions and tribological behaviour. In this paper an empirical relation for Coast
Down Factor (CDF) has been developed for useful interpretation of the CDT-P in order to understand the rotating
system. Observation reveals that CDF has potential benefits which could be used as a diagnostic parameter for
condition monitoring in order to ascertain the tribological behaviour of lubricants in journal bearings.
KEY WORDS: Coast Down Time, Coast Down Time Phenomenon, Deceleration, Coast Down Time - Profile,
Condition monitoring, Diagnostic parameter.
1.0 INTRODUCTION
Fluid film bearings seldom operate to the expected
standard with inferior lubrication and performance.
Continuous/sustained operation of journal bearing can
lead to changes to good oil in film stiffness and
damping characteristics, load carrying capacity, oil
film temperature and stability of the rotor.
Continuous monitoring of lubrication practice and
wear would facilitate analysis on wear / lubricant
degradation. It would also help to detect the oil
contaminants as well as the deterioration of the
lubricant. The main purpose of a good maintenance
programme is to achieve optimum bearing life.
Failure free running of any rotating equipment
depends on the effective maintenance programme
adopted for bearing. The selection of a reliable
condition monitoring technique becomes important to
properly diagnose and asses the performance of the
lubrication and the deterioration of the lubricant for a
journal bearing (Ramachandran et.al,1996). Tribomonitoring is considered to be more effective and
reliable for rotating machines supported between
bearings (Ran Barron 1996). The performance of the
journal bearing is entirely dependent on the functions
of the lubrication related to the basic properties of the
15
lubricant like viscosity, density, operating speed as
well as the thermal properties like temperature and
pressure (Ramachandran et.al, 1996 a).
Any rotor system will come to a stop when the power
supply is cut-off to the system. The momentum
gained by the rotor system during the sustained
operation will gradually dissipate until the system
comes to a halt. This phenomenon during the
deceleration period is known as Coast Down
Phenomenon (CDP). The time elapsed from the
moment the power supply is cut off until the system
comes to rest is known as Coast Down Time (CDT)
(Craig 1996 and Daughertyet.al,1976). Extensive
investigations were conducted by Xistris et al 1974 on
vertically supported motors by rolling element and
established that CDT monitoring could be used as a
potential health condition monitoring tool. CDT
monitoring is simple as well as economical to
implement. Ramachandran, 1992, Santhanakrishnan
et.al, 1983 conducted experiments on a flexible rotor
system with hydrodynamic journal bearings to
investigate the influence of the lubricant on CDT and
found that the deceleration speed vs. CDT resembled
the Stribeck diagram of friction.
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
Previous research had shown that optimization in
relation to selection of the lubricant under a given
condition could be achieved through CDT monitoring
(Edwin Browne et. al,.2005).
In this paper Coast Down Time- Profile (CDT-P) is
first obtained to ascertain the tribological behaviour
of lubricant inside a journal bearing by varying
operating conditions, like different cut-off speeds,
different lubricants and different lubricant line
pressures.
Furthermore Coast Down Factor (CDF) a
dimensionless factor is deduced, using an empirical
relation, which is developed to interpret the CDT-P.
CDF is defined as a ratio of speeds measured at
constant intervals of time during coast phase of any
rotating system until the rotor system reaches a
permanent stop after power supply is cut off to the
rotating system, with respect to the initial speed drop
at the first time interval. Since a marginal deviation is
noticed among the CDT –P, arriving a diagnostic
decision, based on the changes of CDT-P in the
transition regions and on the trend of speed reduction
during the deceleration period ,is found to be little
difficult and complex . Moreover the CDF trend is
expected to reflect a change magnified in order to
understand the behaviour during deceleration of a
rotor system. The present investigation is attempted to
study CDF as a potential parameter that could be
integrated into the condition monitoring programme.
2. EXPERIMENTAL SETUP
order to position the journal at the centre of the
bearing clearance, a pre load frame, consisting of a
rolling element bearing with three support springs and
set screws, was mounted on the base frame, very
close to the rotor between the drive side support and
rotor. The selected lubricant was circulated through
the journal bearing by a gear pump. The rotor system
was driven by a variable speed AC motor.
Instrumentation with an update time of 195
millisecond with built in RS-232 PC interface was
used for recording time. Bal Pac 1200 vibration data
collector was used for measuring the vibration at a
steady running state. The critical speed for the set up
was computed approximately at 6000 rpm.
Experiments were conducted for different cut-off
speeds, different lubrication and a range of
lubrication line pressures to analyse the tribological
behaviour of the lubricants. Different cut-off speeds
like 1000 rpm, 2000 rpm, 3000 rpm, 4000 rpm and
5000 rpm were selected to run the rotor system along
with selected lubricants, under different values of
lubricant line pressure for a considerable amount of
time, to attain sufficient momentum. Four different
lubricants, good oils SAE 90, SAE 40, used oils SAE
90 and SAE 40 were used for experiments with three
different lubricant line pressures 80 kPa, 100 kPa and
120 kPa. During the steady state operation of the rotor
system, the vibration data was recorded in both
vertical and horizontal directions from both the drive
end bearing and journal end bearing. Power to the
rotor system was made to trip at the selected cut-off
speed and the rate of change of speed was recorded
using the instrumentation during the deceleration
period until the rotor comes to a halt.
Properties of lubricants:
SAE 90 *SAE 90 SAE 40 **SAE 40
Good
Used Good
Used
Oil
Oil
Oil
Oil
Viscosity
@40oC - 161.3
140.9 151.3
110.9 in mm2/s
Density
@15oC - 0.89944 0.8758 0.8989 0.8965
in g/cm3
Water content Nil Nil
Nil
Nil
Sulphur- 0.84
1.24 0.99
1.28
% wt
*SAE 90 used oil:
Experimental set-up shown in figure 1 was used for
the investigation.
Sample of oil collected from a power transmission
gear box of an automobile vehicle which had
completed one useful life cycle time of running
45,000 km.
Figure.1: Experimental set-up.
The rotor system consisting of a rotor weighing 800
grams was mounted at the centre of a 10 mm shaft
and supported by bearings. The drive end of the shaft
was supported by an anti-friction bearing and the non
drive end was supported by a full journal bearing. In
16
** SAE 40 used oil:
Sample of oil collected from automobile engine
lubrication which had completed
one useful life
cycle time of running 5000 km.
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
Specification of the journal bearing:
Length of the journal
= 25.4 mm
Diameter of the journal
= 25.06 mm
Diameter of the journal bearing = 25.38 mm
Clearance of the bearing
= 0.32 mm
SAE 4 0 Go o d
Oil - 8 0 kPa
SAE 4 0 Go o d
Oil - 10 0 kPa
SAE 4 0 Go o d
Oil - 12 0 kPa
SAE 4 0 Us ed
Oil - 8 0 kPa
SAE 4 0 Us ed
Oil - 10 0 kPa
SAE 4 0 Us ed
Oil - 12 0 kPa
2500
Speed
2000
3. RESULT AND DISCUSSIONS
1500
1000
500
Figure 2 depicts the typical characteristics of a CDT-P
expected of a journal bearing to emphasize that the
CDT-P is just the reverse of Stribeck frictional curve.
The shape will be correlated to the frictional
characters described by Raimondi & Boyd design
curve.
0
0
390
780 1170 1560 1950 2340 2730
CDT in milliseconds
F ric tio n
Figure.4: CDT-P: SAE 40 Oil- 2000 RPM
I
II
SAE 9 0 Go o d
Oil - 8 0 kPa
SAE 9 0 Go o d
Oil - 10 0 kPa
SAE 9 0 Go o d
Oil - 12 0 kPa
SAE 9 0 Us ed
Oil - 8 0 kPa
SAE 9 0 Us ed
Oil - 10 0 kPa
SAE 9 0 Us ed
Oil - 12 0 kPa
3500
III
3000
Speed
2500
Speed
I Hydrodynamic Lubrication Zone
II Elastohydrodynamic or Mixed Lubrication Zone
III Boundry Lubrication Zone
I Hydrodynamic Lubrication Zone
2000
1500
1000
500
II Elastohydrodynamic or Mixed
Lubrication Zone
0
0
585
III Boundary Lubrication Zone
Figure.2: Friction Vs Speed
SAE40 Good
Oil - 80 kPa
SAE40 Good
Oil - 100 kPa
SAE40 Good
Oil - 120 kPa
SAE40 Used
Oil - 80 kPa
SAE40 Used
Oil - 100 kPa
SAE40 Used
Oil - 120 kPa
1000
Speed
800
Figure 3: CDT-P: SAE 40 Oil – 1000 RPM
600
400
200
390
780
1170
SAE 4 0 Go o d
Oil - 8 0 kPa
SAE 4 0 Go o d
Oil - 10 0 kPa
SAE 4 0 Go o d
Oil - 12 0 kPa
SAE 4 0 Us ed
Oil - 8 0 kPa
SAE 4 0 Us ed
Oil - 10 0 kPa
SAE 4 0 Us ed
Oil - 12 0 kPa
4500
4000
3500
3000
2500
2000
1500
1000
500
0
0
585 1170 1755 2340 2925 3510 4095 4680
CDT in milliseconds
Figure.6: CDT-P: SAE 40 Oil-4000 RPM
SAE 90 good oil at 80kPa was found exhibiting a
distinctive performance as expected from a good
lubricant. The CDT-P obtained for SAE 90 good oil at
80kPa was very close to Figure 1. The generic profile
of the coast down behaviour exemplifies the typical
frictional characteristics of journal bearing of the
rotor system under investigation in (Edwin Browne
et.al, 2005). CDT-P for SAE 90 good oil at 80kPa has
0
0
Speed
Figure.5: CDT-P: SAE 40 Oil -3000 RPM
Observing the data, which were obtained during the
steady state of running, it is evident that the CDT is
increased with the increase in cut-off speed. The
CDT-P for, SAE 40, good oils and used oils for all the
tested cut-off speeds with different lubricant line
pressures are given in Figures 3 - 7.
1200
1170 1755 2340 2925 3510
CDT in milliseconds
1560
CDT in milliseconds
Figure.3: CDT-P: SAE 40 Oil – 1000 RPM
17
Volume04, Number 01, January - June 2008
shown a distinct and smooth curve in both the
hydrodynamic lubrication and boundary lubrication
zones, which has very closely followed the inverse of
Stribeck curve. CDT was found increasing with the
increase of cut-off speeds (Edwin Browne et al11).
35
E
Caledonian Journal of Engineering
10
5
0
SAE 90 oil , used at all tested pressures and cut-off
speeds, exhibited CDT-P with lot of deviation
throughout the deceleration period, when compared
with that of CDT-P of good oil. The degradation of
the used oil decreases the CDT and increases the
vibration amplitude (Edwin Browne et al11).
0
SAE 4 0 Go o d
Oil - 8 0 kPa
SAE 4 0 Go o d
Oil - 10 0 kPa
SAE 4 0 Go o d
Oil - 12 0 kPa
SAE 4 0 Us ed
Oil - 8 0 kPa
SAE 4 0 Us ed
Oil - 10 0 kPa
SAE 4 0 Us ed
Oil - 12 0 kPa
5000
Speed
4000
3000
2000
1000
1170
S AE 90 Go o d
Oil - 80 kP a
S AE 90 Go o d
Oil - 100 kP a
S AE 90 Go o d
Oil - 120 kP a
S AE 90 Us e d
Oil - 80 kP a
S AE 90 Us e d
Oil - 100 kP a
S AE 90 Us e d
Oil - 120 kP a
60
40
20
0
0
585
1170 1755
CDT
2340
E
Figure.9: CDF- SAE 90 Oil -2000RPM
80
70
60
50
40
30
20
10
0
S AE 90 Go o d
Oil - 80 kP a
S AE 90 Go o d
Oil - 100 kP a
S AE 90 Go o d
Oil - 120 kP a
S AE 90 Us e d
Oil - 80 kP a
S AE 90 Us e d
Oil - 100 kP a
S AE 90 Us e d
Oil - 120 kP a
0
780
1560 2340 3120
CDT
Figure.10: CDF-SAE 90 Oil-3000 RPM
S AE 90 Go o d
Oil - 80 kP a
S AE 90 Go o d
Oil - 100 kP a
S AE 90 Go o d
Oil - 120 kP a
S AE 90 Us e d
Oil - 80 kP a
S AE 90 Us e d
Oil - 100 kP a
S AE 90 Us e d
Oil - 120 kP a
80
60
E
6000
780
CDT
80
The degradation of the lubricant decreases the CDT
and increases the vibration level which complements
the earlier findings (Edwin Browne et. al, 2006).
As there were little deviations noticed among the
CDT-P, a distinct conclusion based CDT-P analysis
was not possible. In order to study the CDT-P in a
meaningful way as one of the condition monitoring
parameters for a rotor system, a dimensionless factor
has been defined as
Coast Down Factor (CDF)
denoted with a letter ‘E’ as Edwin’s factor, which
can be calculated using the following empirical
formula.
En = {Cs – Nn) / (Cs-N1)}
En - Coast Down Factor at Tn
Cs - Cut-off speed
N1 – Rotor speed after first interval
milliseconds (T1).
Nn – Rotor speed measured at successive
intervals in milliseconds (Tn).
390
Figure.8: CDF-SAE 90 Oil-1000 RPM
E
Less viscosity and variations in the bulk properties
make the CDT-P or SAE 40 oil, different from the
expected form. CDT-P confirms that SAE 40 oil is
not a suitable lubricant for the selected journal
bearing under investigation. SAE 40 good oil at
100kPa was found producing CDT-P very close to the
expected one but the vibration amplitude was found to
be more whereas the CDT was less.
S AE 90 Go o d
Oil - 80 kP a
S AE 90 Go o d
Oil - 100 kP a
S AE 90 Go o d
Oil - 120 kP a
S AE 90 Us e d
Oil - 80 kP a
S AE 90 Us e d
Oil - 100 kP a
S AE 90 Us e d
Oil - 120 kP a
30
25
20
15
40
20
0
0
0
780 1560 2340 3120 3900 4680 5460 6240
CDT in milliseconds
0
975
1950 2925 3900
CDT
Figure.11: CDF- SAE 90 Oil-4000 RPM
Figure.7: CDT-P: SAE 40 Oil -5000RPM
18
Caledonian Journal of Engineering
SAE 90 Go o d
Oil - 80 kP a
SAE 90 Go o d
Oil - 100 kP a
SAE 90 Go o d
Oil - 120 kP a
SAE 90 Us ed
Oil - 80 kP a
SAE 90 Us ed
Oil - 100 kP a
SAE 90 Us ed
Oil - 120 kP a
200
150
E
Volume04, Number 01, January - June 2008
100
50
0
0
1170 2340 3510 4680 5850
CDT
complements the author earlier findings with
validation from vibration data (Edwin Browne et
al10). The changes in the bulk properties and low
viscous for SAE 40 good oil are the reasons for
getting a different CDF trend as well as different CDF
values for different cut-off speeds. Comparatively low
CDF values confirm that the SAE 40 oil is not a
suitable lubricant for the rotor system under
investigation. Among the graphs obtained for CDT-P
and CDF, it is clearly illustrated that the CDF graphs
are better profiled to indicate the performance of
lubricants distinctly, during deceleration. The
functional characteristics of journal bearing under
various regimes of lubrication are fully understood by
CDF for rotor system under investigation.
Figure.12: CDF-SAE 90 Oil -5000 RPM
4. CONCLUSION
Figure 8-12 the trend curves plotted for E and CDT
values to analyse and interpret the CDT-P of the rotor
system tested with SAE 90 oil for different speeds
and different lubricant line pressures.
Figure 13-17 are the trend curves plotted for E and
CDT values to analyse and interpret the CDT-P of the
rotor system tested with SAE 40 oil for different
speeds and different lubricant line pressures.
It was observed that the trend plot of CDF for both
SAE 90 and 40 good oils at 80kPa were distinctively
positioned well above the other curves with different
line pressures and at different conditions. This
indicates that there exists a potential function related
to CDF when analysed between different operating
conditions for a rotor system. The steady state
operation of the rotor system allows the journal
bearing to operate within the region of hydrodynamic
lubrication. The lesser speed difference for the SAE
90 good oil at 80kPa, at the first interval as soon as
the power to the rotor was tripped, signifies that the
rotor was subjected only to the fluid frictional
resistance. As the speed reduced and when the rotor
entered the mixed lubrication zone the CDF value was
found increasing. The CDF was found reaching
maximum when the rotor came to rest following
through the boundary lubrication zone. It was
observed that when using different lubricants or
different lubricant line pressures, the fluid resistance
in the hydrodynamic lubrication zone was getting
changed, the effect of which had been noticed in the
form of dominant speed reduction during the first
interval. This signifies the behaviour of the lubricants
in the journal bearing. It was observed that SAE 90
good oil at 80kPa was showing an improved
performance exhibiting the typical characteristics of
the good lubricant. CDF obtained for SAE 90 oil
confirms that the best suited lubricant for the tested
rotor system is SAE 90 oil at 80kPa, which
19
In the present investigation, the tribological behaviour
of lubricants in a rotor system was studied under
different operating conditions. Results are in
agreement with earlier findings that CDT increases
with an increase in cut-off speed. The degradation of
the lubricant decreases the CDT and increases the
vibration level which complements the earlier
findings (Edwin Browne et al11, 12). This paper
presented the usefulness of CDF properties to
overcome the perceived difficulties encountered with
CDT-P in demarking the transition regime during
deceleration. The CDF values indicate the
characteristic behaviour of the lubricants when tested
with different operating conditions. It was found that
the trend curves and analysis of CDF, determined at
equal intervals of time during deceleration of the rotor
system until the rotor stopped, convey potential
information for diagnosing the condition of lubricants
in a rotor system which would be useful for proactive
maintenance.
REFERENCES
[1] Craig.R.J (1976) Application of coast down
monitoring techniques for vertical shaft motors,
DTNSRDC Rep, 76, p.13.
[2] Daugherty.T.L., Craig. R.J., January (1976) Coast
down time as a mechanical condition indicator,
DTNSRDC Rep, 4547.
[3] Edwin Browne. R., De Silva.A.K.M.,
Ramachandran.K.P. Harrison.D.K.
Sharif.M.EL
(2005) An evaluation of bearing lubrication and the
selection of lubricants using CDT analysis as a
condition monitoring parameter, Regional conference
in Recent trends in Maintenance Management,
Sultanate of Oman, Paper no 4, p.25-29.
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
[4] Edwin Browne. R., De Silva.A.K.M.,
Ramachandran.K.P., Harrison.D.K.
(2006) CDT
analysis is used as a condition monitoring parameter
to study the Tribological behaviour of bearing
lubricant under different operating pressure, Porc.
ESDA 2006, 8th Biennial ASME conference, Torino,
Italy, ISBN: 0-7918-377903, ESDA 2006-95021, p.111.
[5] Edwin Browne. R., De Silva.A.K.M.,
Ramachandran.K.P., Harrison.D.K. (2006) Evaluation
of tribological behaviour in journal bearing using
Coast Down Time analysis, LUBMAT 2006,
European conference in lubrication management and
technology, Preston, UK, ISBN 1-901922-58-8, p.9.
[6] Ramachandran.K.P. and Ramakrishna.A. (1996)
Oil analysis for failure prevention of plant machinery,
National seminar on failure analysis, HIMER, p.8893.
[7] Ramachandran.K.P. and Ramakrishna.A. (1996)
Lubrication scheduling in manufacturing industries
and its optimisation, Transaction of Industrial
product finder, p.244 -248.
[8] Ramachandran K.P. (1992) Coast down time
analysis as a condition monitoring tool, Indian
Journal of Maintenance, National Productive
Council, 11, p.45-46
[9] Ran Barron (1996) Engineering Condition
Monitoring Practices, Methods and Application
(Longman, UK)
[10] Santhanakrishnan.G., Prabhu.B.S. Rao. B.V.A.
(1983) An investigation of tribological effects on
coast down phenomenon in horizontal machinery,
Journal of wear, 91, p25-31.
[11] Xistris.G.D, Watson.D.C (1974) Proc.
“Mechanical
Failures
Prevention”
Group,
Gaithersbarg, MD, National Bureau of Standards,
Washington, DC.
[12] Xistris G.D., Watson.D.C (1975) ASME Prepr.,
75-DE-6, New York.
20
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
PROBALISTIC ANALYSIS OF A SYSTEM WITH TWO TYPES OF
REPAIRMAN AND PATIENCE TIME WHEREIN THE INITIAL
REPAIR IS UNDERTAKEN BY THE ORDINARY
REPAIRMAN
Vandna Bhagat
Dept. of Humanities & Applied Science
Advanced Institute of Technology & Management
Vill. Aurangabad, Distt. - Palwal (121102), Haryana, India
ABSTRACT
Two-unit cold standby system with two types of repairman is studied. The failed unit is first undertaken by
an ordinary repairman for repair who may not be able to do complex repairs. Idea of patience time, i.e., the
maximum time of waiting for an expert while the ordinary repairman is trying to repair the failed unit, is
also introduced. The expert repairman may or may not be found available when required. This model has
been compared with the two models wherein the expert is called first to do the repair, if available;
otherwise ordinary repairman is called who if shows inability of repairing the failed unit, the expert is
called.
unit waits for repair till the availability of the expert
repairman whereas in Model 2, the expert repairman
is made available immediately by paying some
additional amount. However, the ordinary repairman
may take a lot of time to declare himself unable to
complete the repair successfully. Thus, we should
not wait till such declaration after a very long time.
We should wait up to some limited amount of time
called as patience time.
1.0 INTRODUCTION
A large literature exists in the areas of reliability of
standby systems under the assumption that the
perfect repairs are done for the failed units. Some
researchers such as (A. Kumar, S.K.Gupta and
G.Taneja, 1996 ), (R.K.Tuteja and G.Taneja, 1992)
(R.K.Tuteja, G.Taneja and A.Malik, 2000-2001)
(R.K.Tuteja, R.T.Arora and Gulshan Taneja, 1991)
(S.K. Singh and R.P. Singh,1989), and (V.Goyal
and K.Murari, 1984) considered the two types of
repair, i.e., by an ordinary repairman and by an
expert with assumption that ordinary repairman may
not be able to do some complex repairs and then
expert is called. They considered immediate
availability of the expert whenever required.
However, the expert may not always be available
whenever required. Rizwan (S.M.Rizwan, 2007)
discussed reliability analysis of two unit system with
two repairmen wherein ordinary repairman may not
be available on requirement but the expert is
available on requirement. Taneja et.al (G.Taneja,
V.Naveen and D.K.Madan, 2001) analysed
reliability and profit analysis of a system with an
ordinary and an expert repairman wherein the latter
may not always be available (G.Taneja, V.Naveen
and D.K.Madan, 2001) and also assumed that on
failure of a unit, an expert repairman is called first to
do the repair, if available. If not available, then
ordinary repairman is called who may not be able to
do some complex repairs. They discussed two
models. If the ordinary repairman finds himself
unable to repair the unit, then in Model 1, the failed
We in the present paper, introduce the concept of
such patience time while dealing with a two-unit
cold standby system with the assumption that the
failed unit is first undertaken by the ordinary
repairman who may not be able to do some complex
repairs. If the ordinary repairman is unable to repair
the failed unit, an expert is called if he is available.
If he is not available, we wait till the expert becomes
available or both units get failed or the patience time
is completed whichever is earlier. Here, the patience
time is maximum time of waiting for the expert
repairman. It is assumed that the expert repairs all
the units which fail during his stay at the system.
The model is analysed stochastically by making use
of semi-Markov processes and regenerative point
technique and the expressions for various measures
of system effectiveness such as mean time to system
failure, steady state availability, total fraction of
busy time of ordinary repairman, total fraction of
busy time of expert repairman on ordinary/special
visit. Expected number of visits by an ordinary and
an expert repairman are found out. Profit is also
calculated using the above measures. Graphs are
21
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
plotted for particular case .The model is also
compared with the models discussed by G.Taneja,
V.Naveen and D.K.Madan (G.Taneja, V.Naveen
and D.K.Madan, 2001).
Bi(t), (Bi(e)(t))
NOTATIONS
Bsi(t)
O
cs
λ
p
q
a1
operative
cold standby
constant failure rate of the
operative unit
probability that the expert
repairman is available
probability that expert repairman
is not available
probability
that
ordinary
Wi(t)
Vi(t),(Vi(e)(t))
repairman is able to repair the
failed unit
a2
probability
that
ordinary
through any other regenerative
state.
probability that ordinary (expert)
repairman is busy at instant ‘t’
given that the system started from
regenerative state i at t = 0
probability that expert repairman
on his special visit is busy at
instant t given that the system
started from regenerative state i at
t=0
probability that a repairman is
busy with the system initially in
regenerative state i is busy at time
t without passing through any
other regenerative state
expected number of visits of an
ordinary (expert) repairman in
(0,t] give that the system from
regenerative state i at t = 0
2.0 TRANSITION PROBABILITIES
AND MEAN SOJOURN TIMES
repairman is unable to repair the
failed unit
g1(t), G1(t)
The transition diagram showing various states of
transition of the system is shown in Figure.1. The
epochs of entries into the states 0, 1, 2, 3, 5, 6 and 8
are regenerative points and thus these are
regenerative states. States 4, 5, 7, 8 and 9 are down
states. The non-zero elements pij are given by:
p.d.f. and c.d.f. of time to repair
by ordinary repairman
g2(t), G2(t)
p.d.f. and c.d.f. of time to repair
by expert repairman
h(t), H(t)
w(t), W(t)
Fr
Fre
Fres
FR
FRe
FRes
φi(t)
p.d.f. and c.d.f. of patience time
p.d.f. and c.d.f. of waiting time
failed unit under repair of ordinary
repairman
failed unit under repair of expert
repairman
failed unit under special repair of
the expert
repair is continuing from previous
state by the ordinary repairman
repair is continuing from previous
state by the expert repairman
special repair by the expert is
continuing from previous state.
c.d.f of first passage time from
p01 = 1, p10= a1g1*(λ), p12 = pa2g1*(λ), p13 =
qa2g1*(λ), p14 = 1−g1*(λ),
p11(4) = a1[1−g1*(λ)], p15(4) = a2q[1−g1*(λ)], p18(4) =
a2p[1−g1*(λ)], p20 = g2* (λ),
p27 = 1−g2*(λ), p22(7) = 1−g2*(λ), p32 =E1*(λ), p35 = λ
E2*(λ), p36 = E3*(λ) ,p56 =1,
p60 = g2*(λ), p69 = 1−g2*(λ), p66(9) = 1−g2*(λ), p82= 1
By these transition probabilities, it can be verified
that
p10 + p12 + p13 + p14 = p10 + p12 + p13 + p11(4) + p15(4)
+ p18(4) = 1,
regenerative i to failed state
Ai(t)
probability that the system is up at
p20 + p27 = p20 + p22(7) = 1, p32 + p35 + p36 = 1, p56 =
1, p60 + p69 = p60 + p66(9) = 1, p82 = 1
instant t given that system started
from regenerative state i at t = 0
Mi(t)
Also µi, the mean sojourn time in state i are
probability that system is up
initially in regenerative state i is
up at time t without passing
22
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
+ q13(t) © A3(t) + q15(4) (t) © A5(t) + q18(4) © A8(t)
*
*
µ0 = 1 , µ1 = 1 − g1 (λ ) , µ2 = 1 − g 2 (λ ) , µ3 = E1*
λ
λ
λ
*
1
−
g
(
λ
)
(λ), µ6 =
2
A2(t)
λ
= M3(t) + q32(t) © A2(t) + q35(t) © A5(t) +
A3(t)
q36(t) © A6(t)
The unconditional mean time taken by the system to
transition for any regenerative state j, when it (time)
is counted from epoch of entrance into that state i is
mathematically stated as :
∞
mij =
∫ t dQij (t) = − qij* ′(0)
0
∫ G1(t)dt=K1(say)
A6(t)
A8(t)
= M6(t) + q60(t) © A0(t) + q66(9)(t) © A6(t)
= q82(t) © A2(t)
M2(t)=
The steady state availability of the system is given
by
A0 = lim s A0*(s) = N1/D1
0
∞
∫ G 2 ( t )dt = K 2 (say)
0
m60 + m69 = µ2, m60 + m66(9) = K2
s →0
∞
where N1 = µ0 p20 p60 (1−p11(4)) +µ1 p20 p60 + µ2[p60
(p18(4) + p12+ p32) + p20 p13 (1−p32) + p15(4) p20] + µ3
p13 p20 p60 and D1 = µ0 p18(4) p20 p60 + K1 p20 p60 + K2
[p60 (p12+p18(4)+p13 p32) + p20 (p15(4) + p13 − p13 p32) +
p20 p60 (p13 p35 + p15(4))] + k3 p13 p20 p60
∫ t [e−λt⎯E1(t) + λe−λtE2(t) + e−λt
0
E3(t)] dt = K3 (say)
3.0 MEAN TIME TO SYSTEM
FAILURE
Using probability arguments and recursive elations
for Bie(t), BSie(t), Bi(t), Vie(t), VSie(t) and Vi(t), we
obtain the following measures in steady-state:
φ0(t) = Q01 (t)(s) φ1(t)
φ1(t) = Q10 (t)(s) φ0(t) + Q12(t)(s) φ2(t) + Q13(t)(s)
φ3(t)+Q14
φ2(t) = Q20 (t)(s) φ0(t) + Q27(t)
φ3(t) = Q32 (t)(s) φ2(t) + Q35(t) + Q36(t)(s) φ6(t)
φ6(t) = Q60 (t)(s) φ0(t) + Q69(t)
The total fraction of the time for which the expert
repairman is busy in his ordinary visit (B0e) = N2/D1
The total fraction of time for which the expert
repairman is busy on special visits (BS0e) = N3/D1
Now, the mean time to system failure (MTSF) when
the system starts from the state 0, is
T0 =
= q56(t) © A6(t)
M3(t)= e−λt⎯H(t)⎯W(t) ; M6(t) = e−λt⎯G2(t)
∞
m 32+ m35 + m36 =
A5(t)
Where M0(t)= e−λt; M1(t)= e−λt⎯G1(t) ;
e−λt⎯G2(t);
Thus,
m01 = µ0, m10 + m12 + m13 + m14 = µ1,
m10 + m12 + m13 + m11(4) + m15(4) + m18(4) =
m20 + m27 = µ2, m20 + m22(7) =
= M2(t) + q20(t) © A0(t) + q22(7)(t) © A2(t)
The total fraction of time for which the ordinary
repairman is busy (B0) = N4/D1
**
1 − φ 0 (s ) N
=
lim
s →0
s
D
The expected number of visits per unit time by the
expert repairman (V0e) = N5/D1
where N = µ0 + p01µ1 + µ2 (p01 p12 + p01 p13 p32) +
K3 p01p13 + µ2 p01 p13 p36
and D = 1 −
p10 − p12 p20 −
p13 p36 p60 −
p13 p20 p32
The number of special visits per unit time by the
expert repairman (VS0e) = N6/D1
The number of visits by ordinary repairman per unit
time (V0) = N7/D1
Where
N2 = K2 p60 [p13 p32 + p12 + p18(4) p22(7)]
N3 = p20 K2 [p60 (p13 p35 + p15(4)) + p15(4) + p13
(1−p32)]
N4 = K1 p01 p20 p60
4.0 AVAILABILLTY ANALYSIS
A0(t)
= M0(t) + q01(t) © A1(t)
= M1(t) + q10(t) © A0(t) + q11(4) (t) © A1(t)
A1(t)
+ q12 (t) © A2(t)
23
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
N5 = p20 p60 [p12 + p18(4) + p13 p32].
N6 = p20[p13{p35 + p66(9)} + p15(4) p60 + p66(9)]
N7 = (1−p11(4)) p20 p60
(ii)
and D1 is already specified.
5.0 PROFIT ANALYSIS
The expected total profit incurred to the system in
steady state is given by
P = C0 A0 − C1 B0 -C2 B0e − C3(V0e+ VS0e) − C4 V0
− C5 BS0e
(iii)
Where
C0 = revenue per unit up time of the system.
C1 = cost per unit time for which the ordinary
repairman is engaged in repairing the failed
unit.
C2 = cost per unit time for which expert repairman is
busy (after his ordinary visit) in repairing the
failed unit.
C3 = cost per ordinary visit and special visits by the
expert repairman
C4 = cost per visit by the ordinary repairman.
C5 = cost per unit time for which expert repairman is
busy (after his special visit) in repairing the
failed unit
It is, therefore, concluded that if cost per unit time
for which the expert is busy, is such that P-P1>0
then we should call the ordinary repairman first and
if P-P1<0 the expert repairman should be called first
to repair the failed unit.
8.0 COMPARITIVE STUDY OF THE
PRESENT MODEL WITH THE
MODEL 2 DISCUSSED IN [2]
From Figure.3 it is clear that the difference of
profits (P-P2) decreases on increasing the values of
cost (C5). Following conclusions can be drawn:
6.0 GRAPHICAL INTERPRETATION
(i)
For the graphical representation, the following
particular case is considered
g1(t) = α1 e−α1t , g2(t) = α2 e−α2t , h(t) = β1 e−β1t ,
w(t) =β2 e−β2t
The behaviour of the MTSF and the profit w.r.t.
failure rate (λ) for different values of repair rate (α1)
have been studied through graphs wherefrom it has
been seen that as failure rate increases, MTSF as
well as profit decreases. However, their values
become higher for higher values of repair rate (α1).
(ii)
(iii)
7.0 COMPARITIVE STUDY OF THE
PRESENT MODEL WITH THE
MODEL 1 DISCUSSED IN [2]
Figure.2 shows the behaviour of difference of
profits (P-P1) w.r.t. cost (C5) for different values of
patience rate (β1). It is clear from the graph that
(i)
model of G.Taneja, V.Naveen and
D.K.Madan is better or worse than the
present model.
If β1 = 15 and other parameters are fixed
then these two models are equally good if
C5 = 7556. If C5 > 7556 or < 7556 then first
model of G.Taneja, V.Naveen and
D.K.Madan is better or worse than the
present model.
If β1 = 25 and other parameters are fixed
then these two models are equally good if
C5 = 8000. If C5 > 8000 or < 8000 then first
model of G.Taneja, V.Naveen and
D.K.Madan is better or worse than the
present model.
If β1 = 5 and other parameters are fixed
then these two models are equally good if
C5 = 6627. If C5 > 6627 or < 6627 then
second model of G.Taneja, V.Naveen and
D.K.Madan is better or worse than the
present model.
If β1 = 15 and other parameters are fixed
then these two models are equally good if
C5 = 7341. If C5 > 7341 or < 7341 then
second model of G.Taneja, V.Naveen and
D.K.Madan is better or worse than the
present model.
If β1 = 25 and other parameters are fixed
then these two models are equally good if
C5 = 7750. If C5 > 7750 or < 7750 then
second model of G.Taneja, V.Naveen and
D.K.Madan is better or worse than the
present model.
It is, therefore, concluded that if cost per unit time
for which the expert is busy, is such that P-P1>0
then we should call the ordinary repairman first and
if P-P1<0 the expert repairman should be called first
to repair the failed unit and even by paying some
extra amount if not available.
If β1 = 5 and other parameters are fixed
then these two models are equally good if
C5 = 6835. If C5 > 6835 or < 6835 then first
24
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
types of repairman, Journal of Decision and
Mathematical Sciences, 5-6, p.59-74.
REFERENCES
[1] A. Kumar, S.K.Gupta and G.Taneja (1996)
Comparative study of the profit of a two server
system including patience time and instruction time,
Microelectron.Reliab., 36(10), p.1595-1601.
[5] R.K.Tuteja, R.T.Arora and Gulshan Taneja
(1991) Stochastic behaviour of a two unit system
with two types of repairman and subject to random
inspection, Microelectron.Reliab., 31(1), p.79-83.
[2] G.Taneja, V.Naveen and D.K.Madan (2001)
Reliability and profit analysis of a system with an
ordinary and an expert repairman wherein the latter
may not always be available, Pure and Applied
Mathematika Sciences, LIV (1-2), p.11-25.
[6] S.K. Singh and R.P. Singh (1989)) Stochastic
analysis of complex system with two types of repair
facility and patience time for repair, International
Journal of Management and systems, 5, p.143-156.
[7] S.M.Rizwan (2007), Reliability Analysis of a
two unit system with two repairman, Caledonian
Journal of Engineering, .3, p.1-5.
[3] R.K.Tuteja and G.Taneja (1992) Cost benefit
analyses of two server, two unit, warm standby
system with different types of failure;
Microelectron.Reliab., 32, p.1353-1359.
[8] V.Goyal and K.Murari (1984) Cost analysis of a
two-unit standby system with two types of
repairman, Microelectron. Reliab, 24, p.849-855
[4] R.K.Tuteja and G.Taneja and A.Malik (20002001) Reliability and profit analysis of a two-unit
cold standby system with partial failure and two
25
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
26
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
STABILITY ANALYSIS OF MULTI DIMENSIONAL DISCRETE
POLYNOMIAL EMPLOYING EQUIVALENT ONE-DIMENSIONAL
POLYNOMIAL
Sivanandam S.N. and Rajan.S
Department of Computer Science and Engineering
PSG College of Technology, Peelamedu, Coimbatore – 641 004, India
Email : sns@mail.psgtech.ac.in , sr_tce@rediffmail.com
ABSTRACT
In this paper, the stability analysis of multi dimensional discrete polynomial is carried out with the help of
its equivalent one-dimensional polynomial along with the suggested necessary conditions and Marden
table. The proposed algebraic procedure is simple and straight forward in application and illustrated
through examples.
KEYWORDS: Stability, Multi dimensional, One dimensional, Marden table, Necessary condition.;
H ( z 1 , z 2 ,..., z k ) =
1.0 INTRODUCTION
A( z 1 , z 2 ,..., z p )
B( z 1 , z 2 ,..., z q )
……………………………………..…………...1
where A(z1,z2,…,zp) and B(z1,z2,…,zq) are real
mutually prime polynomials.
The stability is the main desirable feature of all
kinds of systems and in designing a given
system, it is important to choose the system
parameters so as to avoid the possible occurrence
of unstable condition. The stability problem of
multidimensional polynomials is receiving more
attention in recent years in view of the emerging
widespread applications. The multi dimensional
discrete polynomials generally occur in the fields
of image processing, geophysics and in
processing of bio-medical, physical, sonar and
radar data (Tzafestas, 1986). Other applications
arise in obtaining realizability properties of
impedances of networks and transmission lines
which represent multidimensional systems.
For stability investigation, Anderson and Jury
(Jury, 1974), gave the conditions for the
denominator polynomial B(z1,z2,…,zq) to be non
q
zero in the region I z i ≤ 1. In general, the
i =1
stability condition is that,
B( z 1 , z 2 ,..., z q ) ≠ 0 , for all
q
I
i =1
zi ≤ 1
…………………………….....…………..2
Equation (2) can be restated as (q-1) necessary
conditions and one sufficient condition as given
from equations (3) and (4) respectively:
The stability investigation of multidimensional
discrete polynomial is very interesting and many
schemes have been reported in (Strintzis, 1977,
Jury, 1974, Bose, 1974 & 1979, Zaheb, 1980,
1982 & 1984, Tzafestas, 1988, Plotkin, 1985,
Bauer, 1991, 1992 & 1994), each scheme has its
own merits and applications. In this paper, a
simple algebraic procedure is presented to test
the stability of multidimensional systems.
Necessary conditions:
B( z 1 ,0 ,0 ,...,0 ) ≠ 0
B( z 1 , z 2 ,0 ,...,0 ) ≠ 0
z1 ≤ 1
{z1
} {
}
= 1 ∩ z2 ≤ 1
.
.
.
2.0 STABILITY THEOREM OF
MULTI DIMENSIONAL SYSTEM
B( z 1 , z 2 ,..., z q −1 ,0 ) ≠ 0
⎫
⎧q −1
⎨ I z i = 1⎬ I
i
=
1
⎭
⎩
{z q−
A linear time invariant multidimensional discrete
system (Jury, 1974) can be represented by a
multivariable transfer function of the form,
1
}
≤1
…………………………………....…………….3
27
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
i)
At z = 1, F(1)>0
ii)
At z = -1, F(-1)>0 (for neven)……………………………..6
F(-1)<0 (for n-odd)
iii)
|a0|<|an|
Sufficient condition:
⎧ q −1
⎫
⎨ i I=1 z i = 1⎬ I
⎩
⎭
B( z 1 , z 2 ,..., z q ) ≠ 0
{z
q
}
≤1
……………….…………………………………4
If the conditions stated in equation (6) are
satisfied, then Marden table (Marden, 1966) is
used for testing Fn(z) which is given in Table 1.
Thus the problem of testing the stability
condition in equation (2) for a q-variable
polynomial is equivalent to the problem of
testing the necessary conditions (3) and the
sufficient condition given in equation (4).
Table 1: Marden table for Fn(z) in equation (5)
In this paper, a simple algebraic scheme is
proposed to test the equations given in equation
(3) as well as the equation (4). This scheme is
straight forward and easy to apply compared to
other schemes given in (Strintzis, 1977, Jury,
1974, Bose, 1974 & 1979, Zaheb, 1980, 1982 &
1984, Tzafestas, 1988, Plotkin, 1985, Bauer,
1991, 1992 & 1994).
Fn (z)
an
Fn(z)
a0
bn
Fn-1(z)
b0
cn
Fn −2 (z)
The respective equation given in equations (3)
and equation (4) is converted into an equivalent
one-dimensional polynomial, which in turn is
tested utilizing the proposed necessary
conditions and Marden table (Marden, 1966).
The main idea used in obtaining the onedimensional equivalent polynomial is inversion
of every variable and coalition of all the inverted
variables into a single variable in z with |z|<1.
The resulted polynomial F(z) is handled easily
by the proposed procedures. The proof for using
the inverse of ‘z’ is given in Appendix.
Fn-2(z)
.
.
c0
.
.
F0 (z)
z0
F0(z)
z0
2
3
.
an-
an-
1
2
a1
bn-
a2
bn-
1
2
b1
cn-
b2
cn-
1
2
c1
.
.
c2
.
.
(m1)
a1
m
.
(m2)
a2
.
.
an-2
b1
an-1
b0
an
.
.
bn-1
c0
bn
.
.
.
cn
a0
The first step to formulate Marden’s table is to
reverse the coefficients of the given
characteristic polynomial in equation (5) i.e.,
n
Fn ( z ) = a n z + a n −1 z
n −1
+ a n−2 z
n−2
+ ... + a1 z + a 0
………………..……………………….…….7
Using equations (5) and (7), the first two rows
are formed in Marden table given in Table 1. It is
observed that when ‘z’ is inverted in the equation
3.1 Proposed Necessary Conditions
Let F(z) be an n-th degree one-dimensional
polynomial,
n-1
1
Fn −1 (z)
3.0 PROPOSED PROCEDURE
n
Row/Column
1
), equation (7) is formed. Thus,
z
Fn ( z ) | 1 = Fn ( z ) is obtained.
(5) ( z →
n-2
F(z) = Fn(z) = a0z +a1z +a2z +...+an-1z+an
………………………………………………….5
with a0>0.
z→
The proposed necessary conditions for testing
the equation (5) are,
z
The elements in the third row are calculated as
given below:
28
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
bn = a0 a n −1 − a n a1
Step 4: Use z1→z2→z3→…..→zk→z and get the
respective one-dimensional equation of
B1(z1,z2,z3,….,zk).
bn −1 = a0 a n − 2 − a n a 2
……………..8
.
.
Step 5: Apply the proposed necessary condition
as given in equation (6) to the one
dimensional equivalents.
b0 = a02 − a n2
Step6: If proposed necessary conditions are
satisfied, invoke Marden table.
The fourth row forms the reversal of coefficients
of the third row. The above computations are
repeated to formulate the other rows and this
completes the formulation of the entire Marden
table. Based on Marden table in Table 1, for a
system to be stable, the constant terms b0,
c0,…,z0
of
the
computed
Step 7: Ascertain the stability using Marden
polynomials i.e., the proposed necessary
conditions are applied over Marden
polynomials and if satisfied for all
Marden polynomials upto second
degree, then the system is stable else
declare the system is unstable.
Fn−1 ( z ) ,
Fn−2 ( z ) ,…, F0 (z) respectively, should be all
positive. If any of the constant term is negative
then the system is unstable.
Step 8: Stop the above proposed algorithm is
applied for the illustrative examples.
The flowchart depicting the process of
algorithmic flow is as shown in Figure
1.
Instead of applying the above condition, the
Marden polynomials Fn−i ( z ) where i=1,2,3,…
are individually tested with the proposed
conditions given in equation (6).
The discussed proposed procedure is given in an
algorithmic form in the forthcoming section.
4.0 PROPOSED ALGORITHM
The various steps involved in the proposed
algorithm are as follows:
Step 1: Read the given multi-dimensional
polynomial B(z1,z2,z3,….,zq)
Step 2: Formulate the necessary conditions and
sufficient condition for B(z1,z2,z3,….,zq)
equivalent to that in the equations (3)
and equation (4)
Step 3: With the inversion principle,
Let
z1 →
1
1
1
, z2 →
,..., z q →
z1
z2
zq
Get all the respective inverted polynomials for
each necessary condition and sufficient condition
as B1(z1,z2,z3,….,zk).
Figure.1: Flowchart for the proposed algorithm
29
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
5.0 ILLUSTRATIONS
At z= -1, F3(-1) = 4 > 0 (even
polynomial)………………………….15
The proposed algorithmic procedure is applied to
the following illustrations
and for |a0|<|an|; |0|<|4|
The discrete polynomial with three variables
from (Strintzis, 1977) is written as:
Step 6: The proposed necessary condition is
satisfied for F3(z) as shown in equation
(15), hence Marden table is invoked as
given in Table 2.
B( z1 , z 2 , z 3 ) = z 3 + z1 + z12 z 2 − z 2 + 4 …..9
Table 2: Marden table for F3(z) in equation (14)
5.1 Illustration 1
Applying the proposed algorithm discussed in
section 4 to equation (9),
1
0
1
4
F34(z)
4
4
1
0
0
4
1
16
0
16
-16
4
64
0
240
4
240
64
-16
F33(z)
F32 ( z )
F32(z)
( z 2 = 0 and z 3 = 0)
B( z1 , z 2 ,0) = z1 + z12 z 2 − z 2 + 4
0
F33 ( z )
Step 1: Read the three dimensional polynomial
given in equation (9).
Step 2: Formulate the necessary and sufficient
conditions of equation (9),
B( z1 ,0,0) = z1 + 4
F34 ( z )
( z 3 = 0)
Step 7: The second degree Marden polynomial
from Table-2 is,
B( z1 , z 2 , z 3 ) = z 3 + z1 + z z − z 2 + 4
2
1 2
. ……………………………………………….10
F32(z)=240z2+64z-16……..…………16
Step 3: Applying the inversion principle and
formulating inverted polynomials of
equation (10), i.e,
Applying the proposed necessary condition to
equation (16),
1
1
1
, z2 →
, z3 →
z1
z2
z3
B ( z1 ,0,0) = 4 z1 + 1
F32(1) = 288 > 0
z1 →
F32(-1) = 160> 0 (even
polynomial)………………………….17
B ( z1 , z 2 ,0) = z1 z 2 + 1 − z12 + 4 z12 z 2
and |a0|<|an| ⇒ |16| < |240|
B ( z1 , z 2 , z 3 ) = z12 z 2 + z1 z 2 z 3 + z 3 − z12 z 3 + 4 z 3 z12 z 2
………………………………………………...11
From equation (17) it can be observed that F32(z)
satisfies the proposed necessary conditions
declaring the given original polynomial
B(z1,z2,z3) is stable.
Step 4: Using z1→z2→z3→z for equation (11),
i) F1(z)=B1(z1,0,0)= 4z+1……………12
Also, the third degree Marden polynomial F33(z)
satisfies the proposed necessary conditions
which further declares the given polynomial is
stable in nature.
ii) F2(z)=B1(z1,z2,0)= 4z3+1…………13
iii) F3(z)=B1(z1,z2,z3)=4z4+z3+z..........14
Step 5: Applying the proposed necessary
conditions to equation (14),
Step 8: Stop
This conclusion is same as that given in
(Strintzis, 1977).
At z=1, F3(1) = 6 > 0
30
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
The proposed necessary condition is applied to
equation (24):
5.2 Illustration 2
The discrete polynomial with three variables
from (Strintzis, 1977) is considered here:
B( z1 , z 2 , z 3 ) = z 3 +
z 1 + 6 z 12 z 2
i. F2(1) = 6 > 0
− z2 + 2
ii. F2(-1) = -4 < 0………….…………………..25
…………………………………………...……18
iii. |1| < |5|
Applying the proposed algorithm [Step 1 – Step
8 in Illustration 1] to equation (18), the following
are obtained:
The necessary conditions are satisfied for F2(z)
in equation (24).
B1 ( z1 ,0 ,0 ) = 2 z 1 + 1
=
B1(z1,z2,z3,0)
=
3.
F3(z)
5z2+1………………………………………….26
B1 ( z1 , z 2 ,0 ) = z 1 z 2 + 6 − z 12 + 2 z 12 z 2
……………………………………....………..19
With z1→z2→z, equation (19) becomes,
i)
The conclusion for equation (26) is same as that
of the equation (25).
=
B1(z1,0,0)
=
2z+1
F1(z)
|z|<1…………………………….……20
4. F4(z)=B1(z1,z2,z3,z4)=
z1 z2+z2 z3+z1z2 z3+z1 z3 z4+5z 1z2 z3z4
………………………………………...………27
With z1→z2→z3→z4→z for equation (27),
ii) F2(z) = B1(z1,z2,0) = 2z3+6 = z3+3
………………………………………………...21
F4(z) = 5z4+2z3+2z2……...................................28
Applying the proposed necessary condition to
equation (21),
F4(z) in equation (28) is handled with the
proposed condition, which gives,
At z=1, F2(1) = 4 > 0
i)
At z= -1, F2(-1) = -1+3 = 2 > 0 (odd
polynomial)
At z=1, F4(1) = 9 > 0
ii) At
Thus for F2(z), the second necessary condition is
violated, indicating the given discrete
polynomial is unstable.
z=
-1,
F4(-1)
= 5 > 0 (even
polynomial)………29
iii) |a0|<|an| ⇒ |2| < |5|
This conclusion is same as that available in
(Strintzis, 1977).
iv) From equation (28),
F5(z) = z2F4(z)………………………………...30
5.3 Illustration 3
F4(z) satisfies proposed necessary conditions
implying F5(z) also satisfy necessary condition
because F5(z) is derived from F4(z), thus it is not
necessary to formulate Marden table for F4(z).
From (Bose, 1974), the discrete polynomial with
four variables is written as,
B( z1 , z 2 , z 3 , z 4 ) = z 3 z 4 + z1 z 4 + z 4 + z 2 + 5
……………………………….………….……22
Applying the proposed algorithm,
∀ |z| ≥ 1
1. F1(z) = B1(z1,0,0) = 5 ≠ 0
……………………………….………...…….23
Since the proposed necessary conditions are
satisfied for all necessary (F1(z) to F3(z)) and
sufficient condition (F4(z) and F5(z)), the given
discrete polynomial in equation (22) is found to
be stable.
This conclusion obtained using the proposed
approach is in agreement with (Bose, 1974).
2. F2(z)=B1(z1,z2,0,0)=5z2+1………………….24
31
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
applied over it, to analyze the stability
conditions. The proposed approach is simple and
direct in application and illustrated with suitable
examples.
6.0 DISCUSSION
The salient points noted in the illustration are
brought out in this section. Illustration 1
employed a three dimensional polynomial and at
first, the necessary and sufficient conditions are
evolved from the three dimensional polynomial.
For all the necessary and sufficient conditions
derived, inverted polynomials are formulated and
each inverted polynomial is converted to its
equivalent one-dimensional polynomial. The
proposed necessary conditions were applied over
these one-dimensional polynomials and if
satisfied, formulated Marden table else declares
the system to be unstable. From the Marden table
formulated,
Marden
polynomials
were
computed, over which the proposed necessary
conditions were applied and stability was
analyzed. It should be noted that the Marden’s
table is to be computed only if the formulated
one-dimensional equivalent degree is greater
than 2. For illustration 1, the proposed necessary
conditions were satisfied for the one-dimensional
equivalent polynomials declaring the given
three- dimensional characteristic polynomial is
stable. In illustration 2, the proposed necessary
conditions are violated for the second onedimensional polynomial of given original
polynomial, declaring the given system is
unstable. Illustration 3 shows a four dimensional
polynomial, wherein all of its necessary and
sufficient conditions derived satisfied the
proposed conditions, and declared the given
system is stable.
8.0 ACKNOWLEDGEMENT
The authors acknowledge with gratitude, the
support and facilities provided by PSG College
of Technology , Coimbatore, India and fellow
research scholars to carry out this research work.
REFERENCES
[1] B.D.O. Anderson and E.I. Jury (1974)
Stability of Multidimensional Digital Filters,
IEEE Transactions on Circuits and Systems,
21(2), p. 300-304.
[2] E. Walach and E. Zaheb (1982) Generalized
zero sets of multi parameter polynomials and
feedback stabilization, IEEE Transactions on
Circuits and Systems, 29(1), p.15-23.
[3] E. Walach and E. Zaheb (1982) Ndimensional stability margins computation and a
variable transformation, IEEE Transactions on
Acoustics, Speech and Signal Processing, 30(6),
p.887–893.
[4] E. Walach and E. Zaheb (1980) Sign test for
multivariable
real
polynomials,
IEEE
Transactions on Circuits and Systems, 27(7),
p.619–625.
The main advantage of the proposed procedure
is, it is simple and direct in application for any
kind of multi dimensional discrete polynomial
under consideration. The proposed procedure can
be extended to design of unknown parameters
that exist in multidimensional characteristic
polynomials with minimal computational effort.
[5] E. Zaheb (1984) Another simplification in
Multidimensional
Stability
tests,
IEEE
Transactions on Acoustics, Speech and Signal
Processing, 32(2), p.453–455.
[6] L. Leclerc and P. Bauer (1994) New Criteria
for Asymptotic stability of one and multi
dimensional state space digital filters in fixed
point arithmetic, IEEE Transactions on Signal
Processing, 42(1), p.46–53.
7.0 CONCLUSION
In this paper, an algebraic procedure is proposed
to analyze the stability of the given
multidimensional discrete polynomial. The
multidimensional polynomial is converted to its
equivalent one dimensional polynomial and
necessary conditions and Marden table are
[7] M.G. Strintzis (1977) Test for stability of
Multidimensional filters, IEEE Transactions on
Circuits and Systems, 24(8), p.432–437.
32
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
[8] M. Marden (1996) The Geometry of Zeros of
a Polynomial in a complex variable, (NY, USA:
American Mathematical Society, 2nd Edition,).
⎛ 1
⎜⎜
⎝ zk
⎞
⎞ ⎛
1
⎟⎟
⎟⎟ = ⎜⎜
x
jy
+
k ⎠
⎠ ⎝ k
(a.2)
Multiplying equation (55) with its complex
conjugate,
[9] M.N.S. Swamy, L.M. Roytman and E.I.
Plotkin (1985) Planar Least Squares Inverse
Polynomial and Prcatical BIBO stabilization of
N-dimensional linear shift invariant filters, IEEE
Transactions on Circuits and Systems, 32(12),
p.1255–1259.
⎛ 1
⎜⎜
⎝ zk
[10] N.K. Bose and P.S. Kamat (1974)
Algorithm for stability test of Multidimensional
Filters, IEEE Transactions on Acoustics, Speech
and Signal Processing, 22(5), p.307–314.
[11] N.K. Bose (1979) Implementation of a new
stability test for N-dimensional filters, IEEE
Transactions on Acoustics, Speech and Signal
Processing, 27(1), p.1-4.
⎛ 1
⎜⎜
⎝ zk
[12] P. Bauer and E.I. Jury (1991) BIBO
Stability of Multidimensional (m-D) Shiftvarying Discrete Systems, IEEE Transactions on
Automatic Control, 36(9), p.1057–1061.
⎞ ⎛
1
⎟⎟ = ⎜⎜
⎠ ⎝ x k + jy k
⎛ x − jy k
= ⎜⎜ k2
2
⎝ xk + y k
⎞
⎟
⎟
⎠
⎛ x
= ⎜⎜ 2 k 2
⎝ xk + y k
⎞
⎟−
⎟
⎠
⎞
⎟⎟
⎠
⎛ y
j ⎜⎜ 2 k 2
⎝ xk + y k
⎞
⎟
⎟
⎠
⎞
⎟⎟ = Ak − jBk
⎠
⎛ x
A = ⎜⎜ 2 k 2
⎝ xk + y k
where,
⎛ y
B = ⎜⎜ 2 k 2
⎝ xk + y k
[13] P. Bauer (1992) Finite word length effects
in m-D digital filters with singularities on the
stability boundary, IEEE Transactions on Signal
Processing, 40(4), p.894–900.
⎞⎛ x k − jy k
⎟⎟⎜⎜
⎠⎝ x k − jy k
⎞
⎟ and
⎟
⎠
⎞
⎟.
⎟
⎠
Based on the values of ‘xk’ and ‘yk’, the
following cases are analyzed,
Case (i)
Let | xk |<1 and | yk|>1
Then, | xk2|<1 and | yk2|>>1
(a.3)
Using equation (56), it can be noted that,
xk2+ yk2>>1
(a.4)
Also,
Ak<1 and Bk<1.
Case (ii)
Let | xk|>1 and | yk|<1
Then, | xk2|>>1 and | yk2|<1
(a.5)
[14] S.G. Tzafestas (1986) Multidimensional
Systems: Techniques and Applications (NY:
Marcel Dekker).
[15]
S.G.Tzafestas, N. Theodorou & A.
Kanellakis (1988) Stability of Multidimensional
Systems:
Overview
and
New
results,
Proceedings of International Symposium on
Circuits and Systems, p. 337-344.
APPENDIX
For conditions in equation (5), equation (4) is
satisfied and this also indicates that,
Ak<1 and Bk<1
Case (iii)
Let, | xk|>1 and | yk|>1
Then, definitely xk2>>1 and yk2>>1
(a.6)
Thus, Ak<1 and Bk<1
Proof for using the inverse of zk
The discrete variable ‘zk’ is represented as,
zk = xk+jyk for k=1 to n
(a.1)
and |zk| > 1.
Taking reciprocal of ‘zk’ to get,
33
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
Case (iv)
Let, | xk|=1 and | yk|=1
Then, xk2+ yk2=2
(a.7)
which implies that, |Ak|=0.5 and |Bk|=0.5
Thus from all the above cases, it is substantiated
that, if the roots of ‘zk’ lies outside the unit circle
⎛ 1
⎝ zk
then its inverse ⎜⎜
⎞
⎟⎟ will have roots within
⎠
unit circle.
34
Caledonian Journal of Engineering
Volume04, Number 12, January- June 2008
REVIEW ARTICLE
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
BEARING FAULTS DETECTION USING VIBRATION ANALYSIS
AND INFRARED THERMOGRPHY TECHNIQUES
Ali Mohammed Al-Khanbashi1; Khalid F. Al-Raheem2
Caledonian College of Engineering, Sultanate of Oman
1 Undergraduate Mechatronics program student, CCE, alkhanbashi2004@hotmail.com
2 Senior lecturer, Mechanical and Industrial Engineering, CCE
ABSTRACT
Bearings and their vibration play an important role in the performance of all mechanical systems. In many
cases, the accuracy of the instruments and devices used to monitor and control the mechanical system is
highly dependent on the dynamic performance of the bearings. In addition, many problems arising in
machines and motors operation are linked to bearing faults. Thus, fault detection of a system is inseparably
related to the diagnosis of the bearing assembly. Therefore, in this project the spherical roller bearing has
been selected to study and diagnose its defects and faults using two types of condition based maintenance
techniques, vibration analysis and infrared thermography. Then, these two techniques have been compared
to find out which is the best one to monitor the bearing faults.
KEY WORDS: Vibration analysis, Bearing fault detection, Infrared Thermography, and Short Time
Fourier Transform (STFT)
An international paper for (Atul Andhare and
Dhanesh Manik, 2007) presented results of
experiments performed towards diagnosis of
defects in tapered roller bearings using vibration
monitoring. The usage of time-domain expressed
the roles of vibration parameters such as RMS
level, kurtosis, skewness and peak to valley.
They extracted results for different tapered roller
bearings were as the following: the RMS levels
were showing in case of bearings with roller
defects, the axial vibration levels were found to
be higher than corresponding radial vibration.
The final result showed that the overall vibration
RMS level is a better indicator of bearing defect
detection than the peak value, particularly for
outer race defects.
1. INTRODUCTION
Maintenance includes all operations such as
monitoring, inspections, adjustments repairs and
/or doing whatever is necessary to keep a
machine, facility, a piece of equipment or
transportation vehicle in proper working order.
Maintenance aims to minimize the downtime and
downtime costs in order to achieve the maximum
use of resources without any interruption to the
production schedule. There are several types of
maintenance some of them condition based
maintenance.
Condition Based Maintenance (CBM) is an
automatic process that determines when a fault
has occurred (or is going to occur) in a system,
and subsequently diagnoses the cause of the
fault.
Choi, H. and Williams, 1989 has shown the
time-domain for analyzing the vibration is more
effective to extract the bearing fault feature. In
this paper, Time-domain using the vibration
parameters of RMS and kurtosis. With the
additionally obtained the histogram is the used
technique. Consequently, the purpose is to
diagnose whether the bearing is faulty or healthy
and that will be figured out by studying the
effectiveness of RMS and kurtosis on the
In this project the vibration analysis and infrared
thermography techniques have been used to
detect the spherical roller bearing faults located
in clinker cooler fan used by Oman Cement
Company. The vibration signals have been
analyzed using STFT as the analyzing tool in
Matlab Software.
35
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
extracted signal. The fault detection passes by
some steps, beginning with getting the fault
signal in time domain and ending with finding
values of RMS and kurtosis using the equations
and that can be done via MATLAB.
PC for STFT analysis using a MATLAB code.
The characteristic frequencies of the bearing
have been calculated using the bearing
characteristic frequencies equations (See the
Appendix). The BCF for the tested bearing are:
9.12, 11.8, 7.45 and 0.434 times the shaft
rotational speed in (Hz), for outer fault, inner
fault, rolling element and cage fault respectively.
For the applied rotational frequency of 1480 rpm
(i.e. 24.66 Hz), the calculated fault frequencies
are 224.8 Hz, 293.06 Hz, 183.82 Hz and 10.7 Hz
for outer, inner, rolling element and cage fault
respectively.
The approach is applicable to diagnosing
machine faults under complicated conditions
such as low signal-to-noise ratio (SNR) and
varying speeds. Although in this paper timefrequency analysis is carried out based on the
STFT, it is believed that the proposed rationale
will still hold when other sophisticated timefrequency analysis techniques, such as WignerVille distribution, Wigner higher order
distribution, or continuous wavelet transform are
used ( L. Zhu 2007) [2].
The bearing thermal images have been collected
and recorded using infrared camera IR50 for
healthy and faulty bearings in two directions:
horizontal and vertical. The distance between the
infrared camera and bearing location is 0.5
meters.
The thermal imaging technique is an efficient
tool for locating and analysing the subsurface
defects in the GRP pipe. The testing results show
that infrared thermography test is a reliable nondestructive method for detecting any cracks
present in the GRP pipe (A.Alnoobi, 2006).
The defect of spherical roller bearing because of
the freedom of motion in three dimensions,
analysis of the spherical roller bearing requires a
total of 18 displacement and velocity coefficients
(Craighead, 1992).
Figure.1: Experimental Setup
The purposes of this project are to diagnose the
bearings faults using vibration analysis and
infrared thermography techniques, and compare
the data obtained to know the proper technique
to be used in fault detection.
3. VIBRATION AND THERMAL
IMAGES ANALYSIS RESULT
The vibration results in form of STFT map for
both healthy and faulty bearings are shown in
Figure 2. The colour bar shows the value of
vibration magnitude ranging from the maximum
red color to the minimum blue colour. Red
colour illustrates the low vibration magnitude
and blue colour illustrates the high vibration
magnitude.
2. EXPERIMENTAL SETUP
The experimental setup in this project is shown
in Figure 1. The clinker cooler fan supported by
two spherical roller bearings with serial number
of 22216E, pitch diameter of 110 mm, roller
diameter of 14.5 mm and contact angle of zero.
An accelerometer type CMSS2200 with magnet
base attached to the bearing housing and
connected with vibration analyzer type
MICROLOG CMVA65 is used to measure and
record the time domain vibration signal in three
directions (vertical, horizontal and axial), using
different bearing conditions (healthy and faulty).
The recorded signals have been transmitted to
The range of vibration magnitude for STFT of
healthy bearing is 65 to 85 mm.sec-2, but in case
of faulty bearing the vibration magnitude range
is 100 to 120 mm.sec-2. The vibration magnitude
for STFT map in terms of faulty bearing is more
compared with healthy bearing as range of
magnitude. By the examining of STFT maps the
bearing fault can be detected.
36
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
The thermal images for healthy bearing are
shown in Figure 3 (a, b) which show that the
temperature of the bearing in both directions is
32о C. The thermal images for faulty bearing are
shown in Figure 3 (c, d) which show that the
temperature of the bearing has been increased to
47.8о C at vertical direction and 46.6 о C at
horizontal direction.
The thermal images have been captured for
healthy bearing and faulty bearing using infrared
camera in two directions (vertical and
horizontal). The difference in temperature for
each bearing depends on the distance between
infrared camera and bearing location.
Vertical direction (healthy bearing)
Vertical direction (faulty bearing)
1
0.9
20
0.8
0
0.9
0.7
-20
0.8
0.6
-40
0.5
-60
0.4
-80
0.3
-100
20
0
0.7
-20
Frequency
Frequency
1
0.6
-40
0.5
0.4
-60
0.3
0.2
-80
-120
0.2
0.1
0
-100
-140
0
0.5
1.0
1.5
Time
2.0
2.5
0.1
3
0
-120
0
0.5
1.0
Vertical Direction
1
20
0.8
0
0.7
-20
0.6
0.9
-20
-60
-60
0.3
-80
-100
0.2
-120
0.1
1.5
Time
2.0
2.5
-100
-120
0
-140
1.0
-40
0.5
0.4
0.3
0.1
0.6
-80
0.4
0.2
0
0.7
-40
0.5
20
0.8
Frequency
Frequency
0.9
0.5
0
0.5
1.0
1.5
Time
3
Horizontal Direction
2.0
2.5
Horizontal Direction
Axial direction (faulty bearing)
Axial direction (healthy bearing)
1
1
0.9
20
0.9
20
0.8
0
0.8
0
0.7
-20
0.6
-40
0.5
-60
0.4
0.7
Frequency
Frequency
2.5
Horizontal direction (faulty bearing)
Horizontal direction (healthy bearing)
0
2.0
Vertical Direction
1
0
1.5
Time
-80
0.3
-100
0.2
-20
0.6
-40
0.5
-60
0.4
0.3
-80
0.2
-100
-120
0.1
-140
0
-120
0.1
0
0
0.5
1.0
1.5
Time
2.0
2.5
3.0
0
0.5
1.0
1.5
Time
2.0
2.5
Axial Direction
Axial Direction
Figure.2: STFT maps for bearing vibration signals in different directions, Column (a), for healthy bearing,
column (b), for Faulty Bearing.
37
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
*>32.0°C
32.0
32.0
30.0
28.0
26.0
*<24.0°C
(b) Horizontal Direction
(a) Vertical Direction
*>46.6°C
*>47.9°C
45.0
45.0
40.0
40.0
47.8
46.6
35.0
35.0
30.0
*<30.7°C
*<28.9°C
(d) Horizontal Direction
(c) Vertical Direction
Figure.3: bearing thermal images in vertical and horizontal directions, (a), (b) for healthy bearing, and
(c), (d) for faulty bearing.
4. CONCLUSION
Based on the obtained results, both the
techniques can be used for bearing condition
monitoring. By comparing the vibration analysis
with thermal image techniques results for
bearing fault detection the following points can
be concluded:
•
The initial cost for the infrared camera is
more than the vibration analysis equipments.
•
The application of vibration analysis
technique is more appropriate for
mechanical fault detection than the thermal
distribution detected by the thermal camera,
because the mechanical vibration movement
is easier to detect using vibration analysis.
•
The information extracted regarding bearing
condition monitoring can be more effective
for processed image (two dimensions data)
than the vibration analysis (one dimension)
if a proper image processing technique has
been used.
•
The analysis of one dimensional data as in
the vibration signal is easier and more
flexible when compared to the analysis of
the two dimensional data as in the thermal
images.
5. ACKNOWLEDGEMENT
This is an undergraduate project conducted in
collaboration with the Caledonian College of
Engineering and Oman Cement Company, under
the supervision of Mr. Khalid Fathi, Senior
Lecturer at CCE.
38
Caledonian Journal of Engineering
Volume04, Number 01, January - June 2008
REFERENCES
−Outer Race Defect Frequency =
n ⎛ BD
⎞
fr⎜1− cosβ ⎟ (Hz)
2 ⎝ PD
⎠
[1] A.Alnoobi. (2006), Non-destructive testing
and evaluation of GRP pipe using thermal
imaging technique, undergraduate project in
Mechanical & Industrial Engineering, CCE
Oman.
n ⎛ BD
⎞
−Inner Race Dfect Frequeny = fr⎜1+ cosβ ⎟ (Hz)
2 ⎝ PD
⎠
PD ⎡⎢ ⎛ BD
⎞⎤
− Rolling Element Defect Frequency =
fr ⎢1− ⎜ cosβ ⎟ ⎥⎥ (Hz)
PD
BD ⎣⎢ ⎝
⎠ ⎦⎥
[2] Atul Andhare and Dhanesh Manik. (2007)
Diagnosis of localized defects in tapered roller.
Where PD = Pitch Diameter (mm).
BD = Boll or Roller diameter (mm).
Fr = rotating speed of the shaft (Hz).
n = number of balls or rollers.
β = contact angle (degree).
2
−Cage Defect Frequency =
[3] Choi, H. and Williams, W. J. (1989).
Improved Time-Frequency Representation of
Multi-component
Signals Using Exponential
Kernels, IEEE Trans in Acoustics, Speech and
Signal Processing, 37(6), p.862-871.
[4] Craighead I.A. (1992), An analysis of the
steady-state and dynamic characteristics of a
spherical roller journal bearing with axial
loading, Institute of Mechanical Engineers,
Proceeding of International Conference on
vibration in rotating machinery, University of
Bath.
[5] John S. Mitchell (1981) Machinery analysis
and monitoring, 2nd Ed. (Tulsa-Oklahoma: Penn
Well Publishing Company,).
[6] L.Zhu, H. Ding and X. Zhu. (2007)
Synchronous averaging of time-frequency
distribution with application to machine
condition monitoring Journal of Vibration and
Acoustics, 129, p.441-447
[7] R. Barron. (1996) Engineering condition
monitoring, 1st Ed. (New York: Addison Wesley
Longman Inc)
[8] Xavier P.V. & Patric O. Moore (2001)
Nondestructive testing handbook Vol.3 Infrared
&thermal testing, 3rd Ed. (American Society for
Nondestructive Testing).
APPENDIX
Bearing Characteristic Frequencies equations:
39
fr ⎛ BD
⎞
⎜1− cosβ ⎟(Hz)
2 ⎝ PD
⎠
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analysis
Caledonian Journal of Engineering
Published by Caledonian College of Engineering, CPO Seeb 111, OMAN
Volume04, Number 01, January-June 2008
Papers
Virtual Cells for Manufacturing Systems Under Turbulent Environment – A Review of
Thrust Areas
R.V.Murali…………………………………………………………………………………………...1
Removal of Copper Ions from Effluents Using Coconut Shell Coke in a Fixed Bed
Adsorber
S Feroz and Shah Jahan…………………………………………………………………………...7
Coast down Factor to Investigate The Tribological Behaviour of Lubricants in Journal
Bearing.
R. Edwin Browne, Dr. K. P. Ramachandran, Dr. A.K.M. De Silva, Prof. D.K.
Harrison……..……………………………………………………………………………….…….15
Probalistic Analysis of a System with Two Types of Repairman and Patience Time
Wherein the Initial Repair is undertaken by the Ordinary Repairman
Vandna Bhagat………………….……………………….…….………..….………………..……21
Stability Analysis Of Multi Dimensional Discrete Polynomial Employing Equivalent
One-Dimensional Polynomial
Sivanandam S.N.and Rajan S……………………………………………………………...…….27
Bearing Faults Detection Using Vibration Analysis and Infrared Thermogrphy
Techniques
Ali Mohammed Al-Khanbashi; Khalid F. Al-Raheem .…...........................................……35