Mining equipment and systems : theory and practice of exploitation and reliability

285 Pages·2010·12.206 MB·xiii, 282 p. : ill. ; 26 cm\285

by  Jacek M Czaplicki

MINING EQUIPMENT AND SYSTEMS
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Mining Equipment and Systems
Theory and Practice of Exploitation
and Reliability
Jacek M. Czaplicki
Mining Mechanization Institute, Silesian University of Technology,
Gliwice, Poland

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Library of Congress Cataloging-in-Publication Data
Czaplicki, Jacek M.
M ining equipment and systems : theory and practice of exploitation and reliability /
Jacek M. Czaplicki.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-415-87731-2 (hardcover : alk. paper) -- ISBN 978-0-203-85280-4
(e-book) 1. Mining engineering. 2. Mining machinery. I. Title.
TN146.C93 2010
622.028’4--dc22
2009044089
ISBN: 978-0-415-87731-2 (Hbk)
ISBN: 978-0-203-85280-4 (Ebook)
© 2010 by Taylor and Francis Group, LLC
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Contents
Preface and acknowledgements vii
About the author ix
List of major notations xi
1. Introduction: terotechnology and the theory of exploitation 1
2. Exploitation theory 7
2.1. Fundamentals 7
2.2. Exploitation theory in mining—preliminaries 10
3. Statistical diagnostics 13
3.1. Randomness of a sample 15
3.2. Outliers analysis 17
3.3. Stationarity testing of sequences 23
3.4. Stationarity testing of variance in sequences 27
3.5. Cyclic component tracing 31
3.6. Autocorrelation analysis 39
3.7. Homogeneity of data 42
3.8. Mutual independence of random variables 45
3.9. Mutual dependence of random variables 47
4. Exploitation processes—case studies 55
4.1. An exploitation process of an underground monorail suspended loco 56
4.2. An exploitation process of a truck in a shovel-truck system 63
4.3. An exploitation process of a power shovel 69
4.4. Exploitation processes of a continuous miner and a shuttle car 71
5. Reliability models applied for a single piece of equipment 79
5.1. Belt conveyors 79
5.2. Hoisting installations 88
5.3. Hoist head ropes 92
6. Systems of machines operating in parallel 119
7. Systems of machines in continuous operation 125
7.1. Introduction 125
7.2. Principles of reduction of series systems 129
7.3. Case studies 131
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vi Contents
7.4. System calculations 147
7.5. Quick approximation of system output 148
7.6. Semi-Markov systems 149
8. Cyclic systems—selected problems 167
8.1. A general model of queue theory 167
8.2. Mathematical classification of cyclic systems 170
8.3. The repairman problem 171
8.4. The Palm model 172
8.5. A system without losses 175
8.6. Erlangian systems 177
8.7. The Takács model 183
8.8. The Maryanovitch model 188
8.9. The randomised Maryanovitch model 192
8.10. The G/G/k/r model for heavy traffic situation 199
9. Combined systems 209
9.1. A shovel-truck system and in-pit crushing 209
9.2. A shovel-truck system and an inclined hoist of the Truck Lift type 224
9.3. A stream of extracted rock—shaft bin—hoist 242
10. Special topic: homogeneity of a shovel-truck system 263
References 271
Subject index 281

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Preface and acknowledgements
In Poland the mining industry is several centuries old. It boomed in the nineteenth and twentieth
centuries and still has good prospects for the future. As a result, mining engineers in this country
have undertaken a lot of good research. Unfortunately this work is sometimes unknown in the
world literature. For this reason I feel that it is useful to publish the results of some of this research
in English.
It is almost fifty years since the first papers on the application of reliability theory to mining
problems were published in the United States. Developing rapidly in the late 1950s and 1960s,
reliability theory quickly found a wide application in mining engineering. However, in a relatively
short time, Central European researchers engaged in reliability investigations found that very
often these examinations should encompass a wider scope of considerations, wider than the area
connected strictly with reliability problems. In such a way the theory of exploitation came into
being.
My experience in this area began in 1973 when I worked on my M.Sc. thesis on the reliability of
the head ropes of mine hoists. At the beginning of my scientific career I was engaged exclusively
with reliability problems. Time passed and my interests enlarged beyond the analysis of the reli-
ability of mine machines and their systems and found myself in the area of the theory of exploi-
tation. After several years of experience in this field I feel that it is time to share the knowledge
gained in a wider forum.
This book presents my view on reliability and exploitation problems in mining—both practical
and theoretical. The composition of this book is somewhat different from others in this regard.
Most texts are usually ordered according to the theoretical scheme exclusively. In this book theo-
retical problems are formulated in connection with practical problems and appropriate literature
is cited so that readers may increase their knowledge about a given aspect. Furthermore, the data
presented here is gathered from several mines located in different countries. Some readers may
treat this book as a presented set of mathematical tools useful in the analysis of problems of the
exploitation and reliability of mining equipment and its systems.
Incidentally, where literature from the field of reliability in mining is concerned, it appears that
there is a lack of an internationally recognised textbook in this field. I hope and is intended to help
to fill this gap.
In my two books written in English, I presented an outline of the theory of modelling, analysis

and calculation of mine equipment systems apart from methods for the calculation of rail transport
systems or mine readiness systems.
This book is dedicated—first of all—to students of mining faculties and schools of mining with
a specialisation in mine mechanisation all over the world. They have always been close to my heart,
no matter in which part of the world I have lectured. Some chapters of the book may be interesting
for those who specialise in earthmoving enterprises. Students of mathematics searching for practi-
cal applications of models of mathematical statistics, reliability theory, renewal theory and queue
theory might find some chapters interesting as well. I presume that mining engineers will also
find some parts helpful. Additionally, I hope that my dear academic colleagues working at mining
universities will also find this book interesting, and useful in their educational work.
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viii Preface and acknowledgements
I would like to express my very warm thanks to Ms Michele Simmons for language editing and
Janjaap Blom, Senior Publisher CRC Press/Balkema - Taylor and Francis Group and his open and
extremely professional team for their reliable and efficient cooperation.
Jacek M. Czaplicki
Mining Mechanization Institute
Silesian University of Technology, Gliwice, Poland

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About the author
Jacek M. Czaplicki has been an academic lecturer for more than thirty
years and is continuously associated with his home University. He did
however leave his school for a couple of years’ lecturing in African
universities.
He worked for three years at the Kwara State College of Technol-
ogy, Ilorin, Nigeria on a UNESCO project. A few years later he was
appointed to Zambia Consolidated Copper Mines Ltd and worked as a
lecturer at the School of Mines of the University of Zambia as part of
a World Bank project.
Jacek Czaplicki received a Master of Science in Mine Mechaniza-
tion from the Silesian University of Technology, Gliwice, Poland. He
also obtained a Doctorate degree in Technical Sciences. Later he sub-
mitted a thesis and passed all requirements, obtaining a D.Sc. degree in Mining and Geological
Engineering with a specialization in Mine Machinery at the same home University. Actually, he is
a Professor of Mining Engineering.
He has published more than a hundred and thirty papers and about ten books in Poland and
abroad. His specialization comprises mine transport, reliability and computation of mine machin-
ery and their systems and reliability of hoist head ropes. He is an internationally recognized spe-
cialist in mine mechanization.

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List of major notations
A – steady-state availability
B – accessibility coefficient
E – expected value, mathematical hope
G – general case, general distribution
H, H – statistical hypotheses
0 1
H(t) – renewal function
k – number of repair stands
L – rope length, the expected daily mass of rock hoisted out from the production level
L – number of theoretically possible states
t
m – number of trucks directed to accomplish transportation task
M – (Markov), exponential distribution
n – number of shovels in system
N – sample size
P, p – probability
P(p) – probability that d power shovels are in work state
kd
P(p) – probability that b trucks are in work state
wb
q – number of winds executed by hoist/rope
r – reserve size, number of spare trucks
r(a) – autocorrelation coefficient
r(S) – Spearman rank correlation coefficient
r (n) – critical value of Spearman rank correlation coefficient
α
R – empirical Pearson correlation coefficient, estimator
R (ϕX)Y – reliability (survival) function of rope
ϑ
S – empirical standard deviation
S – area of rope cross-section, metallic area of rope
n
t – time
t (N ) – quintile of order α of Student’s t-distribution with N degrees of freedom
α
T – mean time of truck work cycle
c
T(h) – mean time of hoist work cycle
c
T – hoist disposal time per day
d
T – mean time of truck travel (haulage + dump + return)
t
T, T – mean time: repair, work
n p
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xii List of major notations
u – residual
u – quintile of order α of the standardised normal distribution
α
v, V – rank
y – shaft bin volume
Z – random variable, total daily mass delivered to shaft in given underground level
Z' – mean adjusted loading time by shovel
α – level of significance
Δ – time loss function for truck
θ – empirical total number of cracks of wires of hoist head rope
Θ – theoretical total number of cracks of wires of hoist head rope
κ – repair rate (fault coefficient)
λ – intensity of object failures, parameter of exponential density function
λ(t) – hazard function
μ – intensity of object repair
ρ – correlation coefficient in population, flow intensity rate in service system
ρ(P) – the Pearson correlation coefficient
X, Y
σ – standard deviation of random variable
τ – proportional coefficient indicating how many times is longer the mean time of truck
loading by front-end loader compared to the adjusted mean loading time by shovel
ϑ – random variable, total number of cracks of wires in a moment of rope withdrawal
ϕ (X ) – the standardized density function of random variable N(0, 1)
N
Φ (X ) – the standardized distribution function of random variable N(0, 1)
N
B(a, b) – beta distribution with parameters a, b
F(2N, 2N) – F-Snedecor probability distribution with (2N, 2N) degrees of freedom
Ga(k, ς ) – gamma distribution with parameters k, ς
N(m, σ ) – normal distribution with parameters m, σ
t(N) – Student’s distribution with N degrees of freedom
χ2(N) – chi-square distribution with N degrees of freedom
– decisions made by system controller (truck dispatcher)
– exploitation repertoire
– set of power shovels
– method of utilization
– set of natural numbers
( ) – exploitation process of shovel-truck system
– maintenance system
– sufficient maintenance system
1
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