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224.Журнал Сибирского федерального университета. Сер. Техника и технологии №6 2013

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Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Журнал Сибирского федерального университета
2013
Journal of Siberian Federal University
6 (6)
Техника и технологии
Engineering & Technologies
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CONTENTS / СОДЕРЖАНИЕ
Ebrahim Ghandehari,
Shahrokh Shojaeian and Javad Pourabadeh
An Improved Multi-Objective Bpso-Based Method for Radial
Distribution Networks Reconfiguration
? 617 ?
М.Ю. Чернецкий, А.А. Дектерев, А.П.Бурдуков
p=???2?%? ,?????%"=?,? -=*????%?% ?%!??, ???*%?,?C?!??%?%
?,??%??????%??%?% ?/!?
? 625 ?
Editorial Advisory Board
Chairman:
Eugene A. Vaganov
Members:
Josef J. Gitelzon
Vasily F. Shabanov
Andrey G. Degermendzhy
Valery L. Mironov
Gennady L. Pashkov
Vladimir V. Shaidurov
Vladimir V. Zuev
Editorial Board:
Editor-in-Chief:
Mikhail I. Gladyshev
Founding Editor:
Vladimir I. Kolmakov
Managing Editor:
Olga F. Alexandrova
Executive Editor for Engineering &
Technologies:
Vladimir A. Kulagin
Vladimir A. Kodnyanko
Numeric-Analytical Method for Determining the Communication
Equations of Laplace?s Transformants of the Universal Radial
Unit of Externally-Pressurized Gas Bearings
? 637 ?
Sergey S. Dobrosmyslov,
Vladimir I. Kirko, Gennady E. Nagibin,
Oksana A. Resinkina and Zahar I. Popov
Characteristic Physical$Mechanical and High$Temperature
Electric Properties Semicinductor Ceramic Based SnO2 with
Addition MnO2 and CuO
? 650 ?
Т.Н. Патрушева,
С.А. Подорожняк, Г.Н. Шелованова
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?%K!%2?%?2?
"
C%?3C!%"%??,*%"%L ?!???
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?????????? ? ?? ??? ???. 660041 ??????????, ??. ?????????, 82a.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Editorial board for Engineering & Technologies:
Vladimir Kulagin Series Editor, Siberian Federal
University, Russia
Yury Alashkevich Siberian State Technological
University, Russia
Sereeter Batmцnkh Institute of Heat Engineering
and Industrial Ecology Mongolian Academy of
Sciences, Mongolia
Yuri Biba Dresser-Rand Company, USA
Carsten Drebenstedt Technische University
Bergakademie Freiberg, Germany
Yury Galerkin Saint Petersburg State Polytechnic
University, Russia
Gennady Gritsko Institute of Petroleum Geology and
Geophysics Russian Academy of Sciences, Siberian
Branch, Russia
Georg Guggenberger Institute of Soil Science Leibniz
University Hannover, Germany
Lev Endzhievsky Siberian Federal University, Russia
Feng-Chen Li School of Energy Science and
Engineering Harbin Institute of Technology, China
Vladimir Makarov Siberian Federal University, Russia
Aleksandr Mineev Siberian Federal University, Russia
Vladimir Moskvichev Special Designing and
Technological Bureau ?Nauka? Krasnoyarsk
Scientific Center of the Russian Academy of
Sciences, Siberian Branch, Russia
Bernard Nacke Institute of Electrotechnology Leibniz
University of Hannover, Germany
Oleksandr Nemchin CEO of the State Research
Institute of Innovative Technologies in Power
Energy and Energy Efficiency of the Fuel and
Energy Ministry of Ukraine, Ukraine
Valeriy Nikulin Kamsk Institute of Humanitarian and
Engineering Technologies, Russia
Oleg Ostrovski University of New South Wales,
Australia
Harald Oye Norwegian University of Science and
Technology, Norway
Vasili Panteleev Siberian Federal University, Russia
Petr Polyakov Siberian Federal University, Russia
Victor Timofeev Siberian Federal University, Russia
Ibragim Khisameev Kazan State Technological
University, Russia
Anatoly Shvidenko International Institute for Applied
Systems Analysis, Austria
Galina Chiganova ? Siberian Federal University,
Russia
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Journal of Siberian Federal University. Engineering & Technologies 6 (2013 6) 617-624
~~~
??? 621.316.1
An Improved Multi-Objective Bpso-Based Method
for Radial Distribution Networks Reconfiguration
Ebrahim Ghandehari,
Shahrokh Shojaeian* and Javad Pourabadeh
Islamic Azad University, Khomeinishahr branch
P.O. Box 84175-119, Isfahan, Iran
Received 15.01.2013, received in revised form 28.04.2013, accepted 09.09.2013
The present paper will introduce an improved BPSO algorithm for radial distribution networks
reconfiguration. In this regard PSO algorithm has extensively been used in many of the previous
literatures; however, here a new method will be introduced in order to update swarm position which is
not only simple and fast but also has high accuracy. The objective function has four weighted components
representing load balancing, total losses of network, voltage deviation and system reliability. The
test network is a standard distribution system with 3 feeder and 16 switches. Accuracy and speed of
proposed method are compared with three other well-known algorithms to ensure its efficiency.
Keywords: BPSO algorithm, Reconfiguration, Restructuring, Distribution network.
Introduction
Transmission of electrical energy is the most important task of distribution systems and due to
the yearly growing of consumers? loads; these networks will become larger and more complex. Most
of distribution networks all over the world are radial and every consumer is fed just from one side.
Since these distribution networks are complex and also many plants have been made, it can cause
different states for the consumers? feeding. But there are a lot of switches in distribution networks
which can change the structure of the network. These switches can be divided into two categories
including sectionalizing (normally close) switches and tie (normally open) switches. Change in the
structure of network by altering status of its switches which called reconfiguration or restructuring,
not only determine the type of consumers feeding but also has more applications. Some of these
applications include load balancing, minimizing total losses of system and improving voltage deviation
and reliability of network. Utterly reconfiguration is useful when some faults occur in the network.
This activity minimizes de-energized loads after faults. So the existing switches are used for both
management and maintenance, but the existing paper focuses only on system management. Some other
applications of network reconfiguration include increasing capacity of network, reconfiguration with
fewest switches, system development, finding optimum place for distributed generation (DG), etc. that
are not the subject of the study here. Since there are a lot of switches in the network, reconfiguration
issue is a complex optimization problem which has a lot of limitations. Some of these limitations are
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: Shojaeian@iaukhsh.ac.ir
# 617 #
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Ebrahim Ghandehari, Shahrokh Shojaeian? An Improved Multi-Objective Bpso-Based Method for Radial Distribution?
radial structure of network and consumers voltage deviation. Finding optimal structure of network
on the one hand and its applicability on the other hand is very important, in a way that if practical
limitations aren?t neglected, the optimal answer won?t be acceptable [1?9].
Recently, reconfiguration has been carried out by practical experience of operators, but
today operation of distribution networks is an engineering challenge, because optimal solution is
always considered and due to mass and complexity of these problems, the only possible way is to
use specialized software. The main goal of optimization is minimization of costs and improving
services. There are a lot of methods for reconfiguration which has advantages and disadvantages.
Already many literatures studied reconfiguration problem and a lot of methods has been applied
on it. The results of these studies provide acceptable solutions. Reconfiguration problem was fi rst
considered in [1] in order to minimize total losses by a heuristic and hybrid optimization algorithms.
In [2] reconfiguration was done by branches changing. This heuristic method closes one switch and
opens the other switch, then calculates the network losses. Changing the status of the switches can
be done by a lot of algorithms, but since power system problems are combinatorial optimization,
they are difficult to solve by traditional linear or nonlinear methods [3]. Authors of recent literatures
use optimization methods such as genetic algorithm (GA) [4, 5], fuzzy systems [6, 7], bee colony
(BC) [8, 9], simulated annealing (SA) [10,11], Tabu searches [12,13], heuristic algorithms (that are
not in the scope of this paper) [14, 15]etc. Recently PSO algorithm is considered in [16, 17], because
it has some advantages ,namely, simple structure, good speed and high accuracy. This paper uses
this algorithm, too.
One more important issue in the reconfiguration problem is objective function. The most
important objective in the recent literatures is loss minimization. But there are more objectives which
can be considered, too, such as reliability [17], voltage deviation [18], load balancing [19], transient
behaviors of the network [20] and smart grid interactions [21] and so on. Usually one or two objectives
are optimized simultaneously but some times more than two objectives are considered as optimization
[22]. This paper optimizes four objectives including load balancing, total losses of network, voltage
deviation and system reliability.
Bpso algorithm
Recently, PSO algorithm has previously been used at many literatures for reconfiguration problem
and has a known structure. This algorithm is based on the social behavior of birds (particles) flocking
looking for food. Answers of considered problem can be represented as a particle. At first the particles
initialize randomly. Then every particle will change its position based on the best searching experience
of individual (Pbest) and the best searching experience of population (Gbest). When Pbest and Gbest are
obtained, every particle updates its position by:
???
?????
? ?????? ? ?? ? ??????? ? ? ????? ???? ????? ? ? ?? ? ????????
(1)
? ?? ??????? ????? ?
???
???
?????
? ????? ? ?????
(2)
Where vid is the original velocity of the ith particle, vidnew is the new velocity of the ith particle, w is
the inertia weight, c1 and c2 are the acceleration constants, xid is the previous position of the ith particle,
# 618 #
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Ebrahim Ghandehari, Shahrokh Shojaeian? An Improved Multi-Objective Bpso-Based Method for Radial Distribution?
Fig. 1. Updating a particle position in PSO
xidnew is the new position of the ith particle and rand( ) is a random number ranging between 0 and 1.
Fig. 1 explains how particle positions is updated.
Reconfiguration in the above mentioned form is a binary problem. For this reason, binary version of
PSO (BPSO) should be used. In BPSO algorithm a sigmoid function (3) is used for position updating.
???
??
???????
?
(3)
???
? ? ? ????
Position update at PSO is done in two stages. At first particle velocity is updated by (1). Then with
(2) sigmoid function is calculated and finally new position is obtained by (4).
???
???
???
?? ??? ??????
???????????? ? ? ???????
? ? ?? ???????
??
(4)
New calculated particles positions may be inappropriate. For example, due to loss of radial
structure of the network, some loads will be de energized. So feasibility of generated codes should
be verified. Already some methods were introduced to check these codes everyone whereof has
advantages and disadvantages. This paper proposed a new simple and effective way to update
particles positions.
The fi rst step to solve reconfiguration problem is representation of network structure with
a comprehensive code for computer. To show the status of N switches in a distribution feeder a
string of N bit can be used. For each switch, ?1? shows considered switch status is closed and ?0?
shows it is open. For example, for the feeder shown in Fig. 2 the above mentioned code is (1 1 1
0 1 1 1 1) [23].
Then the problem is to find optimum code for the network which results in minimum value of the
objective function, for a distribution network with N switches there are 2N possible codes which all of
them are not necessarily appropriate. Eliminating inappropriate codes solution space will be reduced
significantly.
The main idea of this paper is a new method for particles position updating. At the first step, an
appropriate code is considered and updated normally. Then the feasibility code is checked. For the
appropriate codes the algorithm will be continued. Inappropriate codes will be updated again by (4).
# 619 #
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Ebrahim Ghandehari, Shahrokh Shojaeian? An Improved Multi-Objective Bpso-Based Method for Radial Distribution?
Fig. 2. Simple structure of a network
Fig. 3. The3-feeder distribution network used for simulations
This procedure should be continued until the updated code become one of the possible codes. This
method has not only a good speed, but also perfect accuracy. It is clear that generated codes certainly
are one of the appropriate structures of network. The distinction of possible structures is an easy
method too. There are three methods of making distinct codes that will be explained at following
paragraphs. All methods are implemented by logical instructions.
- The First method: Generate a random binary code and restructure the network by it. If all buses
are fed just from one side, this code is appropriate; otherwise, it isn?t. The speed of this method is
low.
- The Second method: Fig. 3 explains this method. Here the network has three feeders and it is
obvious that there must not be any closed loop between them, and all buses must be fed too. So all
connection ways between feeders should be found and every relative code must have just one 0, else
that code is inappropriate. The other important limitation is that switches of loads or feeders should be
1. To explain this method, see Fig. 3. Connection ways between feeders include down branch (codes 13,
14, 26, 25 and 23), left branch (codes 12, 15, 19 and 18) and right branch (codes 17, 21 and 24). In every
above three codes there should be just one 0 to meet network structure feasibility. All appropriate
states of network are equal to multiplication of the number of all collected codes. For example in Fig. 2
the number of appropriate codes is 60, this number is gotten from the multiplication of five down codes
(13, 14, 26, 25 and 23) by four left codes (12, 15, 19 and 18) by three right codes (17, 21 and 24). This
method is harder but very faster and reliable.
- The Third method: Desired codes can be generated manually or by Microsoft Office Excel and
saved in a database. This way is not automatic but is very fast.
Most important advantage of this method is its simple structure, because other similar methods
are very difficult and presumably low speed (due to complicated calculations) [23, 24].
# 620 #
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Ebrahim Ghandehari, Shahrokh Shojaeian? An Improved Multi-Objective Bpso-Based Method for Radial Distribution?
Reconfiguration process
Reconfiguration process needs a fast and accurate load flow method to evaluate objective function.
In this paper the well-known forward/backward load flow methods is used [2]. Then this method has
been rewritten in MATLAB® and become the principal of the work. Then forward/backward load flow
is done to find all bus voltages and power flowing through all sections. Then the value of objective
function is calculated and sent to BPSO algorithm. BPSO algorithm is repeated to meet the desired
convergence.
The objective function
The objective function used in this paper has four weighted components including: load balancing,
total losses of network, voltage deviation and system reliability. It is shown as following:
???????????????????
? ?? ? ?????? ?? ??????????? ???????
(5)
? ?? ?????????????
??? ?????????? ?????
where ?, ?, ? and ? are weighting coefficients which show relative importance of the components.
These coefficients are obtained with historical experiences and strategies of each distribution system
company. In this paper they are chosen 1, 2, 0.0015 and 31respectively. Total losses and cumulative
voltage deviation will be obtained by equations (6) and (7).
? ?????? ????
??? ????
??? ? ???
???
(6)
????
?
?? ????????????????? ????
??? ??? ? ??
????
(7)
where Vi is the voltage magnitude of the ith bus and Pi, Qi, and ri are the active and reactive power and
resistance of the ith section respectively.
In this paper reliability of distribution networks are taken into account by system indices. For
each load center an average failure rate (? in #/year), an average repair time (r in hours), and an average
outage time (U in hours/year) can be calculated [25], where:
(8)
? ? ?? ???
The system reliability indices used in this paper are System Average Interruption Frequency
Index (SAIFI) and System Average Interruption Duration Index (SAIDI). They can be obtained by the
following equations:
?? ??????
? ?? ??
? ??
(9)
?? ??????
? ?? ??
? ??
(10)
Where Ni is the number of customers at ith load point. Reliability is evaluated by equation
(11). Also, considering different weighting factor (?1 and ?2 instead of ?) for SAIFI and SAIDI is
possible.
# 621 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Ebrahim Ghandehari, Shahrokh Shojaeian? An Improved Multi-Objective Bpso-Based Method for Radial Distribution?
(11)
?????????? ???? ?? ?????? ???????
Reliability parameters for considered system are listed in the paper appendix.
Load balancing component will be obtained by the following equation. Ii is total current magnitude
of the ith feeder.
?
??????????
?????? ? ??
???? ? ???? ?
??? ???? ????
(12)
Simulation and results
For a well-known distribution network shown in Fig. 3 which has been used in many previous
researches, the proposed method was applied. Network parameters can be found in [18]. This network
includes 3 main feeders, 13 tie switches and 3 sectionalizing switches. Its nominal power (Sb) is 100MVA.
Fig. 3 shows original condition of the network, at these 15, 21 and 26 state switches are open and other
switches are close. To show the speed and effectiveness of the proposed method, a comparison is made
between this method and three other well-known algorithms. Table 1 shows reconfiguration CPU times
to minimize load balancing, total losses, voltage deviation and reliability of the network by four methods.
All algorithms converge to the same solution. It is clear that running time for the proposed method is
much lower and if the network busses increase, the CPU time difference will be obviously more.
Conclusion
This paper proposed an improved BPSO algorithm for radial distribution networks reconfiguration
which applies a new method to update swarm position. It is not only simple and fast but also has high
Table 1. Simulation results for proposed method and three other algorithms
Algorithm
Solution (open switches)
CPU time
Population
BPSO
17, 19 and 26
1.01
4
ACSA [18]
17, 19 and 26
1.81
5
SA [18]
17, 19 and 26
2.07
500
GA [18]
17, 19 and 26
2.32
5
Fig. 4. Convergence curve of the proposed method
# 622 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Ebrahim Ghandehari, Shahrokh Shojaeian? An Improved Multi-Objective Bpso-Based Method for Radial Distribution?
accuracy. The objective function has a four weighted component including: load balancing, total losses
of network, voltage deviation and system reliability. Test network was a standard network by 3 feeders
and 16 switches. Comparison of the proposed method with three well-known algorithms shows its
better efficiency.
Appendix
Table 2. System indexes of the test network
r
?
Section
r
?
Section
r
?
Section
r
?
Section
4
0.18
15-16
4
0.16
9-12
3
0.16
2-8
2
0.15
1-4
3
0.18
5-11
2
0.15
3-13
4
0.16
8-9
2
0.15
4-5
2
0.14
10-14
3
0.15
13-14
4
0.16
8-10
2
0.15
4-6
4
0.14
7-16
2
0.15
13-15
4
0.16
9-11
3
0.14
6-7
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Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 6 (2013 6) 625-636
~~~
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Received 04.05.2013, received in revised form 02.09.2013, accepted 11.09.2013
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© Siberian Federal University. All rights reserved
Corresponding author E-mail address: dekterev@mail.ru
# 625 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
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[1] ?????????? ? ??????? ??? ???????? ?????? // ????? ? ??????. 2012. ? 4. ?. 28-32.
[2] Sims R.E.H., Mabee W., Saddler J.N., Taylor M. // Bioresource Technology. 2010. V. 101.
P. 1570-1580.
[3] Barz M., Delivand M.K. // Journal of Sustainable Energy & Environment. 2011. Special Issue.
P. 21-27.
[4] Burdukov A.P., Popov V.I., Faleev, V.A. // Thermal Science, 2009. 13(1). P. 127-138.
[5] ???????? ?.?., ????????? ?.?., ???????? ?.?., ????????? ?.?. // ???????????? ???????. 2012. ? 3/1. C. 55-61.
[6] Haider A, Levenspiel O. // Powder Technol. 1989. 58(1). P. 63-70.
[7] ????????? ?.?., ???????? ?.?. // ?????? ??????? ? ??????. 2011. ? 3. C. 37-46.
[8] Cuiping Wang, FengyinWang, QirongYang, Ruiguang Liang // BIOMASS AND BIOENERGY
33(2009) 50-56.
[9] ???????? ?.?., ?????? ?.?., ????????? ?.?. // ????? ?? ?????? ???. 2012. ? 12.
C. 63-71.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ????????? ????????? ???????????? ?????????? ??????? ??????????????????
Numerical Research of Pulverized Combustion
of Micro-Grinded Lignocellulose Raw Materials
Mikhail Yu. Chernetskiya,b,
Alexander A. Dektereva,b and Anatoliy Burdukovb
a
Institute of ThermASophysics SB R
1 ak. Lavrentiev. Novosibirsk, 630090 Russia
b
Siberian Federal University
79 Svobodny, Krasnoyarsk, 660041 Russia
In work the mathematical model is presented and numerical research of burning of micro-grinded
lignocellulose raw materials is executed. This fuel was crushed by means of mill devices with various
degree of power intensity. Verification of mathematical model with use of experimental data on an
autothermal mode of burning of products of processing of vegetable raw materials (straw) on 5 MWt
the stand is executed.
???????? ?????: biofuel combustion, wheat straw, numerical modeling.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 6 (2013 6) 637-649
~~~
??? 621.9: 621.89
Numeric-Analytical Method for Determining
the Communication Equations
of Laplace?s Transformants
of the Universal Radial Unit
of Externally-Pressurized Gas Bearings
Vladimir A. Kodnyanko*
Siberian Federal University
79 Svobodny, Krasnoyrsk, 660041 Russia
Received 03.04.2013, received in revised form 22.08.2013, accepted 30.08.2013
The paper proposes a numeric-analytical method for determining the communication equations
of Laplace?s transformants of dynamic functions of the universal unit of radial externallypressurized gas bearings which movable element makes small radial oscillations in the locality in
its central position. Method and obtained dependences provide links between integro-differential
Laplace?s transformants of the unit such as load capacity and local input and output mass fl ow
rates with transformants of eccentricity and gas lubricant pressure at inlet and outlet of the
unit. It is shown that the local transfer functions of the unit model are rational functions of the
Laplace?s transform variable and all such functions have a common denominator in the form of
a polynomial of this variable. The method allows to calculate the required dynamic criterion of
gas bearings containing this unit with prescribed accuracy. Founded dependences give ready
formulas for calculation dynamic criteria of radial single-row or multi-row ordinary passive or
active externally-pressurized gas bearings in which this unit can be used for description of radial
movement of its movable element.
Keywords: externally-pressurized gas bearing, numeric-analytical method, dynamic functions.
Introduction
In the study of dynamic quality of externally-pressurized gas bearings is used nonstationary
Reynolds? differential equation [1] which describes the dynamic pressure distribution in the thin
gas lubricating gap of loading or throttle unit. Solution of this equation allows to determine the
load capacity of the unit and gas flow rate at its inlet and outlet. The main difficulties in the
calculation of the dynamics of bearings, relate to obtaining solutions of the equation in view of
its nonlinearity.
Within the linear theory, in which integral Laplace transform [2] is applied for research of dynamics
of bearings, the solution of the corresponding linearized differential boundary value problems lies
approximately as the such problems have no analytical quadratures. Known approximate methods
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: kowlad@rambler.ru
# 637 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Vladimir A. Kodnyanko. Numeric-Analytical Method for Determining the Communication Equations?
differ in bulkiness, complexity of the received solution and lack of an assessment of its accuracy
[3,4]. If it is considered that the solution of these problems is only intermediate element, obtaining the
solution of the general integro-differential problem of finding load capacity and gas flow rates deals
with greater difficulties.
Taking into account a tendency of complication of the designs using gas-lubricated units and,
as a result, complication of the corresponding mathematical models, the search of methods for
approximate solutions of noted boundary value problems, which allow to fi nd their decision with
a prescribed accuracy is actual. In this regard numerical methods, for which there is no problem
of analytical quadratures [5], attract attention. The application of these methods allows to receive
the solution of differential problems with an accuracy demanded for practice and possibility of its
assessment.
However the circumstance that the structure of linearized and Laplace?s transformed differential
equation, includes beforehand unknown Laplace?s variable and some Laplace?s transformants for unit
functions, is an obstacle for numerical search of the solution. In this regard numerical and analytical
approach to the solution of the specified problems which will allow to find the solution of the boundary
value problems deserves attention.
Below it is given a method solving this problem with the example of the universal radial gaslubricated unit, making radial movements concerning the central equilibrium position.
Mathematical modeling of unit radial movement
The settlement scheme of the unit is shown in Fig. 1.
The unit consists of the cylindrical plug 1 and shaft 2, making movement at which axes of these
elements keep a parallel arrangement. These elements are separated by a thin gap of compressed gas
under pressure p (z, ?, t); gap thickness h (?, t) = h0 ? e (t) cos (?), where h0 ? gap thickness at a coaxial
arrangement of elements, e ? eccentricity of shaft; z, ? ? longitudinal and circumferential coordinates,
t ? current time.
The boundary value problem for function of pressure, which satisfies to Reynolds?s differential
equation [1], has the form
Fig. 1. Settlement scheme of radial gas-lubricated unit
# 638 #
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Vladimir A. Kodnyanko. Numeric-Analytical Method for Determining the Communication Equations?
? 1 ? ? 3 ?p ? ? ? 3 ?p ?
? ( ph)
,
? 2
?h p
? + ? h p ? = 12 ?
r
?
?
?
?
?
z
?
z
?t
?
?
?
?
?
?? p (0, ? , t ) = p1 (? , t ), p (l , ? , t ) = p2 (? , t ),
?
? p ( z , 0, t ) = p ( z , 2? , t ), ?p ( z , 0, t ) = ?p ( z , 2? , t ),
?
??
??
?
=
p
z
p
z
(
,
?
,
0)
(
),
??
0
(1)
where p1, p 2 ? functions of gas pressure at inlet and outlet of the unit, p 0(z) ? gas pressure at a
coaxial arrangement of elements, r ? the radius of a shaft, l ? unit length, ? ? viscosity of gas
lubricant.
Having taken for scales: pa ? environment pressure for pressures; set from the outside h* ?
thickness of a lubricant gap, r* ? the size and t* ? time scale constants, we will lead a problem (1) to a
dimensionless form
2 2
? 1 ? ? 3 ?P 2 ?
? ( PH )
3 ? P
= 2?
,
? 2
?H
?+ H
2
R
?
?
?
?
?
Z
??
?
?
?
?? P(0, ? ,? ) = P1 (? ,? ), P( L, ? ,? ) = P2 (? ,? ),
?
? P( Z , 0,? ) = p ( Z , 2? ,? ), ?P ( Z , 0,? ) = ?P ( Z , 2? ,? ),
?
??
??
?
?? P( Z , ? , 0) = P0 ( Z ),
(2)
where H (? ,? ) = H 0 ? ? (? ) Cos(? ) ? the dimensionless thickness of a lubricant gap, ? ? shaft eccentricity,
L = l / r* , R = r / r* ? dimensionless length of the unit and shaft radius; Z ,? ? dimensionless longitudinal
coordinate and current dimensionless time; ? =
12 ? r*2
? number of squeezing of a gas film [6].
pa h*2t*
Hereinafter dimensionless sizes are designated by capital letters.
Let?s consider small fluctuations of a shaft concerning its central position. In this case the square
of pressure function can be presented in the form
P 2 ( Z , ? ,? ) = ? ( Z , ? ,? ) = P02 ( Z ) + ?? ( Z ,? )Cos? ,
(3)
where ?? ? a projection function of a deviation from state at a coaxial arrangement of unit elements.
Assuming that eccentricity ? = ?? will be small also, after linearization of a problem (2) and
applications to it Laplace?s transform, linearized problem for Laplace?s transformants can be written
as follows
? d 2 ?? ? ?? s ?
? 2 ? ?1 +
? ?? = ?? sP0 ?? ,
P0 ?
? d X ?
?
??? (0, s ) = ??1 ( s ), ?? ( B, s ) = ?? 2 ( s ),
(4)
where new variable X = Z/R, B = L/R, ? = ? R 2 / H 03 , ? = H 0 / 2 , s ? beforehand unknown variable of
Laplace?s transform,
P0 ( X ) = P102 + (P202 ? P102 )
X
B
(5)
# 639 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Vladimir A. Kodnyanko. Numeric-Analytical Method for Determining the Communication Equations?
? function of lubricant static pressure at a coaxial arrangement of elements, P10 , P20 ? known values
of static pressure at unit inlet and outlet.
Boundary functions in (4), as it appears from (3), are related with transformants of pressure
deviations by relationships
??1 = 2 P10 ?P1 , ?? 2 = 2 P20 ?P 2 .
(6)
Here line from above marked Laplace?s transformants of the corresponding deviations.
Numeric- analytical method of the solution
of a boundary problem (4)
As it is mentioned above, the boundary problem (4) has no analytical decision. It is impossible
to apply to it also numerical methods because boundary transformants and Laplace?s variable s aren?t
known beforehand. Numeric-analytical method of its solution is given below.
According to the principle of superposition [7] we will find a solution of the problem (4) in the
form
?? = T1 ( Z , s )??1 + T2 ( Z , s )?? 2 + T? ( Z , s )?? ,
(7)
Having substituted (7) in (4) and having executed separation of functions, we will receive three
boundary problems for T-functions:
? d 2T1 ? ?? s ?
? 2 ? ?1 +
? T1 = 0,
P0 ?
?d X ?
?T (0) = 1, T ( B) = 0,
1
? 1
? d 2T2 ? ?? s ?
? 2 ? ?1 +
? T2 = 0,
P0 ?
?d X ?
?T (0) = 0, T ( B) = 1,
2
? 2
(8)?(10)
? d 2T? ? ?? s ?
? 2 ? ?1 +
? T? = ?? sP0 ,
P0 ?
?d X ?
?T (0) = 0, T (0) = 0.
?
? ?
Solution of a problem (8)
Having divided the segment [0, B] into even number of parts n we will execute replacement of a
differential problem (8) on finite-differential problem [5]. System of the linear equations concerning
values of required function for internal nodal points can be written as
?T1, j +1 ? (a + b j s )T1, j + T1, j ?1 = 0,
??
?T1,0 = 1, T1,n = 0,
?( j = 1, 2,..., n ? 1),
??
2
where a = 2 +? , b j =
(11)
B
??? 2
,? =
? step of finite-differential grid.
P0 ( j? )
n
Having excluded known values of function on the interval ends, we will receive three-diagonal
system of the equations
# 640 #
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Vladimir A. Kodnyanko. Numeric-Analytical Method for Determining the Communication Equations?
1
0
...
0
0
0
? ?(a + b1s )
? ? T1,1 ? ? ?1?
?
?? T ? ? 0 ?
1
?
(
+
)
1
...
0
0
0
a
b
s
2
?
? ? 1,2 ? ? ?
?
? ? ... ? ? ... ?
...
...
...
...
...
...
...
? ? ?
?
??
0
0
1 ?( a + b j s ) 1
0
0
?
? ? T1, j ? = ? 0 ? .
?
? ? ... ? ? ... ?
...
...
...
...
...
...
...
? ? ?
?
??
0
0
0
...
1 ?(a + bn ? 2 s )
1
?
? ?T1,n ? 2 ? ? 0 ?
?
0
0
0
...
0
1
?(a + bn ?1s ) ?? ?? T1,n ?1 ?? ?? 0 ??
?
(12)
We solve this system by using idea of Cramer?s rule [8].
At first we will find Cramer?s determinant ?T1,n ?1 . In a matrix of the system (12) its last
column we will replace with a column of free members and find determinant of the received
matrix, having opened it on the last column. As n is even, we will receive product of number
?1 and determinant with the upper triangular matrix, on the main diagonal of which units
are located. As such determinant is equal to 1, then ?T1,n ?1 = ?1. Using a boundary condition
T1,n = 0, by means of reverse motion and simple machine-analytical transformations we will
find expressions for missing Cramer?s determinants by a recurrent formula, which follows from
(11)
???T1, j ?1 = (a + b j s )?T1, j ? ?T1, j +1 ,
?
??( j = n ? 1, n ? 2,...,1).
(13)
As T0 = 1 , determinant of a matrix of system (12) is equal to ?D( s) = ?T1,0 ( s ).
As an example the solution of the system (12) is found at R = 1.2, L = 1.5, H0 = 1.2, P10 = 4; P20 = 1;
? = 50; n = 4. The solution of then system is provided by Cramer?s determinants which are polynomials
of variable s:
?T1,0 = ?5.035 ? 9.865s ? 4.832s 2 ? 0.654s3 ,
?T1,1 = ?3.400 ? 4.106s ? 0.938s 2 ,
?T1,2 = ?2.098 ? 1.120s,
?T1,3 = ?1,
?T1,4 = 0,
?D = ?T1,0 = ?5.035 ? 9.865s ? 4.832s 2 ? 0.654s3 .
Thus, values of the T1 function in each nodal point represent the relation of polynomials
T1, j =
?T1, j
?D
, ( j = 0...n),
(14)
i. e. they are rational functions of variable s. Functions (14) have the identical denominator which is
equal to a polynomial of matrix determinant of system (12).
In Fig. 2. and Fig. 3 graphs of the real and imaginary parts of the T1(X, s) function at various values
n and at constant complex value s = 1? i ( i = ?1 ) are shown.
The graphs show that the accuracy of calculations accepted for practice is provided at rather small
number n of division of the integration interval. So, even at n = 4 error of calculations for graph curves
doesn?t exceed 1 %.
# 641 #
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Vladimir A. Kodnyanko. Numeric-Analytical Method for Determining the Communication Equations?
Re T1
Im T1
16
16
8
0.8
8
0.10
0.6
4
4
0.4
n =2
0.05
n =2
0.2
0.0
0.0
0.2
0.4
0.6
0.8
0.00
j/n
0.0
Fig. 2. Real part of T1 function
0.2
0.4
0.6
0.8
j/n
Fig. 3. Imaginary part of T1 function
Solution of a problem (9)
Differential system of linear equations for the values of T2 function at the nodal points has the
form
?T2, j +1 ? (a + b j s )T2, j + T2, j ?1 = 0,
??
?T2,0 = 0, T2,n = 1,
?( j = 1, 2,..., n ? 1).
??
(15)
Having excluded known values of function on the interval ends, we will receive three-diagonal
system of the equations
1
0
...
0
0
0
? ?(a + b1s )
? ? T2,1 ? ? 0 ?
?
?? T ? ? 0 ?
a
b
s
1
?
(
+
)
1
...
0
0
0
2
?
? ? 2,2 ? ? ?
?
? ? ... ? ? ... ?
...
...
...
...
...
...
...
? ? ?
?
??
0
0
1
(
)
1
0
0
a
b
s
?
+
j
?
? ? T2, j ? = ? 0 ? .
?
? ? ... ? ? ... ?
...
...
...
...
...
...
...
? ? ?
?
??
0
0
0
...
1 ?(a + bn ? 2 s )
1
?
? ?T2,n ? 2 ? ? 0 ?
?
0
0
0
...
0
1
?(a + bn ?1s ) ?? ?? T2,n ?1 ?? ?? ?1??
?
(16)
For this system Cramer?s determinant ?T2,1 = ?1. Really, if one opens this determinant on
the fi rst column, we?ll receive product of number ?1 and determinant with the lower triangular
matrix on which main diagonal units are located. Such determinant is equal to unit that proves
the statement.
Using a boundary condition T2,0 = 0, by forward stroke we will find expressions for missing
Cramer?s determinants on a recurrent formula, which follows from (15)
???T2, j +1 = (a + b j s )?T2, j ? ?T2, j ?1 ,
?
??( j = 1, 2,..., n ? 2, n ? 1).
The system (16) has identical with (12) matrix of the system and its determinant.
# 642 #
(17)
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Vladimir A. Kodnyanko. Numeric-Analytical Method for Determining the Communication Equations?
The solution of then system for the same as at 3.1 parameters is provided by Cramer?s determinants
which also are polynomials of variable s:
?T2,0 = 0,
?T2,1 = ?1,
?T2,2 = ?2.098 ? 0.698s,
?T2,3 = ?3.400 ? 3.220s ? 0.584s 2 ,
?T2,4 = ?5.035 ? 9.865s ? 4.832s 2 ? 0.654s3 .
Values of the T2 function in nodal points also represent the rational expressions
T2, j =
?T2, j
?D
, ( j = 0...n).
(18)
Solution of a problem (10)
By analogy to 3.1 and 3.2 we will write the system of the linear equations concerning values of
the T? function in nodal points
?T? , j +1 ? (a + b j s )T? , j + T? , j ?1 = ?c j s,
??
?T? ,0 = 0, T? ,n = 0,
?( j = 1, 2,..., n ? 1),
??
(19)
where с j = ?? 2 P0 ( j? ).
Having excluded zero values of function on the interval ends, we will receive three-diagonal
system of the equations
1
0
...
0
0
0
? ?(a + b1s )
? ? T? ,1 ?
? c1 ?
?T ?
?
?
?c ?
1
?(a + b2 s ) 1
...
0
0
0
?
? ? ? ,2 ?
? 2 ?
?
? ? ... ?
? ... ?
...
...
...
...
...
...
...
?
?
??
?
?
T
0
0
1
?
(
+
)
1
0
0
=
?
s
a
b
s
,
j
?
j
?
?
??
? cj ? ,
?
? ? ... ?
? ... ?
...
...
...
...
...
...
...
?
?
??
?
?
T
0
0
0
...
1
(
)
1
?
+
a
b
s
?
? ? ? ,n ?2 ?
?cn ? 2 ?
n?2
?
?c ?
0
0
0
...
0
1
?(a + bn ?1s ) ?? ?? T? ,n ?1 ??
?
? n ?1 ?
(20)
Now we will find Cramer?s determinant
c1
c2
...
?T? ,1 = ? s c j
...
cn ? 2
cn ?1
1
0
...
0
0
0
...
0
0
0
?(a + b2 s ) 1
...
...
...
...
...
...
0
1 ?( a + b j s ) 1
0
0
.
...
...
...
...
...
...
0
0
...
1 ?(a + bn ? 2 s )
1
0
0
...
0
1
?(a + bn ?1s )
(21)
Having opened (21) on the first column, we will find out that minors of the received sum are equals
to opposite on a sign Cramer?s determinants of the system (12). On this basis
# 643 #
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Vladimir A. Kodnyanko. Numeric-Analytical Method for Determining the Communication Equations?
n ?1
?T? ,1 = s ? c j ?T1, j .
j =1
Using a boundary condition T? ,0 = 0, by a forward stroke we will find expressions for missing
Cramer?s determinants on a recurrent formula, which follows from (19)
???T? , j +1 = (a + b j s )?T? , j ? ?T? , j ?1 ? c j s ?D ,
?
??( j = 1, 2,..., n ? 3, n ? 2).
(22)
At numeric-analytical definition of polynomials (22) their members at j > n are equal to zero,
therefore they can be dropped.
For the same as at 3.1 and 3.2 values of parameters corresponding Cramer?s determinants are
equal to
?T? ,0 = 0,
?T? ,1 = ?82.176 s ? 11.483s 2 ? 0.0855s3 ,
?T? ,2 = ?100.676 s ? 67.373s 2 ? 9.270s3 ,
?T? ,3 = ?69.280 s ? 36.829s 2 ? 5.180s3 ,
?T? ,4 = 0.
Values of T? function in nodal points are determined by a formula
?T? , j
T? , j =
D
, ( j = 0...n).
Transformant of unit load capacity deviation
Load capacity of the unit is defined by a formula [1]
2?
l
0
0
w = r ? cos(? )d? ? ( p ? pa )dz.
(23)
Having taken for scale of forces complex f* = ? r*2 pa according to (3), (6), (7) we will receive a
formula for Laplace?s transformant of dimensionless load capacity deviation of the unit
B
?W =
R 2 ?? ( X , s )
dX = W1 ?P1 + W2 ?P 2 + W? ?? ,
2 ?0 P0 ( X )
(24)
where
B
B
B
T1dX
T dX
R 2 T? dX
, W2 = P20 R 2 ? 2 , W? =
.
2 ?0 P0
P0
P0
0
0
W1 = P10 R 2 ?
(25)
As T-functions are rational functions and they have common polynomial ?D(s) of their
denominators, having applied to their numerators Simpson?s rule [9] for numerical integration of grid
functions, we will find first Laplace?s transformant dynamic equation of the unit
?D( s ) ?W + ?W1 ( s )?P1 + ?W2 ( s )?P 2 + ?W? ( s )?? = 0,
# 644 #
(26)
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Vladimir A. Kodnyanko. Numeric-Analytical Method for Determining the Communication Equations?
Re W1
Im W1
0.9
0.15
0.8
16
0.7
8
0.10
4
n =2
n =2
0.6
0.05
4
0.5
8
16
0.00
0.4
0.0
0.2
0.4
0.6
0.8
X
0.0
Fig. 4. Real part of W1 function, s = X (1?i)
0.2
0.4
0.6
0.8
X
Fig. 5. Imaginary part of W1 function, s = X (1?i)
where ?W1 , ?W2 , ?W? ? the polynomials of variable s received by elementary transformations at
numeric-analytical integration of Cramer?s determinants of (13), (15), (22) on Simpson?s rule calculation
process.
In that case for the examples of calculations, given above, polynomials are received
?W1 ( s ) = 5.051 + 4.757 s + 1.368s 2 + 0.098s3 ,
?W2 ( s ) = 2.079 + 2.438s + 0.886s 2 + 0.098s3 ,
?W? ( s ) = 21.760 s + 14.6876s 2 + 2.335s3 .
Local transfer functions (25) are clearly equal to
W1 =
?W?
?W1
?W2
, W2 =
, W? =
.
?D
?D
?D
Submission about impact of number n on the accuracy of carrying capacity transformant for
different values of variable s give graphs in Fig. 4 and Fig. 5.
From these graphs it is visible that sufficient accuracy for practical calculations is provided at
n = 4.
Transformant of longitudinal deviation
of local flow rates on inlet and outlet of unit
The mass flow rate in the direction of longitudinal coordinate on a chord r ?? of the small length,
given to its angle, is defined by a formula [1]
r
q=?
12 ??T??
?j+
??
2
?
?j?
??
2
h3 p
?p
d? ,
?z
(27)
where ?, T, ? ? universal gas constant, absolute temperature of gas and its viscosity.
# 645 #
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Vladimir A. Kodnyanko. Numeric-Analytical Method for Determining the Communication Equations?
Assuming that temperature and viscosity as constants and having taken for the scale of mass flow
rates a complex q* =
h*3 pa2
, we will receive a formula for defining the corresponding dimensionless
6 ??T
mass flow rate in any cross section of the unit
Q = ? RH 3
?P 2
.
?Z
(28)
Taking into account (3), (5), (6) after linearization of formula (28) Laplace?s transformant of flow
rate deviation can be written as
?
d ?? ?
?Q( X , s ) = ? ? DQ 0 ?? + H 03
?.
dX ?
?
(29)
where DQ 0 = 3H 02 (P102 ? P202 )/ B.
Transformant of a local flow rate deviation at a unit inlet
For definition of this transformant we will use the relation (7). We will find derivative of function
?? using initial unilateral trinomial formulas for Cramer?s determinants of the corresponding grid
T-functions [5]
?D1, j =
d ?T j (0, s )
dX
?
??T j ,2 + 4?T j ,1 ? 3?T j ,0
2?
, ( j = 1, 2, ? ).
(30)
Formulas (30) provide the second order of accuracy concerning a grid step v.
Using (29), (30) we will receive a second communication formula of unit model for transformant
of input flow rate deviation ?Q1 ( s) with corresponding transformants of eccentricity and both pressures
at inlet and outlet of unit
?D( s ) ?Q1 + ?Q1,1 ( s )?P1 + ?Q1,2 ( s )?P 2 + ?Q1,? ( s )?? = 0,
(31)
where ?Q1,1 ( s) = 2 P10 H 03?D1, j , ?Q1,2 ( s) = 2 P20 H 03?D1,2 , ?Q1,? ( s ) = DQ 0 ?D + H 03?DT ,? .
For the above examples we obtain polynomials
?Q1,1 ( s ) = 79.65 + 316.1s + 237.6s 2 + 43.42s3 ,
?Q1,2 ( s ) = ?10.52 + 3.857 s,
?Q1,? ( s ) = ?261.0 + 1141.8s ? 857.9s 2 ? 156.0s3 .
The submission of influence of number n on accuracy of calculation of a transformant of input
local flow rate at various values of Laplace?s variable s is given by graphs in Fig. 6 and Fig. 7.
The graphs show that to ensure acceptable accuracy of the real part of Q1 function n = 4 is enough,
the imaginary part in this case requires n > 4.
Transformant of a local flow rate deviation on a unit outlet
We will define derivative of function (29) using end unilateral trinomial formulas for Cramer?s
determinants of the corresponding grid T-functions [5]
# 646 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Vladimir A. Kodnyanko. Numeric-Analytical Method for Determining the Communication Equations?
Im Q1,1
Re Q1,1
16
8
-10
n=2
4
10
-20
4
-30
5
8
-40
16
n =2
-50
0.0
0.2
0.4
0.6
0.8
0
X
0.0
Fig. 6. Real part of Q1,1 function, s = X (1?i)
?D2, j =
d ?T j ( B, s )
dX
?
0.2
0.4
0.6
0.8
X
Fig. 7. Imaginary part of Q1,1 function, s = X (1?i)
3?T j ,n ? 4?T j ,n ?1 + ?T j ,n ? 2
2?
, ( j = 1, 2, ? ).
(32)
Formulas (32) also have the second order of accuracy.
As a result we will receive a third communication formula of unit model for transformant of an
output flow rate deviation ?Q 2 ( s) with corresponding transformants of the unit
?D( s ) ?Q 2 = ?Q2,1 ( s )?P1 + ?Q2,2 ( s )?P 2 + ?? DQ 0 + ?Q2,? ( s ) ?? ?? ,
where ?Q2,1 ( s) = ?2 P10 H 03?D2, j , ?Q2,2 ( s) = ?2 P20 H 03?D2,2 , ?Q2,? ( s) = ? H 03?D2,? .
For the examples given above polynomials are received
?Q2,1 ( s ) = 42.07 ? 24.78s,
?Q2,2 ( s ) = ?19.91 ? 96.29 s ? 67.24s 2 ? 10.86s3 ,
?Q2,? ( s ) = ?261.0 ? 23.59 s ? 29.47s 2 ? 2.261s3 .
Submission of influence of number n on accuracy of calculation of a transformant of output local
flow rate at various values of Laplace?s variable s is given in Fig. 8 and Fig. 9.
For the given values of parameters sufficient accuracy for practice is provided at n = 4?8.
Conclusion
The equations (26), (31), (32) allow to establish relations of integro-differential Laplace?s
transformants of carrying capacity ?W ( s) and local mass flow rates ?Q1 ( s), ?Q 2 ( s) at inlet and outlet
of the unit with transformants ?? ( s), ?P1 ( s), ?P 2 ( s) of eccentricity and pressures at inlet and outlet of
unit. Required accuracy of the calculation of T-functions can be provided by selecting the number n of
partitions of integration interval.
These equations give ready formulas for calculating the dynamic criteria containing such units of
radial one-row, multi-row ordinary passive or active (with zero or negative compliance of carrier gas
films [10]) externally pressurized and other gas bearings, in which radial movement of their movable
elements is made.
# 647 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Vladimir A. Kodnyanko. Numeric-Analytical Method for Determining the Communication Equations?
Re Q2,1
Im Q2,1
4
-0.5
n =2
4
2
16
-1.0
0
8
-1.5
-2
-2.0
16
-4
-2.5
8
-6
-3.0
-8
-3.5
-10
n =2
4
-4.0
0.0
0.2
0.4
0.6
Fig. 8. Real part of Q2,1 function, s = X (1?i)
0.8
X
0.0
0.2
0.4
0.6
0.8
X
Fig. 9. Imaginary part of Q2,1 function, s = X (1?i)
References
[1] Constantinescu V.N., ?Gas lubrication,? Moscow, Mashinostroenie, 1968, 709 (In Russian).
[2] Bessekersky V.A., Popov E.P., ?Automatic control theory systems,? Petersburg, Profession,
2003, 752 (In Russian).
[3] Kodnyanko V.A., Shatokhin S.N., ?Research of dynamics of gas-static bearing with a double
throttling of gas in injection pipeline,? ?Russian Engineering Research,? 1978, ?. 6, 90?95 (In
Russian).
[4] Kodnyanko V.A., Shatokhin S.N., ?Load and flow characteristics of gas-static bearing with
active compensation of gas flow rate,? ?Russian Engineering Research,? 1980, ? 6, 108?112 (In
Russian).
[5] Demidovich B. P., Maron I. A., Shuvalova E. Z., ?Numerical Methods of Analysis,? Moscow,
Fizmatgiz, 1963, 660 (In Russian).
[6] Pinegin S. V., Tabachnikov J. B., Sipenkov I. E., ?Static and dynamic characteristics of
externally-pressurized gas bearings,? Moscow, Nauka, 1982, 265 (In Russian).
[7] Haberman, R., ?Applied Partial Differential Equations,? Prentice Hall, 2004, 167.
[8] Gantmacher, F. R., ?Applications of the Theory of Matrices,? Dover Publications, 2005, 423.
[9] Dwight G., ?Tables of integrals and other mathematical formulas,? Moscow, Nauka, 1973, 228
(In Russian).
[10] Tkachev A.A., Kodnyanko V.A., ?Two-row radial gas-static bearing with lubricant-outflow
regulator,? Russian Engineering Research, 2009, V. 29, ? 9, 926-929 (In Russian).
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Vladimir A. Kodnyanko. Numeric-Analytical Method for Determining the Communication Equations?
????????-????????????? ????? ???????????
????????? ????? ?????????? ????????????
??????????? ??????????? ?????
??????????????? ???????????
?.A. ????????
????????? ??????????? ???????????,
?????? 660041, ??????????, ??. ?????????, 79
????????? ????????-????????????? ????? ??????????? ?????????? ????????????
???????????? ??????? ??? ?????????????? ??????????? ????? ??????????????? ???????????,
????????? ??????? ???????? ????????? ????? ?????????? ????????? ? ??????????? ???
???????????? ?????????.
????? ? ?????????? ??????????? ????????? ?????????? ????? ???????-????????????????
?????????? ???????????? ??????? ??????????? ? ????????? ???????? ???????? ?? ????? ?
?????? ????? ? ??????????????? ??????????????? ? ???????? ???????????? ???? ?? ?????
? ?????? ?????. ????????, ??? ????????? ???????????? ??????? ????? ???????????? ?????
???????????? ??????? ?????????? ?????????????? ??????? ? ??? ??? ????? ??????? ?????
????? ??????????? ? ???? ???????? ???????????? ???? ??????????.
????? ????????? ????????? ????????? ???????? ???????? ???????? ???????????,
?????????? ?????? ????, ? ??????? ???????? ?????????.
????????? ????????? ?????? ???? ??????? ??????? ??? ??????? ????????? ????????
???????? ?????????? ????? ???? ?????????? ??????????, ??????????? ??????? ?????????
??? ???????? ??????????????? ???????????, ? ??????? ??????????? ?????????? ????????
?? ????????? ?????????.
???????? ?????: ??????????????? ?????????, ????????-????????????? ?????, ????????????
???????.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 6 (2013 6) 650-656
~~~
??? 666.3
Characteristic Physical?Mechanical
and High?Temperature Electric Properties
Semicinductor Ceramic Based SnO2
with Addition MnO2 and CuO
Sergey S. Dobrosmyslov*,
Vladimir I. Kirko, Gennady E. Nagibin,
Oksana A. Resinkina and Zahar I. Popov
Siberian Federal University
79 Svobodny, Krasnoyarsk, 660041 Russia
Received 05.07.2013, received in revised form 02.09.2013, accepted 10.09.2013
Ceramic semiconductor SnO2-based materials with MnO2 and CuO additives were synthesized at
1300 є? and 1400 є?. There has been carried out an investigation of the physical?mechanical and
high?temperature electric properties. As a result, sintering of the material with MnO2 additive is
shown to be improved at increasing firing temperature. The composition 96 % SnO2-2 % Sb2O3-2 %
CuO made at the temperature 1300 є? has the best electrophysical properties (its resistivity is 0.09
mOhm m). The resistivity of the 94 % SnO2-2 % Sb2O3-2 % CuO-2 % MnO2 composition in the hightemperature region is more by a factor of 3. The 96 % SnO2-2 % Sb2O3-2 % MnO2 composition has
nonlinear voltage-currant characteristic, and hysteresis is present.
Keywords: ceramic, tin oxide, conductivity, currant ? voltage characteristic.
Introduction
The tin dioxide based ceramics is being used in many branches of industry ? electronics, electrical
engineering, electrochemistry, catalysis, biotechnology, metallurgy, atomic and chemical industries,
etc. [1]. SnO2 is an n-type semiconductor having the band-gap energy 3.54 eV, whose properties
basically depend on its microstructure and synthesis method. The wide range of use imposes special
requirements on the material properties and thus on the synthesis method.
High-porous polycrystalline materials having a large amount of structural defects are used as
catalysts and semiconductor gas sensors [2?6]. Oxygen vacancies forming in the surface active layers
of the tin dioxide pores are the areas of the physical or chemical adsorption the presence of which
is necessary for the gas sensing ability. On the other hand, high-density SnO2-based ceramics due
to its high electro conductivity at high temperatures is used as the high temperature-electrodes [7],
for instance, in the aluminum electrolysis and glass making [8]. Without glass-forming additives tin
dioxide possesses a low value of sinterability which is caused by the domination of vaporization and
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: dobrosmislov.s.s@gmail.com
# 650 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Sergey S. Dobrosmyslov, Vladimir I. Kirko? Characteristic Physical?Mechanical and High?Temperature Electric?
condensation processes over diffusion ones [9] because SnO2 starts evaporating from the temperature
1100??. And this limits the material densification.
One of the ways to increase the ceramic material sinterability is the addition of fine-grained oxide
materials such as ZnO [10], CuO [11], MnO2 [12, 13], ??? [14], Fe2O3 [13], and to improve electrical
properties V2O5 [6] and Sb2O3 [15] are added. The addition of 1 mol. % CuO is especially effective
because of the liquid phase formation. The Cu-O eutectic is 1080?C [16]. A significant improvement of
the electrophysical properties is provided with the Sb2O3 addition.
The aim of the paper being presented is the investigation of physical-mechanical and hightemperature electrophysical properties of a ceramics based on 96 %SnO2-2 %Sb2O3-2 %CuO with
superdispersed MnO2.
Experimental technique
The specimens were made with the conventional ceramic technology. The initial SnO2 powder
charge was prepared in the aqueous solution of Mn and ?u salts. And then it was preliminarily
subjected to a thermal treatment at 1100 є? followed by grinding. Then the charge was formed into
a specimen using the 5 % polyvinyl alcohol solution as a binder. The specimen burning was carried
out at 1300 є? and 1400 є? for 2 h. For the physical chemical tests the ceramic specimens were made
in the form of cylinders 15 mm in diameter and 10 mm high, respectively. For the electro physical
measurements the specimens of a rectangular shape 5Ч4Ч 50 mm were taken. The specimen?s density
was measured with the hydrostatic weighing method in alcohol and the open porosity according to
the State Standard 2408-95. The resistivity was measured with the four-point probe method in the
temperature range 20-1000 є? [17]. The mechanical properties were measured with the device Instron
3369. The crystalline structure of the ceramics was identified with the X-ray analysis in XRD 6000.
The surface fracture pictures were taken with the scanning electron microscope (SEM) JEOL JSM7001F (Japan).
Experimental results and discussion
In Table 1 there are presented the results of the physical-mechanical properties investigation of the
ceramics and its resistivity values at T = 1000 є?.
The experiment number is in the first column. The charge composition and final firing temperature
are presented in the second and third ones, respectively. The measured values of density, open porosity,
mechanical strength and resistivity are presented in columns 4 to 7.
As follows from the table a complete change of CuO for MnO2 leads to the mechanical and
electrical properties degradation (experiments 1 and 2). The firing temperature increase leads to
increased density and strength and decreased open porosity (? 23 and ? 45). The best composition
of the investigated ones is 94 % SnO2-2 % Sb2O3-2 % CuO-2 % MnO2. This ceramics has the best
physical-mechanical properties (? 7).
The measurement results for the ceramics strength at uniaxial compression obtained with Instron
3369 are presented in Fig. 1.
As can be seen from the figure the ceramics ultimate strength decreases with increasing MnO2
concentration. The Young?s modulus is practically unchanged. A little addition of the glass-forming
CuO phase leads to a significant ultimate strength increase and change of the deformation behavior and
# 651 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Sergey S. Dobrosmyslov, Vladimir I. Kirko? Characteristic Physical?Mechanical and High?Temperature Electric?
Table 1. Physical-mechanical properties and resistivity of the ceramics under investigation
Open
Strength,
porosity, %
MPa
Resistivity,
mOhm*m
T = 1000 єC
?
Charge composition
Firing
temperature, є?
Density,
g/cm3
1
2
3
4
5
6
7
96 % SnO2-2 % Sb2O3-2 % CuO
1300
5.4
17.9
155.3
0.09
2
96 % SnO2-2 % Sb2O3-2 % MnO2
1300
5.5
18.5
91.2
0.80
3
96 % SnO2-2 % Sb2O3-2 % MnO2
1400
6.1
6.1
158.2
-
4
94 % SnO2-2 % Sb2O3-4 % MnO2
1300
5.5
17.2
132.5
0.83
5
94 % SnO2-2 % Sb2O3-4 % MnO2
1400
6.1
5.1
257.6
-
6
90 % SnO2-2 % Sb2O3-8 % MnO2
1300
5.3
18.6
149.7
0.99
7
94 % SnO2-2 % Sb2O3-2 % CuO2 % MnO2
1300
6.6
0.11
424.8
1.7
1
Fig. 1. Dependence of the ceramics strength on the degree of their compression deformation
fracture pattern (from brittle to visco-brittle). On the curves in a number of cases an abrupt material
destruction takes place that serves as evidence of deformation behavior change.
The pictures of the ceramic specimen?s surface fracture are presented in Fig. 2. The fracture
structure also witnesses the change of the fracture pattern from brittle (a) to visco-brittle (b).
As can be seen from the pictures in Fig. 2 in tin dioxide with CuO or MnO2 additives there are
formed pores whose size is 20 ?m in case of 2 % CuO addition (Fig. 2 (1)). In ceramics with CuO and
MnO2 the large pores are practically absent as well as the pores of a less size.
Pictures of the ceramics fractures at 5000-fold magnification are presented in Fig. 3.
The Fig. 3 shows that the destruction of the specimen 96 % SnO2-2 % Sb2O3 -2 % CuO
occurs through particle bodies, but that of the specimen with 2 % CuO and 2 % MnO2 additives
along the grain boundaries. It seems to take place through the glass-forming phase CuMn 2O 4,
Cu1.5Mn1.5O 4 [18].
It is known that when MnO2 is added into polycrystalline tin dioxide, Mn2SnO4 forms on the
grains? surfaces, which interferes with a good material sintering [19]. This does explain a high porosity
of the material and its low strength. In case of MnO2 ? CuO additive combination there takes place the
# 652 #
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Sergey S. Dobrosmyslov, Vladimir I. Kirko? Characteristic Physical?Mechanical and High?Temperature Electric?
(?)
(b)
Fig. 2. Pictures of the materials under investigation obtained with SEM JEOL JSM-7001F, x500;
1 ? pores: (?) 96 % SnO2-2 % Sb2O3-2 % CuO; (b) 94 % SnO2-2 % Sb2O3-2 % CuO-2 % MnO2
?)
b)
Fig. 3. Pictures of the fractures, x5000; 1 ? areas of particles destruction: (?) 96 % SnO2-2 % Sb2O3-2 % CuO;
(b) 94 % SnO2-2 % Sb2O3-2 % CuO-2 % MnO2
formation of CuMnOx-phase (basically, CuMn2O4, Cu1.5Mn1.5O4) [19]) that is a glass-forming one on
the grains? boundaries and promotes sintering.
To improve the electrophysical properties Sb2O3 was used. During the high-temperature sintering
in the polycrystalline SnO2 lattice there takes place a substitution of the tetravalent tin atoms by
pentavalent antimony ones [20] that provides the p-type conductivity and substantially decreases the
energy-gap width. The ceramics receptivity measurement results versus temperature are presented in
Fig. 4.
It has been mentioned above that Sb2O3 is used as an additive improving the material?s electrical
conductivity. In the compositions of Fig. 4 the Sb2O3 concentration (the number of the electrical
charge carriers) is constant. The resistivity depends on the electrical contact between the sintered
particles. The material with the CuO additive has the lowest resistivity (0.9 mOhm m, Table 1,
?1). The Table 1 and Fig. 4 show that when MnO2 is used, the resistivity is independent of this
phase concentration. It is possible to explain this fact by no influence of Mn 2SnO4 on the electrical
contact between the sintered SnO2 particles. The voltage-current characteristics of the specimens
are presented in Fig. 5.
# 653 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Sergey S. Dobrosmyslov, Vladimir I. Kirko? Characteristic Physical?Mechanical and High?Temperature Electric?
Fig. 4. T-dependencies of the resistivity of SnO2-based materials with different additions
?)
b)
Fig. 5. The specimens? voltage-current characteristics obtained in 3 measurements (? = 1000 є?):
1 ? increasing current; 2 ? decreasing current. ?) 96 % SnO2-2 % Sb2O3-2 % CuO b) 96 % SnO2-2 % Sb2O3-2 %
MnO2
The curves show a dependence on the material?s phase composition. In case of the 96 % SnO2-2 %
Sb2O3-2 % CuO composition the voltage-current characteristics are linear which serves as an evidence
of the resistivity being constant at current load increasing (a). In contrast to this, in specimens having
CuO substituted by superdispersed MnO2 the resistivity decreases practically by a factor of 2 with
the current load increasing from 1 to 10 Е (b). The latter can be associated either with a generation
of extra charge carriers on the interphase boundaries of the particles, or with the beginning of a flow
along the boundaries because of the heat generation increased. Moreover, in case of the material with
superdispersed MnO2 voltage-current characteristic shows hysteresis (Fig.1 b) that can be explained
with a later cooling of the SnO2 particles compared to that of the interphase boundaries when decreasing
the current load.
# 654 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Sergey S. Dobrosmyslov, Vladimir I. Kirko? Characteristic Physical?Mechanical and High?Temperature Electric?
Conclusions
1. The specimens of the 96 % SnO2-2 % Sb2O3-2 % CuO composition sintered at 1300 є? have
the best electrophysical characteristics;
2. The substitution of CuO by MnO2 leads to the degradation of the material?s mechanical
properties;
3. The use of the superdispersed MnO2 ? CuO additive combination leads to a substantial increase
of the mechanical strength and change of the fracture mechanism from brittle to visco-brittle;
4. In the compositions with MnO2 ? CuO additives there has been revealed a nonlinearity of the
voltage-current characteristic. When the current load increases, the resistivity decreases. Moreover,
there is revealed a hysteresis of the voltage-current characteristic.
Article was supported by RFBR ? 12-03-31323
?????? ????????? ??? ????????? ???? ? 12-03-31323
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# 655 #
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Sergey S. Dobrosmyslov, Vladimir I. Kirko? Characteristic Physical?Mechanical and High?Temperature Electric?
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??????????? ??????-????????????
? ??????????????????? ????????????????? ???????
???????????? ????????????????? ??????????
?? ?????? SnO2 c ????????? MnO2 ? CuO
?.?. ????????????, ?.?. ?????,
?.?. ???????, ?.?. ?????????, ?.?. ?????
????????? ??????????? ???????????
?????? 660041, ??????????, ??. ?????????, 79
????????????? ???????????? ????????????????? ????????? ?? ?????? ???????? ????? ?
????????? MnO2 ? CuO. ??????????? ??????? ???? 1300 ? 1400 є?. ????????? ????????????
??????-???????????? ? ????????????????? ???????. ????????, ??? ????????? ???????????
?????? ??? ?????????, ??????????? ??? ????????????? MnO2, ?????????? ????????????
????????? ????????. ?????????? ?????????????????? ???????????????? ???????? ???????
??????? 96%SnO2-2%Sb2O3-2%CuO ?????????? ??? ??????????? ?????? 1300 є?(??? 0,09
???Ч?). ??? ??????? 94%SnO2-2%Sb2O3-2%CuO-2%MnO2 ? ??????????????????? ???????
???? ? 3 ????. ??? ??????? 96%SnO2-2%Sb2O3-2%MnO2 ????????????? ?????????????? ?????
?????????? ??? ? ???????????? ??????????.
???????? ?????:
??????????????.
????????,
???????
?????,
??????????????????,
?????????????
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 6 (2013 6) 657-664
~~~
??? 621.362
?????????????????? ???????????
? ?????????????? ????????????????? ?????
?.?. ?????????,
?.?. ??????????, ?.?. ??????????*
????????? ??????????? ???????????,
?????? 660041, ??????????, ??. ?????????, 79
Received 19.02.2013, received in revised form 26.07.2013, accepted 14.08.2013
? ?????? ??????????? ?????????????????? ?????????????? ????????????????? ??????,
??????? ????? ???? ???????????? ??? ???????? ?????????????????? ????????????????.
???????????????? ??????? ? ?????????? ???????????? ??????? ? ??????????? ? ????????
«?????????????????????? ?????????????». ????????, ??? ????????????????? ?????????
??????????????? ???????? ????????? ????????? ? ?????????????? ?????????????
??????????, ??? ???????? ? ????????????? ?????????? ???????????? ??????? ?,
??????????????, ??????????? ?????????????????? ??????.
???????? ?????: ??????????????????, ??????????? ???????, ?????????????? ?????.
????????
???????? ??????????? ??????? ? ?????????? ????? ?????? ? ??????? ????? ??????????
???????, ? ?????? ??????? ????????????? ??????? ??? ???????? ????????????? ??? ????????????? ?????????????. ? ????? ?? ?????? ???? ??????? ?????????? ????????????? ??????? ??
????????? ? ????????????????. ? ???? ????? ?????? ?????????????????? ????????? ? ????????????? ???????? ??????? ?????????????? ???????? ??????? ? ????????????? ??? ?????????????? ????? ???????? ? ???????????? ???????, ??? ??? ?????????? ?? ???????? ? ???????
???????????????.
?????????????????? ?????????????? ????? ???? ???????????? ??? ??????? ? ????? ????????? ??????????. ? ?????? ?????? ??????? ?????????? ???????? ??????????? ??????????
???????? ?????????? ??????????? ????????? (???????????? ????????, ??????? ?????????
?????) ?? ???? ????????????? ???????, ?????????? ??? ??????? ???????????? ???????????
????????? ?????????? ??????? 10?20 °C. ????? ????????????? ????? ?????????? ? ????????????? ???????? ????????????? ????????. ?????? ?????? ????? ??? ???? ?????????? ?????????????????? ?????????? ??? ?????????? (???????? ???????? ????????), ????? ??????? ??????
????????? ??????? ??????????.
?????????????????? ?????????????? ????????? ????????????? ??????????? ?????
?????????? ????????? ??????, ??? ??????? ?????????? ???? ???????? ??????????????
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: sitipro-2011@mail.ru
# 657 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ??????????? ?????????????????? ??????????? ? ?????????????? ????????????????? ?????
??????????. ???????????? ??????? ?????????? ?????????? ??????: ??????????? ???? ???????? ? ??????????? ???????, ????, ?????, ??????????? ??????? ? ??????????? ???????
???? ? ?.?.
????????????? ?????? ??????????????????
?????????????????? ?????????????? ??????????? ? ?????????????? ???????? ??????????
? ???????? ????????????? ??????????? ?? ???? ??????? ?????????. ? ???????? ?????????????????? ?????????? ?????????? ???????????? ??????????????, ????? ??? Si, GaAs, ? ????? ?????
??????? ??????????, ????????, Bi2Te3 ? Sb2Te3.
???????????? ?????????????????? ?????????? ???????? ? ???????? ???????? ??????????????? ? ????????? ????? ????????????, ?.?. ?? p-n?????????.
????????? ???????????????? ?????????????????? ?????????? ???????? ???????????
??????? (?), ???????? ???????????????? (?), ???????? ?????????????????? (?).
??????????????? ????, ??????????? ? ???? ??????????? ??????????? ??????????????
???? ??? ??????? ????????? ??????????? ?? ?????? ??????????? ????, ????? ???? ????????
????? ???????? ?????????? ? ??? ?????????? ??????????? ??????? ? ??????????? ???????????????????? ???? (????????) ??????????, ???????????? ????
E (? p ? n ) � (T? T? ) ,
(1)
??? ?p ? ??????????? ??????? ???????? ????? ?????????????, ?n ? ??????????? ??????? ??????????? ????? ?????????????, Tx ? ??????????? ????????? ???? ??????, T? ? ??????????? ???????? ???? ??????.
??????????? ??????????????????? ????????? ?????????? ?????????????????? ?????????????????? ????????? ? ?????????????? ?? ???????
ZT
? � ?2
�T ,
?
(2)
??? ? ? ???????? ???????????????? ?????????, ? ? ???????? ??????????????????, ? ? ??????????? ???????.
??????????? ????????? ??????????????????? ????????? ????????? ??????? ?????????
?????????? ???????, ?????????????? ?????????? ??? ?????? ?????? ??? ??????????????
???????? ??????? ? ?????????????, ?.?. ??????? ???????????.
?????????????????? ???????? ?????? ???????? ??????? ????????, ??????? ????????????? ????????????? (????? ?????????? ?????? ????? ??????? ????????) ? ????? ??????????? ????????????? (????? ????????? ??????????? ??????? ?????). ?????? ?????????????
????????? ????????? ??????? ? ????? ????????? ???????????? ???????????, ??????? ??????
???????? ??????????????????? ????????? ???????? ???????????? ??? ???????? ??????? ????????????.
??????????? ??????? ??????????? ??????????? ? ????????? ??? ?????????? ????????????, ??????? ???????? ???????????????: ????????? ??????? ?????????????????? ??? ????? ????????????????, ? ?? ????? ??? ??? ???????? ??? ?????????? ??????????? ??????? ????????
???????????? ? ??????? ???????????????:
# 658 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ??????????? ?????????????????? ??????????? ? ?????????????? ????????????????? ?????
?
?
L�T,
(3)
??? L ? ????? ???????.
? ?????? ???????, ???????? ???????????????? ????????? ?? ????? ????????? ? ??????
???????? ????????? ?????????????. ??? ???????? ????? ???????? ???????? ? ????????????
?????????????????? ??????, ? ??????? ?????????? ???????????? ????????? ???????, ?.?. ???
???????????? ??????????????? ???????????. ?? ?????? ??????, ? ???????? ????????????
????????? ?????????? ? ?????? ??????????? ???????? ???????? ???????????????? ?????
?? ????????? ?????????? ???????-???????????? ??????????????? ?????????? ?????. ?????
???????, ???????? ?????? ???????? ? ????, ????? ???????? ???????? ? ??????????? ???????
????????????? ??????? ? ??????????? ????????? ???????????????????. ?????????? ? ???????????? ? ????? ?????????? ????????? ?????????????? ???????? ?????????????? ??? ???????? ?????????????????? ????????? ?????? ?????????, ????????? ???????? ??? ????????????
????????? ??????????? ? ???????????? ????? ????? ??????????.
????????? ?????????? ?????????????????
?????????????????? ??????????
?????????????????? ??????????? ????? ??????? ? ??? ?????????? [1], ?? ????????? ZT
????? ?????????? ????????????? ????????????? ????????????????, ???????????? ????????? ?????????. ????? ?????????????????? ?????????? ????? ????????????? ?? ????????????? ? ???????? ?????????????? ????????????, ???????? ZT ?????? ?????????? ? 3?4.
??????????? ??????????? ?? 2?3 ??????? ?? ? ?????????? ??? ?????????????????? ???????????????? ?? 20 % ? ??????? ????????? ???????? ? ?? ?????????? ? ????????? ????????.
??????? ???????? ZT ? 1 ??? 300 K ????? ??????? ???????????, ?? ??? ???? ??????????
??? ? ????? 60-? ????? ???????? ???? ? ???????? ??????????? ?? ???????????? ???.
???????????? ?????????????????? ????????? ????????? ???? ?????????????? ??????? ????????????? ????????. ????????????????? ?????? CsBiSb ????? ZT = 0,7?0,8 ???
-50?40 °C, BiTe?ZT = 0,9?1,0 ??? 30?50 °C, PbTe?ZT=0,7?0,8 ??? 450-480 °C ? SiGe ? ZT =
0,8?0,9 ??? 800?900 °C [2]. ?????????????????? (?? 100?300 °C) ?????????????????? ?????????? ???????????? ??????????????? ????? ????????????????. ??????????????????? (??
700?900 °C) ?????????????????? ?????????? ????? ?????????? ? ???????? ??????????????
???????????? ???????.
? ????? 90-? ????? ???????? ???????? ????????? ???????????? ?? ????????? ?????????????????? ??????????? ?? ???? ???????? ?? ?????????? ???????? ?????????? ? ?????????????? ????????????????? ??????. ? ?? ????? ????????? ????????????, ??????? ?
?????????? ?????, ?????????? ???????????? ? ???????, ? ????? ???????????? ?????????
? ????????????? ??????????? ????????????? ??????? [3]. ? ?????? [4] ??????????? ????????? ?????????? ?????????????????? ??????????? ? ????????????? Bi 2Te3/Sb2Te3 ? ?-?????
???????????? ?? ???????? ZT = 2,4 ??? 300 K. ??????? ????? ????????? ??????? ? ????
????????????? ?????????? 1 ??, ? ????????? ?????? 5 ??. ???????? ????? ??????????? ??????????? ???? ??????? ?? ???????????? ?????????? ?????????? ????? ???????????????? ? ?? 0,22 ??/?.
# 659 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ??????????? ?????????????????? ??????????? ? ?????????????? ????????????????? ?????
????????? ????????? ? ?? ??????? ? ??? ???? ??????, ???????????? ???????? ? ????????? ??????????????????. ??????? ???????????? ?? ???????? ?? ?????????????? ????????
??? ???????????, ??? ? ???????? ???????? ?????? ? ?????????? ???????????. ????????????????? ?????????? ????????????? ?????????? ???????? ??????? ????????? ? ??????????,
?????????? ????????????? ??????? ????????? 9 ? 15 ?? ? ??????? ???????? ????? ????????
[5]. ? ?????? [6] ????????????? ?????????? ????????????? ? ????????? 20 ?? ? ??????????
???????? ZT ? 1 ??? 200 K.
??? ??????? ?? ??????????? ????????, ??? ????????? ?????????????????? ???????????
? ???????? ??????????? ??????????? ??????? ?????????? ? ????????? ???????????????? ??
???? ????????? ??????? ?? ???????????? ? ??????????????. ?????? ??????? ????? ???????????? ??? ????????? ? ?????????? ????? ??? ??????????? ???????? ??????? ? ???????.
????? ??????? ???? ? ???????? ??????????????, ?????????? ????????????? ??????????????:
????????, ???????? ?????????? ? ??? ???? ?????????????????? ??????????? ? ?????????????
? 6,5 % ?60 ?? ????????? ? ?????? CoSb3 ??? 350 K [7].
???????????? ??????????? ???????? ? ?????????????????? ??????????? ? ??????? PbTe
? ?????????? ??????? PbSe0,98Te0,02 (ZT = 1,3?1,6 ??? 300 K) ?? ????????? ? PbTe ????????? ?
?????? [8]. ? ????? ????????????? ? ?????????? ??????? ?????????? ??????? ????????? ???????, ? ???? ?? ????????? ????????? ????????? ???????, ? ??? ???? ??????? ???????? ?
?????????? ?????????????????? ???????????.
??????? ? ????? ?????????? ?????????? ? ?????? ????????????????? ???????? ????????????, ??? ??? ???? ?? ??????? ????????? ? ??????? ?????????????????? ????????????,
??????????? ??? ???????? ??????????.
????????????????? ?????
? ???????? ?????????????? ??????????????????? ????????? ?????? ?????? ?????? ??????? ??????? «?????????????????????? ?????????????». ? ?????? ??????????? ??????? Si/
por-Si ? GaAs/por-GaAs. ????? ????????????, ??? ? ????? ?????????? ????? ??????????? ????????? ???????????? ??????? ?? ????????? ? ???????? ??????????. ??? ?????????????
???????? ?? ???, ??? ????????????? ???? ?? ??? ????, ??? ??????? ???? ?????????? ? ?????????? ??????????????? ????????????????, ???, ??????????, ? ?????????? ? ????? ?????? ???
?????????? ??????? ???????.
??????????????? ???? ???????? ??????? ???????????? ??????????????????? ???????
?? ??????????? ????????????????? ????????. ? ???????? ??????????? ???????????? ???????
?????????????????? ??????? ? ???????? ?????? HF : C2H5OH = 1 : 1.
??? ????????????? ???? ???????????? ???????? ??????? ? ???????? ?????? n- ? p-?????
???????????? ? ???????????? ????????????, ???????????????????? ??????????? (100) ? ????????????? ???????? ????????? ?????? 5·1017?1018 ??-3. ???????? ????????????? ???????, ???????? ?????????? ?????????????, ?????????? ???????? ? 0,7 ??·??.
????? ?????????????????? ???????????? ??? ?????? ?????, ????? ???????? ????????
???? ???????? 10 ??? ??? ??????????? ??? 30?40 ?? ?? ???????? ?? ????????????? ?? ???????????? ?????????, ??????? ??????? ??????????? ???????. ????? ? ? ????? ????????????
???????? ????? ??????? ???????????? ????????? ???????, ????? ????????? ???????? ??????# 660 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ??????????? ?????????????????? ??????????? ? ?????????????? ????????????????? ?????
???. 1. ????? ?????????????????? ??????: 1 ? ?????????????/?????????????????, 2 ? ???????????
????????????????? ????????, 3 ? ????????????? ??????, 4 ? ??????????? ????????, 5 ? ?????????????
(????), 6 ? ????????????????? ??????
??? ?????????????????? ??????? ????????? ?????????? ???????????? ?????????????? ?????.
??? ????? ???????? ?????????? ? ????????????????? ????????????, ?????????????? ?????
???????? ?????????? ?? ???. 1.
?????????????????? ?????? ???????????? ????? ???????, ?????????, ? ????? ???????,
???????????? ????????? ??????? ? ?????????? ? ?????????????? ??????, ? ? ?????? ? ???????????? ??????????? ?? ????? ????????? ???????????. ??????????? ???????? (2), ?????????? ??????????????? (1), ??????????? ? ?????????? ? ??????????? ????????? (4) ?????
? ????????????? ??????? (3), ??????? ???????????? ???????? ????????????? ????? ?????????????? ? ??????? ????? (5), ??????????? ? ????????????????? ??????? (6), ? ??????????,
? ??????????????? ????? ??????? ?????????????. ??????? ???? ? ????????????? ?????????
????????????? ???????? ???????????????????, ??????????????? ?????????? ??????? ?, ??????????????, ?????? ???????????? ?????????. ???????? ?????????? ????????? ????? ??????? ????????????????? ???????, ??????????? ? ??????? ??????, ? ????? ???????, ? ?????????????? ? ?????????????? ? ? ??????.
?????????? ? ?? ??????????
???????????? ?????????????????? ??????? ?????????? ??????????? ? ?????? ??????????? ??????? ?????????? ??????? 20°, ??????????????? ???????? ???????? ????????????
????????? ???????????. ??? ?????? ??????? ?????????? ????????????? ?????? ??????????
????????? ????. ?????????? ????????? ?????????? ????????? ? ????. 1. ??????????? ????????? ?????????? ????????? ???? ?????????? 1 ??.
?? ?????? ????. 1 ????? ?????????, ??? ??????????? ??????? ??????????????? por-nGaAs/p-GaAs ? 4?5 ??? ????????? ??????????? ?????????? ??? ??????????????????? ?????????? p-GaAs/n-GaAs. ????????????? ???? por-p-GaAs/por-n-GaAs ??????? ? ?????????????
????????? ???????? ? 9 ??? ?? ????????? ? ??????????? ???????????.
??? ?????? ??????????? ?????????? ?????????? ???? ??????? ????????? ?????????:
1. ??????????? ??????? ???????????? ????????? ????????? ?? ???????????? ???????????????? (???????), ? ? ???? ? ?????? ??????????? ??????????, ??????? ????????, ??? ?????????? ???????? ????? ????? ? ???? ????? ?? ????? ????????????? ??????????. ?????????, ???
# 661 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ??????????? ?????????????????? ??????????? ? ?????????????? ????????????????? ?????
??????? 1. ?????????? ????????? ?????????? ?? ??????? ?????????????????? ??????
????????????????? ????????
????????
???????????, ??
???????????
??????? ????
?????, ??/?
p-????
n-????
????????
?????????? ?T, ?
GaAs
GaAs
20
5
0,25
GaAs
Si
20
7
0,35
Si
Si
Si
Por-Si
20
20
1,5
4,2
0,075
0,21
Por-GaAs
Si
20
35
1,75
GaAs
Por-GaAs
20
28
1,4
Por-GaAs
Por-GaAs
20
45
2,25
?? ????? ???????? ? ??? ??????? ??????????? ????????? ?? ??????????? ??????? ?????????
????? ???????? ?? ???????????? ??????? ???? ?????????? ??????????:
? GaAs
? ???? p GaAs / n GaAs
2
? por(GaAs)
250
125 ???/K ,
2
? ???? por p GaAs/por n GaAs
2
2250
2
(4)
1125 ???/K .
(5)
2. ???????? ???? ???????? ??????? ??????????????, ??????? ??????????????????
???????? ???????????? ???????? ????????, ???????? ?????????????????? ??????? ???????? ??? ?????????. ?? ????????? ????? ??? ??????? ??????????? ?????????? ?????????????? ???????? ????? ???????????? ???????? ???????? ?????????????????? ?????????
?????????.
3. ?????????? ??????????? ???? ?? ????????? ????, ??? ???????? ????????? ???????? ??????????? ???? ??????????, ????? ?????????, ??? ???????? ????? ? ????????????????
?????????????? ???????? ?????? ?????????????????? ????? ????????? ?????????, ?, ?????????????, ????? ???????????? ? ??????? ??????????? ???????? ???????? ???????????????? ????????? ?????????. ???????? ???????? ???????????????? ???????? ??????, ?? ????????????
??????, ?????????? 45 ??/(?·K).
? ?????? ?????????????? ?????????? ? ????????? ????????? ?????? ??????????? ??????????? ????????? ?? ??????? (2) ???????? ? ????????? ???????????:
ZTGaAs
0.05 �10 6 ;
ZTpor (GaAs)
(6)
4 � 10 6 .
(7)
????????????????? ???????????? ?????????????? ????? ???????? ????????? ?????????????? ????????????? ??????????????, ??? ???????? ? ????????????? ?????????? ???????????? ???????. ? ????? ?????? ??????????? ????????? GaAs, ??????????? ????????????????? ??????????, ????????? ??????????? ????????? GaAs ? 80 ???. ?????? ????????, ??? ?
??????????? ??????? ????????? ???? ??????????? ??????? ????? ??????????, ?.?. ??????????# 662 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ??????????? ?????????????????? ??????????? ? ?????????????? ????????????????? ?????
?????? ????????? ?????????????? ?? ??????? ?????? ???????????????? ????????? ?????????
??? ?? ????? ???????????? ????????? ??????????????????.
????????? ??????????? ?????????????????? ????????? ???????????? ????????? ?????????????????? ??????????????????? ??????????.
??????????
??????????? ??????????? ???????? ??????????????????? ???????? ?? ?????? ????????
«?????????????????????? ?????????????». ? ??????? ?????????????????? ?????? ??????????? ??????? Si/por-Si ? GaAs/por-GaAs, ?????????? ???????????? ??????? ? ?????????? ??????????? ??? ???? ??????????. ???????????, ??? ??????? ? ???????? ????????? ?????? GaAs/por-GaAs, por-GaAs/por-GaAs, ? ????? por-GaAs/Si ??????????????? ??????????
????????????? ??????? ???????????? ???????? ??????????????????? ?????????? (GaAs/
GaAs, GaAs/Si). ?????? ?????, ??? ????????????????? ???????????? ? ?????????????? ?????????????? ????? ???????? ????????? ?????????????? ????????????? ??????????, ??? ???????? ? ????????????? ?????????? ???????????? ???????. ??????????????, ???????????
por-GaAs, ??????????? ????????????????? ??????????, ????????? ??????????? ?????????
GaAs ? 80 ???.
?????? ??????????
[1] ????? ?. ?. ????????????????? ?????????????. ?.: ???-?? ?? ????, 1956.
[2] ??????? ?., ???????? ?., ???????? ?., ???????? ?. // ?????????????. 2010. ???. 1.
?. 24?26.
[3] ???????? ?. ?., ?????? ?. ?. // ???, 2010. ?. 180. ? 8.
[4] Venkatasubramanian R. et al. // Nature 413, 597 (2001).
[5] Heremans, J. P. et al. // Phys. Rev. Lett. 88 216801 (2002).
[6] Boukai A. et al. // Nature 451, 168 (2008).
[7] Shi X. et al. // Appl. Phys. Lett. 84 2301 (2004).
[8] Harman T. C. et al. // Science 297 2229 (2002).
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ??????????? ?????????????????? ??????????? ? ?????????????? ????????????????? ?????
Thermoelectric Quality Factor
in Low-Dimensional Semiconductor Medium
Tamara N. Patrusheva,
Sergei A. Podorozhnyak and Galina N. Shelovanova
Siberian Federal University,
79 Svobodny, Krasnoyarsk, 660041 Russia
Thermoelectric characteristics of semiconductor systems that can be used to build thermoelectric
converters were investigated. The Seebeck coefficient and the quality factor in the systems ? porous
semiconductor ? semiconductor? were experimentally studied and calculated. It have been shown
that the electrochemical treatment of semiconductors causes the changes in the structure and energy
characteristics of the materials leading to a multiple increase of the Seebeck coefficient and quality
factor of thermoelectric systems.
Keywords: thermoelectricity, Seebeck coefficient, low-dimensional medium, gallium arsenide,
silicon.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 6 (2013 6) 665-673
~~~
??? 548/54
??????? ???????????????
?? ??????? ??????????????? ??????? ?????????
?.?. ??????* (??????????),
?.?. ???????, ?.?. ????????
????????? ??????????? ???????????,
?????? 660041, ??????????, ??. ?????????, 79
Received 18.04.2013, received in revised form 26.07.2013, accepted 14.08.2013
??????? ??????? ??????????????? ????????? ?? ????????? ??? ??????-???????????? ???????.
???????? ??????? ????????????? ?????? ?????????? ? ????????????????????? ?????????
????? ????????? ??????????? ?? ???????? ???????????? «????????????201?». ?????????????
?????? ????????? ????? ??????????????? ? ??????????? ???????? ?-3 ???????????? ?????
???????????. ????????? ?????????? ????????? ????????????? ? ?????????? ?????????
?????????? ?????????.
???????? ?????: ???????????????, ????????.
?????? ?????????? ??????? ????????????,
??????? ??????????? ????, ???????????
????????
???????? ?????? ??? ??????????? ???????? ???????? ????????. ??? ???????? ??????
?? ???????????????, ????????????? ? ????????????? ?????????? ???????????. ? ??? ?????????
??????? ? ?????????????????? ???????, ???????? ?? ??????? ????????? ? ???????? ??????????? Al2O3 ? ???????????, ???? ????????????? ?????? (???), ??????????????? ????????? ????????? ??? ??????????????? ? ???????? ? ?????????????; ???????? ?????????, ????????????
??????????? ??????? ????????? ??? ?????????; ???????? ??????????? ? ?????????; ???????????????? ? ?????? ?????????.
??????? (???. habitus) ? ??????? ????? ????????? [1]. ??????????????? ????????? ????????? ?????????? Al2O3 ????? ?????????? ?????????????? ???????? [2]. ? ?????????? ????????? ???????????? ?????????????? ? ??????????????? ???????, ?????????????? ?? ???. 1 [3].
???????????????? ???????????? ?????? ???????????????? ?????????? Al2O3 ? ??????????????. ??????????????? ????????? ??????? ???????????? ????? ?????????? ??????????
???????? ?? ?????? ?????????, ??? ????? ?????????????? ?????? ??????? ????????? ?????????
Al3+ ????? ???????, ??? ? ????? ???? ??????????????? ????, ????????????????? ????????????
??? 3-?? ??????? ????????? ????????, ??? ??????????? ???????? ?????????? ????? ??????,
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: olga_yushkova_1954@mail.ru
# 665 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????? (??????????), ?.?. ???????? ??????? ??????????????? ?? ??????? ??????????????? ????????
?
?
?
???. 1. ??????????????? ????????? ??????? Al2O3; ? ? ?????????? ???? (???????? ????? 63 ?? ??????
Al); ? ? ??????? ?? ??????????? ??????? Al ? ????????? ?????????; ? ? ?????? ????????????????
?????? R-3c c ??????????? ?? ???? ??????? ???????? ? ????????? (???????? ???????? ?????? ??????
????????) [3]
???????? ?????????? ???? (???. 1?). ????????? ??????????? ?????????? ?????????? ????????, ? ??????? ?????????????? ??????? ????????????? ??? ???????????????, ? ????????????
??????????? ????? ??? Z ????? ??????????? ??????????? ???? ?????, ?????????? ??????? Al
? ?????? ?????????? ? ????????? (???. 1?) [3].
???? ????????? ?????? ??????? ?????? ? ???? ????????, ?????????? ???????????????
???? (62 ? ????????? ??????). ?????? ??????????? ??????????????? ???? ??????? ??
????????? ? ???????????, ??? ?? ??? ? ????????? ?-???????, ???????????? R-???????.
?????? ??????????? ????? ?????? ???????? ????????????????? ????? ?? ?????? ????????? ??????????? ????? ???????? ? ???????????? ?????? ? ??????????? R-?????????? ???
???? ?????????. ? ????? ?? ???????? ????????? ??????? ?????????? ????? ??????????? ?
????? ??????????? ?????. ??????? ? ????????? ??????? ???????????? ???????????? ?????????? ??????????? ????????? ? ?????????? ????????? ?? ???????????????? ?????? Rc,
??????????? ????????? ????????? ????????. ????? ???????? ? ????????? ????????
?????????????? ?????????? ??????? ????? (???. 1?), ??? ???? ????? ???????? ????????????? ?? ???? 3-?? ??????? [3].
??????????, ??? ???????, ?????????? ?? ?????? ????????, ???????? ???????? ???????.
# 666 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????? (??????????), ?.?. ???????? ??????? ??????????????? ?? ??????? ??????????????? ????????
????????? ? ??????
????????? ???????????? ???????? ????????? (???????????????) ???????? ????????????? ???????????? ????????? «?-00 ?» ? ????????????? ???????? (????? ???????????).
?????????? ???? ????????? ???????? ???? 25389-93 (??? 802-76), ????????????? ?
?????????? ?? ???????? ????, ???????????, ??????? ????? ???? ? ???????? ?????? 0,200 ??,
????????.
?????? ????????? «?-00 ?». ?? ??????????? ??????????? ??????? ?????????? ????????
? ?????? ???????? ? ????????, % ????.: SiO2 ? 0,0150,023; Fe2O3 ? 0,0170,022; P2O5 ? 0,0010,002;
Na2O + K 2O ? 0,30,4; H2O ? 0,012,2; ??? ? 0,571,66. ????? ? 638 ? 649 ????????? % ????.:
TiO2 ? 0,004; Cr2O3 ? MnO ? 0,001, V2O5 ? 0,005 ? Ga ? 0,008.
?????????? ?????? ?????????????? ????????? ??, ? % ????.: SiO2 ? 0,023; Fe2O3 ? 0,022;
P2O5 ? 0,002; Na2O + K 2O ? 0,32 + 0,010; H2O ? 2,2; ??? ? 1,66.
???? ????????????? ?????? (???) ????????? 32 ?, ???????? ??????????? ? 69 ?2/?; ?????????? ?-???? ? 2,2 %, ???????? ????????? ? 1,1 ?/??3.
??? ?? ????????? ????????? ???????? ?????????????? ????????: ??????????? ?-3
[4, 5] ??????????? ???????? (???. 2), ? ?????????? ?-3. ????? ????????? ?????????? ????????? ???? ???. ?????? ??????????????? ??????? ? ????????? ?????? ??????? ? ???????????? ?????????.
?-3 ? ??????????????????????? ??????? (???. 2) ? ????? ?????????????? ??????????,
???????????? ?????? ????: ??????????? ? ?????????? ?? ????????? ??????????. ????????
??????? ???????? ????? ???????????, ??????????????? ???????? ??????? ?? ???? ?????????, ?????? ????????? ?????у?, ?????????????? «???????????» ???????? ????????? ? ??????. ? ??????? ??????????? ???????? ????? ??????? ??? (? ????? ?????? ???????? ????
????????? 3 ??, ?????? ??????? ??? (???= 1000 ?) ? ??????? ????????? ?????? (m?). ??????? ???? ???????? 60 % ?????? ??????? ??????.
?????????? ???????? ??????? ?? ???? ????????? ?????????? 425 ??/???. ???????? ???????????????? ?-3 ????? 2,8 ???. ????? ?? ???????? ????????? ?? ????????, ???????? ?? ??????? ??? ? ?????????? ???????.
???. 2. ?????????????? ????? ?????? ??????????? ???????? ?-3: R ? r ? ??????? ?????? ? ????????;
W ? w ? ??????? ???????? ???????? ?????? ? ????????; ? ? ? ? ?????? ???????? ?????? ? ????????
# 667 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????? (??????????), ?.?. ???????? ??????? ??????????????? ?? ??????? ??????????????? ????????
???. 3. ????? ??????? «???????????» ?????? 201?
??? ?????????? ??????????? ????????? ?? ??????????? ?????? «???????????» ??????
201? (???. 3) [6] ?????????? ?????????, ?????????? ?????????? ??????????? ????? ?????? ?
?????????? ?????? ?????????, ?????????????? ? ??????? ??????????? ??????????? ???????
(???), ?????????? 74 ????????.
??? ???????????? ????????????? ????????? ????????????? ??????????? ????????? ???
38 ????????? ????? ?????????, ? ????? ??????????? ????????? ? ????????????? ????????????
(????????????? ?????). ??????? ? ??? ??????????? ? ??????? ??????????????? ????????? ?
????? ?????????? ?????????? ???????? ?? ???? ???????-????????? ???????????????, ??? ????????????? ? ???????? ???, ????? ??????? ????????? ?????????? ? ?????????.
???????????? ? ???? ???????????? ???????? ??????????? ????????? ?????????? ? ?????????? ????????, ????????? ?????? 40 ??. ?? ????? ???????????? ??? ??????? ????????????
????????? ???????? ????? ???????? ????? ????????? ???, ????????? ???? ???????? ?????? ???????? ?????????? ?????? ?????????? ? ????????????? ?????? ?? ????????.
?????????? ???????, ?????????????? ????? ??????? ???? ?????? ??????? ??????? (????????), ????????? ? ????? ?????????? ? ?????? ?? ??????? ? ?? ??????.
?????? ?????????
????????? ??????-???????????? ??????? ????????? ????????? ???????? ???????????
????????? ? ????????? ???????:
? ?????????????????? ?????? ?????????? ????????? ???????? ??????? ??????? ??
???? 25469-93 (??? 2926-74) ? ????????, ? ??????????: ????????????????????? ? (????? ??????????? ? ??????????????) ???????? ?? ??????????? ?????? «???????????»
?????? 201 ? (???. 3) ? ???? ???????????? ????????????. ???????? ????? ?? ???????
??????? ???????? ?????????? ??-?? ????????????? [6].
# 668 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????? (??????????), ?.?. ???????? ??????? ??????????????? ?? ??????? ??????????????? ????????
? ?????????? ? ? Al2O3 ?????????? ??????????????????? ??????? ?? ???? 25733-83.
? ??????????????? ?????? (???) ????????? ? ?????????????? ?????????????? ????????????? ????? «????-3» ?? (Cu K?) ????????? ?? ????????? ???????? ???????????
????? 800 ??/? (2 ??????? ? ??????). ?????????????? ?????????? (d) ????????????
?? ???????? ??????? [7], ? ??????????? ????????????? (?????????????) ????????? ?
?????????????? ???????? ???????????? ????????? ASTM [7].
? ?????? ???????? ? ?????????????? ??????? ???????????????? ? ??????????????
?????????? ????????? ?? ????????? ??????????? ?????????? «???-100».
??????????
?????????? ????????? ??????????? ????????? ???????????? ?? ???. 4 ? ? ????. 1 ? 2.
?? ??????? 4 ?? ??? «?» ??????? ????????????????? ??????????? ??????????? ?? ?????????? ????????, ?; ?? ??? «?» ? ??????????? ??????? ???? ?????? ?? ?? ????????: «?» ? ??????
?
?
???. 4. ???????? ?????? ????????????? ?????? ????????? ?? ??????? (?????????? «??????????? 201-?»).
?? ??? «?» ? ????????????????? ??????????? ??????????? (??), ?; ?? ??? «?» ? ??????????? ??????? ????
?????? ?? ?? ????????; «?» ? ?????? ????????? ??????????? ????? ?? ?????????????????? ? ?? = 5-60 ?;
«?» ? ?????? ????????? ??????????? ????? ?? ?????????????????? ? ?? = 1- 5 ???
# 669 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????? (??????????), ?.?. ???????? ??????? ??????????????? ?? ??????? ??????????????? ????????
??????? 1. ?????????? ?????? ?? ???????? ??????? ??? ????????? ? ?-3 (??????? 10 ?, ??????? ???
1000 ?, ????? ?????) ?? ??? ?????????????????? ??????, %.
???,
?
0
???????? ??????? ??????, ???
- 250
+ 200
- 200
+ 150
-150
+125
- 125+
100
-100
+ 80
- 80
+63
- 63
+45
- 45
+32
- 32
+ 20
- 20
+ 10
- 10
+0
1,3
4,8
6,3
11,6
14,5
17,0
22,4
13,0
5,6
1,8
1,7
5
0
0
0
0
0
0,6
3,0
6,5
15,8
19,6
54,5
10
0
0
0
0
0,4
0,9
2,5
3,8
12,7
18,9
60,8
20
0
0
0
0,3
0,6
1,4
3,8
5,4
13,5
17,6
57,4
30
0
0
0
0,2
0,6
1,3
3,6
5,4
14,2
19,6
55,1
40
0
0
0
0,4
0,7
1,7
4,6
6,9
15,6
18,8
51,3
50
0
0
0
0,2
0,8
1,7
4,4
6,4
14,9
18,5
53,1
60
0
0
0
0,3
0,6
1,4
3,9
5,4
13,7
18,3
56,4
1200
0
0
0,2
0,3
0,7
1,4
3,7
4,8
11,6
15,8
61,5
180
0
0
0
0,3
0,7
1,2
2,6
4,5
9,7
15,9
65,1
240
0
0
0,2
0,3
0,6
1,3
3,0
4,6
10,4
16,0
63,6
300
0
0
0
0,2
0,5
1,3
3,5
4,4
10,8
15,9
63,4
??????? 2. ?????????? ??????????? ??????????? ??????????? ?????????, ??????????? ?? ????????
??????????? ?????? «??????????? 201 C»
???????? ???????? ??????, ???
?????????? ??????????? ??? ???????, % ????.
+100
-100+63
-63+32
-32
2,4
2,1
1,7
1,2
????????? ??????????? ????? ?? ?????????????????? ? ?? = 5; 10; 20; 30; 40; 50; 60 ?; «?» ?
?????? ????????? ??????????? ????? ?? ?????????????????? ? ?? = 1 ? 5 ???.
???? ????????? ???????? ?????????????? ?????????? ??? ???????? ??? ????????? ??
??????????????????? ????????? ASTM [8]:
? ? Al2O3 (ASTM, 46-1212) 0,25508; 0,16015; 0,20853; 0,34797; 0,174; 0,12391 (??);
? ? Al2O3 (ASTM, 29-0063) 0,1400; 0,1980; 0,2390; 0,280; 0,228; 0,453 (??);
? ? Al2O3 (ASTM, 29-1486) 0,1400; 0,1981; 0,2390; 0,280; 0,2285; 0,433 (??);
? ? Al2O3 (ASTM, 46-1131) 0,13911; 0,13959(0.4.1); 0,13959(2.2.12); 0,2728; 0,1986; 0,2006 (??);
? ? Al2O3 (ASTM, 34-0493) 0,1391; 0,240; 0,2113; 0,227 (??).
?????????? ???????????
?? ??????????? ??? ???????? ????? ??????????????? ???????? ??????? ?? ??????????? Al2O3:
?) ?????????????? (? ? Al 2O3 ? ASTM, 46-1131), ????????????? ? ???????????????
???????????? (d) ??????????? ??????? ????????? ?? ??????????????, ??????? 0,1390;
0,1401; 0,1988; 0,1952; 0,238; 0,228 ?? ? ????? ??????? ???????? ?? ?????????????? ?
d = 0,1533 ??;
# 670 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????? (??????????), ?.?. ???????? ??????? ??????????????? ?? ??????? ??????????????? ????????
?) ?????????? (? ? Al2O3 ? ASTM, 2963) ? d = 0,1401; 0,1988; 0,238; 0,228 ?? (?? ????????
????????? ? ???????? ?-Al2O3);
?) ??????????????? (? ? Al2O3 ? ASTM, 46-1212) ? d = 0,254; 0,209; 0,1598; 0,1732 ?
0,345 ??.
????? ?? ? ?-3 ????????????? ??????????? ????????? ?? ??????????????, ????????
?????? ???????? ? d = 0,1390 ??, ????? ??????. ??????? ????????? ?????????? ???????????
?? ?????????????? ??????????.
?????????? ??????????-???????????????? ???????????? ????????? (???. 5) ????????, ???
? ???????? ????????? ??? ??????? ?????? ????????????????. ?? ????? ?????????????, ??????????? ? ?????????????? ???????? ? ?????? ?????????? ??? ??????? ? ?????? ??????????
???. ???? ? ???????? ??????? ??? ?????????? ?? ???????? ? ?????????? ????????, ?? ? ?????????????? ????? ??? ??????, ???????????? ??????? ?? ????????? ? ??????? ? ????????
(???. 5?).
??????????-???????????????? ?????? ???????????? ??????? ??????? ????????? ??????? (???. 5).
???? ??? ??????? ?????????? ????????? ?????, ??? ?????? ???????? ?????????? ?
??????? ???????? ? ??????? ? ????????.
??? ??????????????? ????????? ? ????????? ??????? ?? 5 ?? 300 ? ????????????? ??????
?? ??????? ???????????? ????? ???????????? ??????? ? ????? ??????, ???????????? ??????? ?? ??????? ?????????, ? ?????? ????? 10 ?; 10-20 ? ? 20-80 ?. ?????????? ???? ??????
??????????? ? ???????????? ? ?????? [9].
????????????? ?????? ?? ??????? ????????????, ?????????????? ?? ???. 4, ?????? [8] ?????????: ?) ????????????? ??????, ?????????????? ?? n-????? ? ?? ???????? ????? (n+1) -?????;
?) ????????? ????????? ????????? ?????????? ? ????????? ????? ??????? ?????? ????????????? ???????? (?????? ? ????? ??????; ?????? ? ? ??????), ??????? ? ?????????? ?????? ????? ???????; ?) ???????? ??????? ??????? ???????? ???????????? ?????? ? ???? ??? ????????? ?????, ????? ???????????? ????? ????????? ?у?????? ??????? ??????????? ????????.
?????? [10] ?????????, ??? ?????????? ????????? ??????????? ? ??????????? ???????
? ????????????? ???? ? ? ????? ??????????? ?????????? ???????? ? ???????????????? ???-
?)
?)
???. 5. ??????????????? ?????????: ?) ? ?????????; ?) ? ??????????????? ? ?-3 ? ????? ?????? ?
????????? ????? ? ??????? 10 ? Ч 3000 ? Ч 1500
# 671 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????? (??????????), ?.?. ???????? ??????? ??????????????? ?? ??????? ??????????????? ????????
?????????, ????? ???: ?) ?????????? ??????? ??? ???????????, ?) ??????-?????????? ??????????? ??? ???????????, ???????????? ??? ???????? ? ?????? ???????????, ??????????? ??????????????? ???????, ????????? ???????????????? ????? ???? Al ? ???????????????
??????? [10].
????????? ???????????? ???????????? ????? ??????????? ? ? ?????? ??????? (0?10 ?)
??? ????????? ??????????? ??????????? ? ??????????? ??????? ???????? ? 10?20 ? ? ?????????? ?????? ?? ?????????????? ????????; ? 20?80 ? ? ????????????? ??????, ????????????
??? ?????????? ?? ??????????????? ????????.
???????????? ??????????????? ?? ? ??????? ????????, ???????????? ? ???????, ????????????, ??? ????????? ???????????? ????? ??????????? ?? ???? ??????????? ?????????
???????? ??? ??????????????? ?????????, ? ?????? ??????? ????????? ??????, ? ? ???????? ?
???? ?????????. ? ??????? ???????? ????????? ?????????, ? ? ????????? ?????????? ???????? ???????? ????? ?????????????? ? ??????? ??? ???????.
??????????
?????????? ??????????? ??????????????????? ??????? ??????????????????????? ????????? ???????????? ????? ?????????? (0?300 ?) ? ?????????? ?????????????? ??????.
?????????? ????????? ????? ?? (? ?????????????????? ?? 5 ?? 60 ? ? ?? 1 ?? 5 ???,
???????????? ?? ???????? ???????????? «??????????? 201-?», ??????????? ????? ??????????? ????????????? ??????: ????? 10 ?; 10?20 ? 20?80 ? (? ??????????? ??????? ???????????
??????????? ?? ???????? ? ???????).
?????????? ?????????????? ?????? ????????, ??? ???????????? ????????? ??????? Al2O3
? ??????????????????????? ???????? ???????????? ???? ???????? ? ????????????? ????????? ??????? ?????????, ??????? ????? ?????????, ????????? ?????? ????????????? ??????,
?????????? ? ??????? ????????? ???????????? «??????????? 201-?». ?????????? ??? ??????? ????????????? ?????? ????????? ????? ????????? ??????????? ??? ????????? ???????????: ? 1-? ??????? ? ??????? ?????????; ?? 2-? ??????? ? ?????????? ?????? ?? ??????????????
????????; ? 3-? ? ?? ??????????????? ????????.
??????
?????????? ???????????? ?????????, ??? ?? ? ??????????? ???????? ?-3 ???????? ?
??????????? ???? ?????????? ????????????? ??????, ?????????? ??? ?????????? ??? ????????? ???????????, ?????????? ?? ????????????????? ??.
?????? ???????? ????????????? ??????????????? ?????????? ???????????? ???????
???? ?????? ?? ?? ???????? ??? ???? ???????? ????????????????? ??, ?? ?????????? ???
????????????????? ??????????? ???????????.
?? ??????????? ?????? ?????? ????? ????????????, ??? ??? ??????????????? ?????????
? ????????? ??????? ?? 5 ?? 300 ? ????????????? ?????? ????????? ?? ???????? ????????????
????? ???????????? ??????? ? ????? ??????, ???????????? ??????? ?? ??????? ?????????, ? ?????? ? ????? 10 ? ? ????????????? ?????????, ??????? ???????????? ??? ????????? ??????????? ??????????? ?? ????????? ???????; ????? 10?20 ? ????????? (??? ?????????
??????????? ?????????? ???????) ? ????????????? ??????, ???????????? ??? ?????????? ??
# 672 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????? (??????????), ?.?. ???????? ??????? ??????????????? ?? ??????? ??????????????? ????????
?????????????? ????????, ? 20?80 ? ? ????????????? ??????, ???????????? ??? ??????????
?? ??????????????? ????????.
?????? ?????????? ????? ??????????? ??? ???????????? ??????? ?????????????????
??????????????? ?? ?????????????????? ?????? ?????????.
?????? ??????????
[1] ????????? ????????????????? ???????. ?.: ???. ????????????, 1981. 1600 ?.
[2] ??????????? ?.?. ???????????????. ?.: ????. ??., 1984. 376 ?.
[3] ??????-???????? ?.?. ??????????????? ? ??????????????: ??????? ?.: ???, 2005.
592 ?.
[4] ??????? ?.?. // ???????????????? ??????? ??? ??????????? ???????????. ???????????: ???? ?? ?? ????. 1971. ?. 2340.
[5] ??????? ?.?. // ??????-?????????? ????????? ????????? ? ???????? ???????????? ???????????. ???????????: ???? ?? ?? ????, 1966. ?. 525.
[6] ?????????? ?????? «???????????», ?????? 201 ?. ??????????? ???????? ? ??????????
?? ????????????. ???., 2000. ?. 201.
[7] ?????? ?.?. ??????? ?????????????? ?????????? (?????????, ??????, ????????????
? ?????????? ?????). ?.: ?????, 1966. ?. 2. 360 ?.
[8] ASTM. Diffraction date cards and alphabetical and grouped numerical index of X-ray
diffraction date. Philadelphia, 1946?1985.
[9] ?????????, ?.?. // ???????? ?? ?? ????. ????? ?????????? ????, 1988. ? 5. ???. 2.
?. 51?53.
[10] ???????? ?. ?. // ??????. 1979. ? 6. ?. 60?75.
The Mechanical Activation Influence
on the Habit of Alumina Lattice
Olga V. Yushkova (Belonogova),
Valentina I. Anikina and Angelina A. Kovaleva
Siberian Federal University
79 Svobodny, Krasnoyarsk, 660041 Russia
The effect of mechanical activation of alumina on its physical and mechanical properties has been
studied . It was shown that spontaneous aggregation of particles of activated alumina suppress dusting.
Distribution of particles primary and mechanoactivated alumina after measurement granulometric
size composition on laser graininess meter « ?icrosizer ? 201C» is shown and difference of particles
distribution of is established. Distribution of particles of alumina after mechanical activation in
planetary mill ?-3 is presented by three areas. The explanation of the mechanism of distribution as a
result of crystals variation of alumina is perofrmed.
Keywords: mechanical activation, alumina.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 6 (2013 6) 674-679
~~~
??? 621.315.592
?????????????? ??????? ???? ? ?????????
? ???????? ???????????
?????????????? ????????
?.?. ??????????, ?.?. ????????????,
?.?. ??????????*, ?.?. ?????????, ?.?. ??????????
?
??? «????????»
?????? 660027, ??????????, ???????????? ??????, 1
?
????????? ??????????? ???????????
?????? 660041, ??????????, ??. ?????????, 79
Received 03.04.2013, received in revised form 26.07.2013, accepted 08.08.2013
???????? ????????????????? ?????? ?????????????? ??????? ???? ? ????????? ? ????
??????????? ?????????????? ????????. ??????????? ???????? ????? ?????????? ?
????? ????????? ???? ? ?????????????? Ge ? ????? ????????. ??????????? ???????????
???????????? ????????? ? ??????? ?????????????????? ???????? ? ??????????? ?????????
????????? ? ???????? ???? ? ??????????? ????????? ???????? ???? ? ????????. ??????????
????????????????? ?????? ?????????????? ????????? ? ????? ? ??????? ????? ? ?????????
????????.
???????? ?????: ????????, ?????????????, ???????????? ?????????, ???????, ??????? ????,
??????????????, ????????????????? ??????.
????????
?? ?????????? ???? ??????? ???????? ?????????? ??????????????? ???????? ?????????? ????????? ??? ?????????????? ???????? ?? ?????? ??? ?????, ??? ??? ???????. ?? ????????? ??????? ??????????????? ???? ??? ????, ??? ? ?????????? Ge, ?????????? ?? ?????? ????????????, ???????????? ????????? ????????? ? ???????? 1016 ч 1017 ??-3. ?????? ? ???, ????????
? ???????? ???????? ????? ?? ???????? ????????, ???????????? ????????? ????????????,
????? ????? ????????????? ????????? ??????, ??????????? ?????????????, ?????????????
?????????????? [1].
? ???????? ??????????? ????????????? ??????? ???????? ????????????? ?? ?????????
???????? ???? ????? ????????? (1210 ?) ? ??? ??????????? ?????????? ~ 1223 ?.
????? ???? ???? ????????, ??? ? ?????????? ? ?????? ????????? ????? ?????????? ??????? ???????? GeO2, ???????? ??????????? ???????? PO ( GeO ) ??? ??????????? ???????????
2
2
????????? Ge ?????????? 1,66Ч10 ?15 ??? (1,66Ч10 ?10 ??) [2]. ??? ????????, ??? ??? ???????????
???????? ????????? ? ??????? ???? ???? ??????? ???????? ???????? ?????????? ? ?? ??????*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: shimanaf@mail.ru
# 674 #
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?.?. ?????????, ?.?. ???????????? ?????????????? ??????? ???? ? ????????? ? ???????? ????????????
????? ???????? ?????????? GeO2. ???? ??????????? ???????? ????????? ?????? ?????????
????????, ???????? ???????????? ? ???????? ? ???????????? ????????????? ????????, ? ??????? ?? ????????? ? ????????? ?????????.
???????????? GeO2 ????? ????????????? ? ??????????? ???????? ???????? ??????????,
??????? ? ??? ???????????? ?????????, ??? ???????? ? ????????? ???????????? ??????????????? ????????? ???????? ? ??????????? ??????????, ?? ??? ????????? ????? ?????? ?????? [3]. ???????????? ? ???????? ????????, ? ???? ???????, ???????? ?????????????????
???????? ?????????? ? ?? ????????????? ????????????, ???????????? ??????????????????
??? ??????? ????????????? ???????? ????????. ?????? ?? ?????, ???????????? ????????? ?
?????????? ????????, ???????????? ??? ???????????? ??????????? ????????????????? ????????, ?? ??????? ??????? ????? [1, 3, 4], ?? ?????? ????????? «?????» 1015 ??-3.
???????? ?????????? «???????????» ???????? Ge ???????? ????????? ???????? ???????
?????. ??????? ????? ?????? ???? ????????????????? ?????? ?????????????? ??????? ???? ?
????????? ???????? ? ???????? ??????????? ??????????????.
??????????? ?????????????? ????????
? ????? ????????? ????
??????????? ?????????????? ???????? ????????????, ??? ???????, ? ????? ?????????
???? (Ar, He) ??? ????????, ?????? ???????????? [1]. ? ????? ? ???? ???????????? ???????
?????????????? ??????????? ?????????, ????????????? ? ???????? ????, ? ????????? Ge ?
???????????? ??????????? ???????????? ?????????, ????????????? ? ?????????????, ? ???????????? ???????? ????????? ( PO ) ? ??????? ????.
2
? ??????????? ??????????? ????????????? ????????? ? ??????? ???????? ??????????, ???
???????? ?? ???. 1 [1]. ??? ??????????? ????????? Ge, ?????? 1210 ?, ??? ?????????? 2,2Ч1018 ??-3
???. 1. ????????????? ????????? ? ???????? [1]
# 675 #
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?.?. ?????????, ?.?. ???????????? ?????????????? ??????? ???? ? ????????? ? ???????? ????????????
??? 6,7Ч10-3 ??. %. ??????????? ??????????? ????????????? ????????? ? ???????? ????? 0,45
[5], ??????????????, ????????????? ?2 ? ?????? Ge ??? ?????? ??????????? 14,8Ч10-3 ??. %.
??????? ????????, ??? ? ?????????? ??????????? ????????????? ????????? ? ??????
???????? ????? ?????????? ? ????????? 1 ??. % ??? 1273 ? [6]. ?????? ?????????????? ?2 ?
????????? Ge ???????? ???? ??? ??????????? ??????????? ?????????????, ?.?. ??? 1223 ?.
???????????? ????????? ??? ?????? ???????????, ???????????? ??????? ?????????????, ????????? ~ 0,2 ??. %, ??? ????????????? ??????? ???? ????????? ??=0,002.
????????????????? ???????? ??????? G??? ??????? ????????????; ??? ???? ????? ?
???????? ????? ???? ??????????? ????????? ???????? ? ?????????, ??????, ??? ? ??????
???????? ???????????? ?????? ????? ??????? GeO ? ??? ????????? ????????????? ????????? ???XGeO =0,002. ????? ????????? ?? ??????????? ?? ????????????? ?????????? ??????????? [7]. ?? ???? ?????????? ?????????? ????????? ? ???????? ??????? ??????????
??????????? Ge, ??? XGeO ? 0,002 ?????????? ????????? ????????, ? ?????????????????
?????????? GeO (?GeO) ??? ???? ????? ??????? ?????? ??????? (?GeO =1) [7]. ? ?????? ??????????? ? ??????? ????????????? ?????????? GeO ???????? ???????? ???????? ??? ???????????? ? ????????, ?.?.
?GeO = ?GeO Ч XGeO,
(1)
??? ?GeO ? ??????????? ????????????????? ?????????? GeO.
????? ???????, ??????????? ????????????????? ?????????? ?GeO ???????????? ????????????
?GeO = 1/0,002 = 500,
??????????????, ????????? (1) ????????? ????????? ???:
?GeO = 500 Ч XGeO.
(2)
????????? ???????? ???????????? ?? ???????
2[GeO] = 2[Ge] + O2,
(3)
??? ??????? ???????? ????????? ??????????? ??????? ?????? ??? ??????????? ???????????
??????????
?Go1223 K = 302540 ??.
???????? ??????????? ?????????? ???????? ? ? 2 ( 2GeO) , ???????????? ?? ????????? ???????????? ??????????? ???????? 'G o2 GeO RT ln PO2 ( 2 GeO) , ??? ????????? ??????????? ?????
1,18Ч10 ?13 ??? (1,18Ч10 ?8 ??).
??? ???????????? ????????? ????????? ? ???????? ????????? ????????? ??????????
??????? (3) ????? ???
K
PO' 2 ( 2 GeO )
2
D GeO
PO 2 ( 2 GeO ) ,
??????
# 676 #
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?.?. ?????????, ?.?. ???????????? ?????????????? ??????? ???? ? ????????? ? ???????? ????????????
PO' 2 ( 2 GeO )
2
PO 2 ( 2 GeO ) u D GeO
,
'
??? PO 2 ( 2 GeO ) ? ???????? ????????? ??? ????????? ????????.
? ?????? ????????? (2) ???????? ????????? ??? ????????? Ge ??? ??????????? 1223 ?
??????????? ??????????
2
1,18 u 10 13 500 u X GeO ??? PO' 2 ( 2GeO)
PO' 2 ( GeO )
2
2,95 u108 u X GeO
.
(4)
????????? (4) ????????? ?????????? ??????????? ???????? ????????? ? ??????? ????, ??????????? ??? ????????? ?????????? Ge ? ????????????? ????????? ?? ???? «??????» 1015 ??-3
??? 2,28Ч10 -6 ??. % [Oi], ??????? ?????? ???? ?????? ???, ? ??????? ??????, ????? ????????
'
????????? ??? ?????? ????????? PO 2 ( 2 GeO ) , ??????
PO' 2 ( 2 GeO)
2,95 u10 8 2,28 u10 8
2
1,53 u10 23 ??? ( 1,53 u10 18 ?? ).
????? ???????, ??? ?????????? ???????????? ????????? ? ???????? < 1015 ??-3 ??????????? ???????? ????????? ? ??????? ???? ?????? ???? ???? ???????? 1,53Ч10 -23 ??? (1,53Ч10 -18 ??).
????? ????? ???????? ????? ???????? ??????? ????????? ???? ?? ?????????.
?????????????? ???????? ? ????? ????????
????????? ???????? ? ?????? ??????????? ????????? ???????????? ????? ? ????? ???????? [1]. ???????, ???? ????? ??????? ???????? ? ?????????, ??? ????????, ???????? ??? ????
?????????????. ??? ??????? ??????????? ???????? ?????????
[GeO] + H2 = [Ge] + H2O,
(5)
????????? ??????????? ??????? ?????? ? ????????? ?????????? ? ??? ??????????? 1223 ?
????? ????????? ????????:
?G?1223 ? = -38320 ??, ?1223 ? = 43,4.
??? ??????????? ????????? ???????? ???????? ??????????? ??????, ?????????????, ????? ??????? ?Ge?1. ? ?????? ????? ????????? ????????? ?????????? ??????? (5) ????? ???
K
PH 2O
D GeO uPH 2
,
???
D GeO
PH 2O
K u PH 2
(6)
.
????????? (6) ????????? ?????????? ??????????? ??????????? ???????? ????? ???? ?
???????? ? ??????? ????, ??????????? ? ?????????? ? ????????? ??? ????????? ???? ?????????? ????????? ?? = 2,28Ч10 -8.
???? ??????????? ????????? ???????????? ??? ????? ???????? ? ???????? ??????, ?????? ????? ?????????, ?.?. PH 2O + PH 2 = 1 ??? (~ 105 ??), ? ?????? ????????? (2) ????????? (6) ????????? ????????? ???:
# 677 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ???????????? ?????????????? ??????? ???? ? ????????? ? ???????? ????????????
???. 2. ?????????? ????????? ? ???????? ? ??????????? ?? ??????????? ??????????? ???????? ????
???? ? ???????? ? ??????? ???? [1]
500 u 2,28 u 10 8
? ? 2O
(1 ? ? 2O ) u 43,4
.
(7)
??????? ????????? (7) ???? ????????? PH O = 0,0004945 ??? (~ 49,45 ??), ??? ?????????????
?????????? ~ 0,05 % ????? ????? ? ????????. ??????????? ???????? ???????? ? ??????? ????
??? ???? ?????? ? ????? ????????? PH O = 0,99950955 ??? (~ 105 ??). ???????? ?????????
???????????? ???????? ???????? ???? ? ???????????? ???????? ???????? ? ??????? ???? ?????????? lg 0,0004945 = -3,3.
?????????? ????????? ?????? ?????? ??????????? ? ?????????????????? ???????????? ??????? ?????????? ????????? ? ?????????? ???????? ? ??????????? ?? ???????????
??????????? ???????? ???? ???? ? ???????? ? ??????? ???? [1], ????? n ?? ???. 2 ????????
??????????? ????? ????????, ??? ??????????????? ? ?????????? ???????????? ????????????????? ?????? ?????????????? ??????? ???? ? ????????? ???????? ? ???????? ??????????? ?????????????.
2
2
??????????
??? ????????? ?????????????? ???????? ? ?????? ??????????? ????????? 1015 ??-3 ??
?????? ??? ??????????? ?? ?????? ???????????? ?????????? ????????? ??????????? ????????? ?? ??????? ???? ? ??????? Ge ? ??????? ??? ????? ?????????? ?????????? ????? ? ???????? ?? 0,05 ????. % ???? ??????????? ???????? ????????? ? ???????? ???? ?? 1,53Ч10 ?23 ???
(1,53Ч10 ?18 ??).
?????? ??????????
[1] Claeys Cor L., Simoen E. Germanium-based technologies: from materials to devices. Elsevier,
2007. 449 p.
[2] ????????? ?.?., ??????????? ?.?., ????????? ?.?. ? ??. // ?????? ???. ??????? ? ??????????. 2012. ? 6.
# 678 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ???????????? ?????????????? ??????? ???? ? ????????? ? ???????? ????????????
[3] Taishi T., Ohno Y., Yonenaga I. // Journal of Crystal Growth. 2009. V. 311. Issue 22. P. 4615?
4618.
[4] ????????? ?.?., ????? ?.?., ???????? ?.?. // ??????? ??????? ? ???????. 2003. ? 2. ?. 12?
17.
[5] ??????? ?.?., ??????? ?.?., ????????? ?.?. ????????, ??? ??????????. ????????????:
???. ????????? ????????? ????????? ???????????, 2002. 600 ?.
[6] ????? ?.?. ????????? ??????? ???????. ?. 2. ?.: ???????????, 1970. 474 ?.
[7] ???????? ?.?., ??????????? ?.?. ?????? ???????????????? ?????????. ?: ???????????, 1968. 244 ?.
The Interaction of the Gas Phase
with the Germanium Melt
in the Process of Crystals Growth
Oleg I. Podkopaeva,
Tatyana V. Kulakovskayaa, Aleksandr F. Shimanskiyb,
Aleksandr M. Pogodaevb, Mariya N. Vasilyevab
a
OAO «Germanium»
1 Transportniy proezd, Krasnoyarsk, 660041 Russia
b
Siberian Federal University,
79 Svobodny, Krasnoyarsk, 660041 Russia
A thermodynamic analysis of the interaction of the gas phase with the germanium melt during of crystal
growth was carried out. The processes of crystal growth in inert gas and crystallization of germanium
in a hydrogen atmosphere was considered. Quantitative relationship of oxygen concentration
in the semiconductor Ge with a PO of an inert gas and PH O in hydrogen has been established. A
2
thermodynamic model of the interaction of the gas phase with the germanium melt in the process of
crystals growth was created.
2
Keywords: germanium crystals, gas-phase, oxygen concentration, the melt, interaction, thermodynamic
analysis.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 6 (2013 6) 680-688
~~~
??? 628. 35
???????? ??????? ??????? ???,
?????????? ??????????????? ?????????????
? ????????? ???????? ?????????
?????? ???????????????, ? ???? ?? ???????
?.?. ??????????,
?.?. ??????????, ?.?. ???????*
????????? ??????????? ???????????,
?????? 660041, ??????????, ??. ?????????, 79
Received 17.12.2013, received in revised form 12.08.2013, accepted 30.08.2013
???????? ?????????? ???????????? ?????? ??????????? ????????? ???? ???????????
???????. ?? ????????? ?????????????? ??????? ? ????????????????? ???????????? ??????????
????????? ???????????????? ????, ???????????? ????????????? ??????????, ???????????
???????????? ?????? ???????? ??????-?????????? ??????? ???? ? ???????????????
????????????? ????????. ?????????? ????????????????? ???????????? ???????? ???????
???????????? ???????????????? ??????????????? ??? ?? ??????????? ???.
???????? ?????: ????, ?????????, ?????????????, ????????????-???????? ????????,
???????????, ????????????? ??????????.
????????
???? ?? ??????? ??????? ????????????? ??????????????? ??????? ? ?????????? ??????
??????????????? ? ?????? ??????? ???. ????????? ???????? ??? ???????????????? ????
??????????? ? ???????????? ?????????? ???????? ??????? ????????? ?????? ???????????????, ??? ?????????? ????????? ?????? ???????????????. ?????? ??????????? ??????????
?? ???????? ???????? ?? ????????????? ???????? ??????????, ??????????? ?????????????? ??????????? ?? ?????????? ????? ? ? ????? ?? ????????? ???????????? ??????????????
?????????? ????????? ????????? ???????????????? ??????????.
?????? ?? ???????? ??????? ??? ?????????? ????? ???????????? ??????? ?????????
????????????? ? ?? ???????????. ??? ???????, ?????? ???????? ????????????? ???????? ????????? ?????? ????? ???????????? ???????? ?? ???????????? ????????????? ??????????,
??????????, ??????? ??? ????????????????????? ???????, ? ????? ??????????? ???????.
???? ?? ???????? ??????? ?????? ????????????? ??????? ??????? ???? ? ???????????? ?????? ?????????? ????????? ???????????? ? ??????????????? ????? ??????? ? ?????. ??? ?????????????? ??? ??????? ??????? ???????? ??????? ?????????? ????????? ?? ?????? ???*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: v.a.kulagin@mail.ru
# 680 #
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?????????????? ?????.
? ???? ????? ????????? ????????????? ?????????? ? ????????? ? ???????????? ?????, ????? ???????????, ??????????????? ????????? ????????? ????????? ? ??????? ???. ??????,
???????????? ? ????????? ??????, ???????? ????? ?????? ???????? ?????????????? ??????????? ?????????? ?????, ??????????????????????? ? ??????????????????? ???????????.
???????????? ??????? ???????? ?? ????????????????? ??????????? ??????? ? ??????????????? ??????? ??????? ??????? ???, ????????? ??? ????????????? ??????????????????,
?????????????????????? ????????, ????????????? ? ?????????? ?????????????????? ???????. ????????????? ??????????????? ? ????????????????? ???????? ????????? (????????????? ??????????) ???????????? ??????????????? ????????? ???? ? ?????????? ?????????
?????????? ??????, ??????????? ? ????????????? ??????? ? ???????????? ?????????. ?????????????, ????? ? ????, ? ???????? ????? ????????? ? ??????????????? (?????????) ????????? ? ????? ??????? ????????? ????? ?????????? ?? ??????????? ????, ??????? ?????????
?????? ??? ????. ??????, ???????, ????? ?????????????? ??????????? ? ????? ???????????????? ?????????, ??????? ???????? «????? ? ????».
???????? ? ??????? ????? ??????????? ??????? ????????? ? ????? ? ??????? ???????????? ??????????? ? ???????????????? ???????? ??????? ???? ??? ??????? ?????????
(??????? 100 ???). ?????????????? ???????? ???????? ?????? ?????????? ????????, ?? ????????????? ? ??????? ??????????? ???????. ???????????? ???????? ??????? ?? ????????? ?
???????????? ??????????????? ??????, ??????????????????? ??????? ???????, ?????????????? ????????? ????????, ??????? ? ???? ?????????????? ???????? ? ??.
???????????? ??????? ?? ???????????? ???????? ????????? ????????????? ?????????
????????. ???? ?????????? ? ??????? ????? ????? ??????????? ?????????? ??? ????????
????????????, ? ????? ??????? ????????? ???? ? ????????????? ?????? ????????, ???????????? ??? ??????? ?????????. ????????? ?????????????? ????????? ???????? ?? ??????? ?
???????? ?????????? ??????????? ?? ?????????????? ????????? ?????????????? ????????? ?
72,8·10 -3 ?? 25·10 -3 ??/?2. ??????????? ??????? ????? ????? ?? ??????? ?????? ??????? ??? ?
?????????????? ????????, ??? ??????? ??????????? ??? ??????????? ????????.
????? ????????? ??????? ????????? ??????????????? ??? ? ??????? ?????????? ? ??????? ??????? ? ??????????????? ?????? ???????? ??????? ???????????? ?????????? ????????? ???????.
???????? ?????????? ?????? ????, ??????????????? ??? ??????? ??????????????? ???,
???????? ? ????, ??? ???????, ???????? ????????????, ??????-?????????? ? ?????????????
??????? ???????. ? ????????? ???????? ??????????, ??? ???????, ?????????????? ????????????? ???????????? ???????, ????? ??? ??????????, ????????????, ?????????? ? ???????.
?? ???? ??????????? ??????? ??????????????? ???????. ? ??????????? ??????-??????????
??????? ????????? ???????????? ????????? ? ??????????? ?????????? ?????????, ?????????
? ??????????? ??????????? ??? ?????????? ????????. ? ??????????? ????????????? ??????? ? ?????????, ??????????, ????????????? ????? ? ??.
?? ???????????? ??????? ?????????? ?????????? ????? ???????????, ? ??????? ??????? ? ???????????? ? ?????????????????. ?? ??????-?????????? ??????? ?????????? ???# 681 #
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??????????? ? ?. ???????????.
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?????????????? ??????? «?????????????????». ????????? ?????????????? ? ???? ???????????, ??? ???????, ?? ??????? ?????????? ?? ????????? ? ?????????? ???? ? ???????????
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???? ?????????? ?????? ?????? ??????????? ? ??????? ?????? ????????? ??? ?????????? ??????????????, ????????????? ??? ?????????? ????????? ??????? ?????????????? ???????????? ????????? ? ????????? ????, ??????????????? ??????????? ?????????? ? ??????????? ???????? ???????????????? ???????????, ????????????????? ?????? ????????????
????.
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???????????? ????????????? ?????????? 93 %. ?????? ????????????? ????? ????????? ???????
????? ?? ?????? ? ??????????????, ?? ? ? ???????????? ??????? ??????????????? ??????????????, ?????????????? ?????????? ?????? ??????????? ?????. ???????????? ?????? ???????????? ?????????????? ??????? ?? ???. 3.
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??????? ????????????? ????????? ???? ????????? ???????? ?????????????????? ???????:
? 01?05?2007; ??? ? 14.1:2:4.128-98; ??? 4.1.1262-03.
???????? ????????????? ??? ?????????? ????????? ???????? ???????????? ?????????????? (??) ? ?????? ?????????, ???????? ? ??????? ???? ????????????????? ??????? ??
??????????? «???????-02». ?????????? ????? ???????????? ? ???? ???????????? ?? ???. 4, 5,
? ????? ?????????? ?????? ???????????? ??.
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???. 2. ????????????? ???? ????? ????????????? ????????? ?119
???????????? ?????????????? ????????? ?????????????? 0,0348 ??/? ? 0,03·10 -12 ??/?, ???
???? ???, ? ?????????????, ??????????? ????? ??????? ? ????? ??????????? ????? ?????????????? ???????????.
?????? ???????? ???? ??????? ?????????? ?????? ? ??????? ????, ??????? ????????
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????????? ?? ????? ??? ????????. ?????? (?????? ??????????????? (C2H5)4Pb) ???????????? ?
???????? ??? ???????????????? ???????? ? ????????? ???????, ?????????? ??? ?????????
?????. ??????????????? (???), ??????????? ? ??????????? ????? ????, ? ??? ???????? ??????????????????? ??????????, ?????????? ??????? ????. ?? ???????? ???? ? ????? ?????
??????????? ??????? ????????? ???????????, ?????????? ??????? ???????, ??????? ??????,
????????? ? ??????????? ??????????. ? ???? ?? ??? ???????? ???????????? ????????????? ? ?????????? ???????? ? ????????. «?????? 2.1.5.980-00» ????????? ????????? ????? ?
??????? ??????????????? ?? ???????? ??????, ??? ?????? ???? ??????????? ?? ?????????
???????? ???????????.
??? ????? ????????? ??? ??????? ????????? ????? ???????? ??????? ??????????
????????????-???????? ??????? (???), ?????????? ?????? ???????? ??????????. ????????????? ??????????? ??????????? ??? ?? ?????????? ????? ??????? ? ???, ??? ??? ???????? ????????? ??????????? ?????? ???????????? ???????. ????? ??? ???????? ??????? ?
# 684 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????????, ?.?. ??????????? ???????? ??????? ??????? ???, ?????????? ????????????????
???. 3. ???????????? ?????? ???????????? ??????????????
??????????? ????????????? ???????????? ? ????????? ?????? ???????????? ??????? ? ?????????? ?????, ??????? ??????? ?? ???????????? ???????????. ???????????? ????????????
????????????-???????? ??????? ????? ????????? ????????? ????????????. ??? ????????????? ??????????? ???????????? ?? ??????????? ?????????? ??? ???????????? ?????????
?????????????? ??????????? ??????????? ? ??????????? ???????? ? ???????-?????? ? ?????
?????????????? ????????, ??? ???? ??????????? ?????? ??????? ????? ????????? 50 %.
??????? ????????, ??? ???????????? ? ?????????????? ?????? ??????? ??? ???????? ? ??
????????, ? ??? ????? ? ??????? ?????? ???????????? ????? ??????????, ??????? ?? ???????
????, ????????? ?????, ???? ????????? ????????, ????????? ????????? ???????? ??????????,
???????????? ????????? ???????????, ? ????? ???????? ? ????????????????? ?????. ??? ??# 685 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????????, ?.?. ??????????? ???????? ??????? ??????? ???, ?????????? ????????????????
???. 4. ????????????? L140
???. 5. ????????????? L141
?????? ?????????? ???? 50 ? ?? ????? ?????? ?????????? ?????? ?????? ????? ???????????
?????????? ?? ???????????? ?????????? ???????, ???????????????? ????????, ???????????
????????? ? ?????????. ???????? ?????? ?????????, ??????? ??????? ?????? ???????? ???????? ????????? ??? ?????????? ???????????? ???????? ??? ????????????? ????????? ??????????? ??????.
? ???? ????? ??????? ??????? ???????? ??????????? ????????????? ??? ??????? ??????????????? ? ????????????? ????? ??? ??????? ??????? ??? ???????, ?????????????? ? ?????? ???????? ? ?????????? ????????????????? ?????????.
# 686 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????????, ?.?. ??????????? ???????? ??????? ??????? ???, ?????????? ????????????????
?? ???? ???????????? ??????????? «??????? ????????? ? ??????? ??????? ???» ???
???? ????????? ?????????????? ???????????? ????? ??????????????, ?????????? ???
????? ???????. ?? ????????? ?????????? ?????? ????????? ? ???????? ??????? ???????
????????? ??????? ????????????? ?????? ??????????? ??????? ??? ??????????????? ? ??????????? ???????, ???????????? ?? ????????????? ??? ???????????? ????? ??????? ?????????? ?????. ?????????? ????????? ??????? ?????????????? ???????? ?? ?????? ?????????
???????????????? ????, ?????????? ? ???? ????????? ??????? ??????? ???????????? ?? ????
????????????? ??????????, ??????????? ?????? ???????? ??????-?????????? ??????? ????
? ??????????????? ????????????? ????????.
???? ?????????????????? ??????????? ????? ???? ??????? ? ???????? ???? ???????? ??????????: ??????????????? ??????? ???? ?????? ??????????????? ?????????????? ????????????? ? ???????? ??????????? ???????????? ??????????? ??? ?????????????? ????????
????????????? ?????????????? ? ????????????? ????? ??????? ??????????. ? ???????????
??????????????? ???????? ?????????? ??????? ??????????????? ????????? (P ~ 1000 ???;
T ~ 2000 K ? ?????) [1], ??? ???? ??????????? ??????? ?????????????? ?????????????? ??
????? ?????? ? ??????????? ?????????? ?? ???????? ?????????, ???????????? ?????? ?
????????? ???????????, ? ????? ????????? ?? ??????? ?????????????, ?????????? ????????
???????? ? ? ????????? ?????????? ???????? ???????? ? ????, ?????????????? ??????????
???????????????? ?????? [27]. ???????????? ????????????? ?????????? ??????? ???? ?????
?????? ?? 72, 5 %.
??????????
? ????????????????? ????????????? ??? ??????? ????????? 97,2 % ????? ????????????? ??????? ????? ????????? ? ????????? ????? ???????????????. ?? ????????????? ????????????? ????????? ?? ?????? ?? ????????, ?? ??????? ?????? ?????????????? ????, ??
?? ?????????. ??? ????????? ????????????? ?????? ?? ??????????????? ???????? ???????
?????? ???? ?????????? ???????? ????????? ??????????? ???????? ??????????? [1]. ????????????? ????? ????????? ???????? ?? ?????? ??? ??????????????? ??????? ???????????????, ?? ? ????? ??????????? ?? ?????? ????????, ??????? ?????? ???????? ? ???????
??????????????.
????? ???????, ????????? ????????? ???? ????????? ??????? ????????? ??????? ?????????????, ???????????? ??????????? ???????? ???????????, ??? ???????? ? ????????
???????????????? ??????, ????????????? ??????, ???????? ?? ????????? ???????? ??????????, ???????? ????? ?? ????????? ?????????? ???????? ???????????? ??????????????????
? ?????????????????.
?????? ??????????
[1] ??????? ?.?., ??????? ?.?., ?????? ?.?. ????????????? ??????????. ??????????: ????? ???, 1990. 200 ?.
[2] ?????????? ?.?. ??????????? ???. ? ????. ????. ????. ??????????, 2007. 22 ?.
[3] ?????????? ?.?., ??????? ?.?. // ??????? ????????????? ???????? ???? ???????? ?
???????????? ?????????????????. 2009. ?. 14. ? 6. ?. 242-245.
# 687 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????????, ?.?. ??????????? ???????? ??????? ??????? ???, ?????????? ????????????????
[4] ?????????? ?.?., ??????? ?.?. // ? ???? ??????? ????????. 2010. ? 5 (11). ?. I. ?. 8790.
[5] ?????????? ?.?., ?????????? ?.?., ??????? ?.?. // Journal of Siberian Federal University.
Engineering & Technologies, 6 (2011 4) 665-675.
[6] ??????????, ?.?., ?????????? ?.?., ??????? ?.?. // ???????????? ?????????????????.
2012. ? 3. ?. 26-30.
[7] ?????????? ?.?. ??????????? ???. ? ????. ????. ????. ??????????, 2012. 19 ?.
Problems of Wastewater Containing Emulsified Oil
in the Circulating Water Systems,
Closed Cycles and Their Solutions
Olga G. Dubrovskaya,
Vyacheslav V. Evstigneev and Vladimir A. Kulagin
Siberian Federal University
79 Svobodny, Krasnoyarsk, 660041 Russia
The results of investigation of water treatment system of circulating water carwash stations. Based on
theoretical analysis and experimental studies suggested the installation of the combined type, using
the cavitation technology to simultaneously solve the problems of physico-chemical water purification
and decontamination of biological contaminants. Results of experimental studies have shown cleaning
up contaminated water emulsified oil products to the MPC performance.
Keywords: water, car wash, oil, surface-active substances nye, contamination, cavitation technology.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 6 (2013 6) 689-698
~~~
??? 691.335
??????? ?? ?????? ??????????? ????
? ???????????? ???????
?.?. ???????*, ?.?. ???????, ?.?. ????????????,
?.?. ????????, ?.?. ?????, ?.?. ????????
????????? ??????????? ???????????,
?????? 660041, ??????????, ??. ?????????, 79
Received 10.08.2013, received in revised form 14.08.2013, accepted 02.09.2013
? ?????? ???????????? ?????????? ?? ????????? ? ???????????? ??????? ?? ?????? ???????
????????. ? ???????? ????????????? ??? ??????? ???????? ?????????? ????????????????
??????? ?????? ??? ????????????? ????. ????????? ???????????? ????????? ???????
???????? ??? ???????, ?????????? ????????? ? ??????????????? ???????????. ????????, ???
????????????? ??????? ??????? ????????? ???????? ????????????? ? ?????????? ?? ?????????
????????? ? ???????? ??????-????????????? ? ????????????????? ????????????????.
???????? ?????: ????, ?????, ??????? ??????, ?????????, ???????????????.
????????
?????? ???????? ???????? ?????????? ??????? ????????, ????? ? ????, ??? ???? ? ????
????????? ???????? ??????????? ?????????? ???????????? ?????????? ???????????? ????,
??????? ??????? ?????????? ?????????????? ?? ? ????????? [1].
? ????? ?????? ?????????? ????????????? ???? ? ??? ??????? ??????????????? ????????,
?????????? ? ???? ???? ???????????: ?-??????????? (?????????? 2,07 ?/??3.) ? ? ? ??????????? (?????????? 1,97 ?/??3). ??????????? ????????? ???? ??????? ?? ??????????? ??? ? ? ??????????? ?????????? ??????????? ?????? 106,8 є?. ??? ?????????? ???? 120 є? ???????????
???????? ???????????? ? ?????????? ????, ??? 160 є? ?????? ??????? ???????? ??????????????????? [2].
???????? ??????????? ?? ????????????? ??????????? ???? ??? ????????? ?????????????
? ??????????? ? ????????? ????? ???????? ????? ?? ?????????? ????? ?? ????????? ???????????? ?????????? ?????? ????????? [3].
?????????? ???????? ????? ?????????? ???????, ????? ??? ??????? ????????? ?? ??????
? ????? [4, 5], ?????????? ?????????, ??????? ???????????????, ?????? ?????????????? ? ??????????????????? [6]. ???????????? ??????????? ?????? ?????????? ????????? ?? ??????
?????????????? (????? 120 є?). ????? ????, ??? ????????? ???? ??????????? ????????????
????????? ??????, ????????????? ??????? ????????? ???? ?? ??????? ????????? ? ???????,
? ????????? ????????? ??? [7]. ????? ???? ??? ???????? ??????????? ?????????? ??????????
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: nagibin1@gmail.com
# 689 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ???????? ??????? ?? ?????? ??????????? ???? ? ???????????? ???????
? ???????????, ?????? ???????? ?????????? ??????? ?? ??????????? ???????? ???????, ??????????? ????????? ??????-???????????? ???????? ???????????.
????????????? ????????? ?????????? ????????????? ????????? ??????????????? ??????
???????. ?? ??????????? ???? ????????? ??? ???????, ?? ??????? ???????? ????????????,
?? ???????????? ??????, ???????? ???????????????? (????) [8], ???????? ????? [9], ?????????? ? ?????? [10], ????????????????? [11], ??????????? ??????? ?????????? ???????????
?????????? ?????? ??? ??????? ????????? ? ??????????? ??????????? ?????? ??????????.
?????? ????????? ? ??????????? ??????????? ????????????? ?????? ? ?? ????????????? ? ??????? ?????? ?????????? ??????????? ?????????? ?????????? ??????????? ? ????????????
? ??????????? ?????????????.
??????????? ????????? ????????? ???????????? ???? ????? ????? ???????? ???????????????? ???????????? ? ???? ??? ??????? ?????????: ???????????????, ???????????? ???????, ????? ??? ??????? ??????????????, ???????? ????-?????. ? ??????? [12, 13] ? ????????
???????????? ??????????? ??? ??????????? ????????? ????????????? (???????????????)
????. ???????? ??????????? ???????, ??????? ????????? 26,7 ??? ? ?????????????? ?????
1,0 % [13].
? ????????? ?????? ????????? ?????????? ???????????? ??????????? ??????????, ? ??????? ? ???????? ???????????? ???????????? ???????????????? ????-????, ?????????? ??????? ????????-??????????????? ????????? ????????????? ???????. ????????????? ???????????????? ??????? ??????? ??? ????????????? ???? ???????? ?????? ???????????? ???
???????? ? ????????? ??????????????, ?????????????? ? ???????? ????????????? ?????????
? ?????????? ???????????? ???????.
????????? ? ?????? ????????????
??? ?????????? ???????????? ???? ???????????? ????????? ?????????: ???????????
???? ??? «?????????? ??????», ????-???? ???????????? ???-1, ?????? ????????? ???????????? ????????????????? (???).
???????????? ?????? ??????????????? ??? ? ???????? ????????? ?? ?????????????
????????????? Bruker D8 ADVANCE (CuK? ?????????, ?=0,15406 Е), ???????? ?????? ??
2? ?? 10 ?? 65° ? ????? 0,07°. ?????????? ?????? ?????????? ??????? ??????????? ??????? ?? ???? 5382-91. ?????????? ????????? ???????? ??????????? ???? ? ?????????????
?????????? ?????????? ???????????? ??????? ????????-?????????????? ?????????????
(???) ?? ??????? ARL Optim?x. ??????? ??????? ????????? ? ?????????? ???????? ?????????? ??????????? ?????? ??????????? ???????????? ??????? ? ???????????????? ?? ?
???????????????? ??????????? ???????????? ???, ?? ??????? STA 449 Jupiter (?????
NETZSCH) ? ????????????? ????-????????????? QMS 403 Aeolos (????? NETZSCH) ???
??????? ?????.
?????????? ???????????????? ??????? ????????, ??? ??????????? ???? ??? «??????????
??????» ???????????? ????? ?-???????????. ??????????? ?????? ???????? ?? ??????????,
??-????????, ??-?? ?? ????? ???????????? ? ??????. ???????? ???, ? ??? ?? ????? ?????
?????????? ???????? ?? ????????? 0,7 % ? ? ???????? ??? ?????? ?????? ? ??????, ???????????? ????.
# 690 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ???????? ??????? ?? ?????? ??????????? ???? ? ???????????? ???????
???. 1. ?????????? ??????????? ???????????? ??????? (??????) ????? ???? ??? «?????????? ??????»
?? ??????? 1 ????????? ?????????? ??????????? ???????????? ??????? ????? ???? ???
«?????????? ??????».
? ????????? ?????????? ?? 100 ?? 400 є? ??????????? ????????? ??????????? ????????.
??????????????? ?????? ??? T = 110,3 є? ?????????? ??????? ????????? ?? ?- ? ?-????. ?????? ??????????????? ?????? ??? T = 123,7 є? ????????????? ????????? ????.
? ????????? ?????????? 213?370 є? ??????????? ??????????????? ??????, ??????? ?????????????? ?????? ??????? ?????. ??????????? ?????? ???????? ??????????? ?????????
???? ?????????: ????????? ???? (????-) ? ????????? ?? ? ??????????? ????????? (????-). ?????? ??????? ????????? ???????????? ??? ?????? ????? ? ????????? ?????????? ???????????????? ??????????.
? ?????????? ??????????? ??????????? ???????????? ???????????, ??? ???? ??? «?????????? ??????» ????????????? ???????? ????? 9920 ???????? ???? 127.1-93 «???? ???????????».
??????????????? ?????? ????-????? ???????????? ???-1 ???????, ??? ???????? ?????
? ???? ???????? ????? SiO2. ?? ???? ???????? ???????????? ?????, ??????????? ? ????????
Fe2O3, ?????? ??????? ???, ????????? MgO, ?-C2S (?-2CaO·SiO2), C3A (3CaO·Al2O3), ????????
CaCO3. ?????????? ?????? ????-????? ??????????? ? ????. 1. ?????????? ???????????? ??????? ????-????? ????????? ?? ???. 2.
?? ?????? ??? ??????????? ????????? ??????????? ??? t = 750 є?, ??????????? ? ?????????? ???????? ? ???????????????? ??????????? ????? ????????. ???????? ?? ???? ???????? ?????? ??????????? ??????????? ????????? ??????? ? ????????? ? ?????????. ??? ?????????????? ??????????? ???????????? ? ?????? ???? ??? ??????????? ?????????? ?????????
??????? ? ?????????? ???????????????? ?????????? ?????? ??????? ? ???????????? ??????????? ??? ???????? ???? ???? ?? ???????. ?? ?????? ??? ??????????? ?????????????? ???????????, ???????????????? ??????? ????? ? ??????????? ?? ??????????? ???????????????
?????????? (????? 0,31 %) ??????? ????? ??????? Ca(OH)2. ???????? ????????, ??????????? ??
# 691 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ???????? ??????? ?? ?????? ??????????? ???? ? ???????????? ???????
??????? 1. ?????????? ?????? ????-?????
?????
SiO2
?12O3
Fe2O3
CaO
MgO
SO3
Na2O
K 2O
TiO2
CaO??
???
% ????.
52,64
7,43
6,79
21,02
5,53
0,38
0,34
0,37
0,28
4,56
5,58
???. 2. ??????????? ????-?????
????????????, ?????????? CaCO3 ? ????-????? ?????????? 4,54 %. ????? ???????, ?????????
????? ??????? (?????) ? ??????????? ????? ????????? ? ???? ??????: ??????????????? ? ????
?????? ??????? ??? ? ??????????? ??(??)2. ? ???????? ??????? ????? ????????????? ? ??????????????? ??? ?????????????? ? ?????? ? ??2, ????????????? ? ???????. ???????????????
??????? ?? ?????? ??? ? ??????? ?????????? 400-600 є? , ???????????????? ???????????
????? ????????, ????????? ?? ??????? ????????? ??????????????? ?????????? ????????????
???????, ?????????????? ?? ???? ?????? ????-?????.
???????????? ? ?????? ????????? ???????? ?????? ??????????
? ???????? ???????? ?????????? ??? ??????????? ??????? ?????????? ???????????????????? ????-?????.
??????? ????????????? ????????? ???????. ???? ??????????? ??? ?????????? ????????????? ? ????????? ????? ??? ??????????? 150 є? . ????? ????????? ?????????????? ?????????? ?? 140 є? ????-???? ? ????? ????????????.
??? ???????????? ?????????????? ??????? ????? ????????? ?????????? ????? ???????? ????????????? ??????? ?????????? ?? 140 є? ???????????, ?????????????? ????? ??????
????????? ???????? ?????? ??? ????????? ?????. ?????????? ????? ??????? ????? ?????????? ? ????????????? ????? ???????? 70?70?70 ?? ? ??????????? ?? ??????????? ?????????????. ???????? ??????????? ???? ?????????? ?? ????????? ?????????: ????????? ? ??
???? 12730; ????????? ? ?? ???? 10180; ?????????????? ? ????????? ?????????? ? ?? ????
12730; ??????????????? ? ?? ???? 10060.2-95.
# 692 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ???????? ??????? ?? ?????? ??????????? ???? ? ???????????? ???????
?????????? ? ??????????
?? ??????? 3 ????????? ?????????? ?????????????? ???????????? ???? (?) ? ???????????? ???????? (?). ??? ????? ????????, ????????????? ?????????????? ???? ????????? ???????? ???????? ? ????? ?????????? ??????????.
? ??????? ???????? ???? ???????? ????????? ?????????? ? ????????, ? ??????? ???????????? ??????? ? ??????? ??????? ????. ?? ??????? 4 ?????, ??? ? ????????? ? ???????
???? ???? ????????? ?? ?????? ??????????, ???????? ????????????? ???????? ? ??????????,
????????? ?? 60 ????. % ???? ? 40 ????. % ????-?????. ?????????? ?????????? ????????????
???????? ? ???????? ????????? ?????????. ??????? ????? ???????? ??? ????:
1. ? ?????? ???? ??????? ????? ??????? ????, ??? ???????? ? ??????????? ??? ?????????? ????????? ?????????. ????? ??????????? ????????? ?? ???????????? ?????????? ???? ??
?????. ????? ???????????????? ??????????? ??????????? ??????, ??? ????? ????.
2. ?? ?????? ???? ? ???? ???????????? ???????? ????????? ? ????? ???? ?????????? ?
??????? ???????????????? ???????????.
???. 3. ?????????? ?????????????? (??????????? ??????????? ????????? JEOL JSM-7001F):
?) ????????? ???? ??? ????????????; ?) ?????????? 60 % ???? ? 40 % ????-????
40
V, ???
30
20
10
0
0
10
20
30
40
50
60
?????, %????.
???. 4. ??????????? ??????? ????????? ?? ?????? ??????? ???????? ?? ????????? ??????????
??????????? ? ????-?????
# 693 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ???????? ??????? ?? ?????? ??????????? ???? ? ???????????? ???????
3. ? ??????? ???? ??? ?????????? ??????????? ???????? ?????????? ??????????? ? ??????? ??????? ???????? ?????????? ?????????? ??? ?????????, ?????????? ??????????, ??????????????, ??? ???????? ? ??????? ???????? ??????????? ???????????.
????????????? ???????? ? ???????-????????? ??????????? ???????? ???????? ?? ?????? ??????????? ????? ?????????? ????????? ?????? ???????, ?? ????? ????????? ???????
????????? ????? ????. ???????????? ? ???????????????? ???? ????????? ????? ???????
???????? ??? ???????????? ??????????? ? ???????????? ????? ? ???????????? «??????????
?????? ??????»:
3CaO + 3S = 2 CaS + CaSO3 .
(1)
??? ??????? ???? ???????? ? ???????? ???????? ???????????? ? ??????????? [14]:
CaS + (x - 1)S = CaSx ,
(2?)
CaSO3 + (x - 1)S = CaSx O3 .
(2?)
??? CaSx ???????? ?????????? ? ? =1, 2, 4, 5 [15]. ??????????, ?????????? ????????? ?????? ????, ????? ???? ???????????? ? ?????? ???????, ??????? ?? ???????????? ????????.
?????????? ?????????? ??????? 1, 2? ? 2? ???????????? ????????????? ?????????
??????-???????????? ????????????? ?????? ?????????? [16].
??? ???????????? ???????????? ?????????? ??????? ??????? ??????????? ?? ?????????????????? ?????????????? ???????????. ?????????????? ???????? ??????? ??????????
??? ??????????? ? ??????????????????? ?????????? ?? ????? 40 ?? 60 є?.
?????? ????????? ?????? ??????? ??? ??????? ???????? ??????????? ??? ???????????
?????????????? ????????? ???????????? ?????????? ????????????, ??? ?? ?????????? ????????? ?????????????? ??????? ??????????. ?????? ???????????? ????? ???????????? ??????? ? ??????????????? ????? ?????? ??? ??????????? ??????????? ????????????-?????????
??????? ????? ???????????.
??? ???????????? ???????? ????????? ????? ? ?????? ??????? ?????????? ????????
??????? ???????? ??? ??????? ?????????? ??????????? ? ????-?????????????????? ???????.
?????????? ???????????? ??????? ???????????? ???????? ??????? 60 ????. % ???? ? 40
????. % ????-????? ????????? ?? ???. 5.
??? ????????????? ?????????? ??????? ?? ??????????? ??????? ????????? ???????????? ???????? ?? ??????????? 151,2 є?. ??? ???? ??????????? ??????????? ???????
????? ??????? ???????? ?? 1,49 % ?? ???? ????????? ????, ???????? ?????????, ???????
????????? ???????? (SO2 ? SO3), ????????, ????????? ? ????????? ???????????? ???? ?
???????????? ?????????, ???????????? ? ????????? ???????. ??? ?????????? ??????????
??????? ????????? ? ?????????? ?????????? ???? SO2 (m/z 64) ??????????? ? ????? ???????
?????????. ??? ??????????? 182,5 є? ????????????? ????????? SO2 ????? ??????????, ? ???
??????????????? ?????????? ??????? ???? ??? ??????? ? ?????????? m/z 64 ?? 2,3.10 -12 ?
?? 2,6.10 -11 ? ??? 200 є?. ????? ????? ????? ??????? ????????? 1,4 % ?? ???????? ?????
(???. 5).
# 694 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ???????? ??????? ?? ?????? ??????????? ???? ? ???????????? ???????
???. 5. ???????? ????????? ????? ? ?????? ??????? ?????????? ??? ??????? ???????? ????????????
????????
?? ?????? DSC ???????????? ??? ??????????????? ???????. ?????? ? ?????????? ???
100,8 є?, ??? ????????????? ???????????? ???????? ???? ?? ??????????? ? ??????????? ???????????, ? ?????? ? ?????????? ??? 115,2 є? ? ????????? ??????????? ????.
??? ????????????? ???????????? ???????? ?????????? ?????????? ??????????? ?????? ????????????? (???. 5) ?? ????????? ? ??????????? ????? (???. 1). ?????? ??????
??????????? ???, ??? ?????????? ?????????????? ?????????? ???? (SO2) ? ??????? ???????
(CaO):
SO 2 + CaO = CaSO3 .
(3)
??????????????, ?? ????????? ????? ??????? ???????????????? ???? ???????????? ????????? ?????????? ????. ?????? ???????? ??????????? ?????????? ????? ??? ??????? ??
182 є?.
????? ???????, ????????????? ???????????????? ???? ? ???????? ??????????? ?????????
????????? ????????? ??????? ??? ????????????? ??????????? ? ?????????? ?????????? ?????
?????????? ????? ????????? ???????????? ???.
??? ??????????? ???????????????? ????????????? ??????????? ?????????? ?? ??????
??????? ???????? ????????????????? ?????????????? ?????, ???? ??????????? ???????
???????????. ? ???????? ???????????? ???? ???????????? ?????? ?????????. ???????????
??????????? ?????????????? ??????????? ??????????? ??? ???????? ???????????? ??????????? ????? 67 %.
????????????? ????????? ??????????? ?? ???????? ???????????? ???????: 19,7 ????. %
???? ? 13,2 ????. % ????-????? ? 67 ????. % ??????? ?????????. ???????????? ???????????
????????????? ??????????? ? ????????????? ????????? ?? ????? 40 ?? 80 є? ??????????, ???
# 695 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ???????? ??????? ?? ?????? ??????????? ???? ? ???????????? ???????
??????? 2. ????????? ?????????? ???????????? ??????? ??? ????????? ????????????
???????????, є?
-40
-20
0
20
40
60
80
?????????, ???
44,8
45,7
45,2
45,6
45,2
44,7
45,3
??????? 3. ??????????????? ?????? ??????? ???????????? ???????
????? ??????
???????????????????????
?? ?????????
300
45,2
?????????, ??? ????????
????? ?????????
??????
?????????, %
????? ??
???????????????
43,8
3,1
?? ????? F300
???????????? ????????? ????????? ? ????????? ????????? ?? ?????????? (????. 2), ??? ????????? ???????????? ??????????? ?? ?????????? ??? ????????????? ??????????? ????????.
?????????????? ???????? ?????????? ?? ????????? 0,35 %, ??? ??????????? ?????? ??????????? ?????????? ???????? ? ?????????????? ????.
??? ???????????? ??????????????? ??????? ????????? ? ??????????? ?????? ??? ??????????? ????? 18±2 є? ???, ????? ?????????? ????? ?????????, ???????? ??????????? ? ???????????? ??????? ???? ?? ????? 50 ??. ????????????????? ?????? ????? ?????????????
??? ?????????????? ??????????? ? ?????? ????? (18±2)°? ?????????? ?? ????? 4 ?.
??????? ????? ???????? ?? ??????????? ?????? ????????? ? ?????? ?????????? ??? ??????????? ???? (18±2)°? ? ????????????? ????????? (95±2) %. ????????????????? ?????? ????? ?????????? ?????????? ?? ????? 4 ?. ????? 2-4 ? ????? ?????????? ???????????????? ?????
?????? ??????? ???????????? ?? ?????? ?? ??????????? ????????. ?????????? ????????? ??
??????????????? ??????????? ????????? ? ????. 3.
??????? ??????????????? ?????? ??????? ??????????? ?????????????? ???? ? ???????,
????? 1 %, ??????????? ? ???????????????.
??????????
????????? ???????????? ??????? ????????, ??????????? ?? ?????? ??????????? ???? ?
????-????? ???????????? ???-1.
????????????? ???????????????? ???? ? ???????? ???????????? ??? ??????? ????????
????????? ???????? ????????????? ? ?????????? ?? ????????? ????????? ? ???????? ??????????????????? ? ????????????????? ????????????????. ???????????? ? ????????????????
????? ????????? ????? ??????? ? ???? ??? ???????????? ?????????? ????????? ?? ???? ??????????? ?????????????? ? ?????.
??????????? ??????????? ?????????????? ??????????? ? ????????????? ????????? ??
????? 40 ?? 80 є?. ????????, ??? ???????????? ????????? ????????? ? ????????? ?????????
?????????? ?? ??????????.
???????????????? ????????? ???????? ??????? ???????? ??? ???????. ???????????, ???
? ???????????? ???????????? ????????????? ???????????????? ????????? ??????????????
# 696 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ???????? ??????? ?? ?????? ??????????? ???? ? ???????????? ???????
????????? ???????????? ?????????. ????????? ?????????? ???? ???????? ??????????? ???
???????????? ???? 130 є?. ??? ???????????? ????? 180 є? ??????????? ??????????? ????????? ?????????? ????. ?????? ??????? ??????? ????????? ??? ?????????? ??????? ? ???????
????? ??????????? ? ???????????????????.
???????? ??????????? ?????????? ?????????? ?????????? ??? ????????????? ?????????? ????? ? ?????????? ?? ?????????? ????????? ???????????? ???????????????? ????.
?????? ??????????
[1] ?????? ?.?., ?????????? ?.?., ????????? ?.?. ? ??. // ?????????? ??????????????
???????. 2006. ? 2. ?. 15-24.
[2] ??????, ?.?. ??????? ?.?., ????? ?.?. ?????????? ???????????? ? 5 ?????. ?.: ????????? ????????????, 1965. ?. 4. 11-12 ?.
[3] Pat. 2612473 (2006). Canadian // C. A. 2007.
[4] ???. 40411 ???. // ???. 1989. 19?526??.
[5] ????????? ?.?., ?????? ?.?., ??????? ?.?. // ???????????? ?????????. 2005. ?8.
?. 38-40.
[6] Mohamed A.M.O., El Gamal M. // Proceedings of the 8th UAE University Annual Conference,
2007.
[7] ???????? ?.?., ???????? ?.?., ?????? ?.?. ?????????? ????????????. ?.: ??????? ????????????, 1996. ?. 4. 704 ?.
[8] Currell B.R., Williams A.J., Mooney A.J., Nash B.J. // J.R. West. Washington: American
Chemical Society, 1975. P. 117.
[9] ???????? ?.?., ????? ?.?., ??????? ?.?. ? ??. // ?????? ?????????? ?????. 2003.
?. 76. ???. 3. ?. 506-511.
[10] ???????? ?. ?., ??????? ?. ?., ?????? ?. ?. ? ??. // ?????????????????? ??????????
???. ?. 1997. ?. 39. ? 5. ?. 825-831.
[11] Easterbrook E.K. // XXII IUPAC Macromolecular Reprint, 1971. Vol. II. P. 712.
[12] ?????? ?. ?. // ???????????? ?????????. 2009. ? 12. ?. 75-77.
[13] ?????? ?. ?. // ?????????-???????????? ??????. 2011. ? 8. ?. 29-34.
[14] ???? ?. ???? ?????????????? ????? ?.: ???-?? ??????????? ???-??, 1963. 921 ?.
[15] ??????? ?.?., ??????? ?.?., ?????? ?.?. ????????? ????????? ??????? ????????????? ??????. ?.: ??????????????, 1996. 993 ?.
[16] ??????? ?.?. ??????????? ???. ... ????. ???. ????. ?., 1979. 17 ?.
[17] ????????? ?.?. ??????????? ... ????. ????. ????. ?., 2006. 16 ?.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ???????? ??????? ?? ?????? ??????????? ???? ? ???????????? ???????
Sulfur Concrete with Ash Waste
Gennady E. Nagibin, Rashit A. Nazirov,
Sergei S. Dobrosmyslov, Elena N. Fedorova,
Vladimir E. Zadov and Valentina A. Shevchenko
Siberian Federal University
79 Svobodny, Krasnoyarsk, 660041 Russia
Result for synthesis and researching concrete base on sulfur is shown in this work. Sulfur concrete
was modified ash waste from thermal power station of Krasnoyarsk with a high concentration of
calcium oxide. Sulfur concrete was investigated during heating and strength and frost resistance was
measured. Sulfur concrete with ash waste has low porosity, high physic mechanical and performance
properties.
Keywords: sulfur, concrete, ash waste, strength, frost resistance.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 6 (2013 6) 699-704
~~~
??? 676.15/16.054.1(075)
???????? ??????? ??????????
????? ??????????? ?????
??? ????????????? ?????????? ?????????
?.?. ???????*, ?.?. ?????????
????????? ???????????????
??????????????? ???????????,
?????? 660049, ??????????, ??. ????, 82
Received 05.04.2011, received in revised form 12.04.2011, accepted 19.04.2011
?????????????? ???? ????????????????? (????????????????) ?????????? ????????? ???????
??????????, ?????????? ????? ????? ??????????? ????????????? ??????? ?????? ?????
??? ????????????? ?????????? ??????? ????????? ????????????? ??????????? ?????????
???????? ???????. ???????? ????????? ??? ???? ???????? ????? ??????, ?????????? ??????
??????? ?????????. ? ????? ?????????? ????????????????? ??????????? ???????????????
?????????? ?????????.
???????? ?????: ???????, ????????, ?????????, ?????????, ???, ????????????? ??????????,
????????, ??????? ??????, ???? ????????, ???? ???????????.
????????
??? ??????? ??????????? ?????????????? ? ???????? ????????? ? ???????????? (?????????????) ??????????? [1] ??????? ????????? ????????????? ??????? ???????????? (??????????????? ? ??????????? ????? ???????????? ?????) ???????????? ????? ?????? ? ???????????? ????? ??????? ????????????? ??????? ?????? ?? ?????:
? ??????????? ? ??????????????? ?????? ???????????? ?????? ??????;
? ???????????? ? ????? ???????????.
?????????? ?? ?????? ?????? ?? ???????????? ????? ??????????? ???????? ???????? ?????????? ????? ??? ??????????.
??? ???????????? ???????? ??????? ?????????? ?????? ????????? ??????? ???????. ???????? [1], ??? ???????? ?????? ???????:
? ??????? ?? ???? ???????????;
? ?????????? ??????????? ? ???????? ?????????? ??????? ?????? ????? ?????? ? ???????;
? ????? ??????????, ??????????? ??? ?????????? ???? ????????????? ?????, ???????
??????? ???????? ???????? ?????? ????? ???????????? ????????????? ?????? ???????
?????? ????? ?????? ? ???????.
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: mapt@sibstu.kts.ru
# 699 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ?????????. ???????? ??????? ?????????? ????? ??????????? ????? ??? ??????????????
?? ??????????? ??????? ????????? ?????????? [13], ?????????? ??????? ???????????
?????????? ?????????, ??? ?????????? ???? ??? ????????????????? (????????????????). ??????
?? ?????????? ?? ??????????. ??????????????, ??? ??? ????? ??????????: ??????????????????
????????????, ????????????? ???????????? ???????????????, ???????????? ?????? ????????
??????????????? ???????????.
????? ????????????, ??? ?????????? ???? ?????????? ? ??????? ???????? ???????
????????????? ??????????? ???????? ????? ????? ??????? ?????? ????? ?????????
???????? ??????? [1].
????????? ? ?????? ????????????
?? ??????? ????????? ????? ?????? ??????????? ???????? ????????? ?????????????
??????????? ?????????? ?????? ?????? ? ???????. ??? ??????? ????????? ??????? ?????? 4
?????????? ???? ??????, ?????????????? ? ??????? ???????? ??????? 6 ? ??????? ???????
5 (ABc) ?????????? ???? ???????, ?????????? ? ???? ??????????:
???. ????????? ????????????? ??????????? ?????????? ?????? ?????? ? ???????: 1 ? ??????????,
???????????????? ???? 2 (?????????) ? 3 (????????); 4 ? ??????? ?????? ???? ??????; 5 ? ???????
?????? ???? ???????; 6 ? ?????????? ???????? ??????; r ? ?????? ?????????? ???????? ?????? 6; rX ?
?????? ?????????? 1; R ? ?????? ???????? ???????? ?????? 7; ? p ? ???? ??????? ??????? ?????? 4
???? ?????? ? ??????? r; ? c ? ???? ??????? ??????? ?????? 5 ???? ??????? ? ??????? r; ? ? ???? ????????
??????? ?????? 4 ???? ??????
# 700 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ?????????. ???????? ??????? ?????????? ????? ??????????? ????? ??? ??????????????
? ????????, 4 (ABp), ????? ??? ???????????? ? ????? A ??? ? ? ???? ??????? y;
? ?????????????, 4 ( AcB ?c), ????? ???????? ?? ???? ?.
? ?????????? ???????? ????? A ????????????? ??:
? ?????????? ???????? ?????? 6 ? ????????? A';
? ??????? ?????? 5 ? ? ????????????? ????????? A X, ?????????? ???????????? ??????
??????????? ??????? ?????? 4;
? ??????? ?????? 5 ? ? ????????????? ????????? A X, ?????????? ???????????? ??????
X
??????????? ??????? ?????? 4 ( AcB ?c) ? 5 (ABc), ?????????? ????? ????? ???? D ??? .
???????????? ????? Bp ????????????? ?? ???????? ???????? ?????? ? ????????? Bp'.
?????:
? OA ???????? ???????? r ???? AA' ??????? ???????? ?????? 6 ??????????? ?????????
??????? ???????????? ?????? ?????? ? ???????;
? OCc, OCp, ???????????????? ?????? ACc, ACP, ???????????? ??????? ?????? 5
c
(AB ), 4 (ABP), ???????? ?? ?????????????????, ??????????????, ??? ?????????? ????, ?
??????????????? ?????? ???????????? ?????? O;
? AOX ???????? ???????? rX ?????????? 1 , ???????????? ????? ???????? ??????? ??????
p
AB ?? ???? ?;
? ????????? [1] ????????? ??????? rX ??? ????????????? (??????????????) ??????????
A
[2] ??????? ????????? ????????????? ??????? ???????????? (? D ???
???????????? ? ????????? ?????.
??? ? P > ? C:
D P D C ? ????? A)
??? ?????? rx
E
sin E � cos(D c )
2
r � sin D p [
cos D p ]2 ;
E
cos � sin(D p D c E)
2
(1)
??? ??????? rx
E
sin E � cos(D p )
2
r � sin Dc [
cos Dc ]2 .
E
cos � sin(D p Dc E)
2
(2)
2
2
??? ? P = ? C = ?:
??? ?????? ? ??????? rx
E
sin E � cos(D )
2 cos D]2 .
r � sin D [
E
cos � sin( 2D E)
2
2
(3)
?????????? ????????, ???:
? ????????? (1), (2) ? (3) ???????? ???????????????, ?. ?. ???????????????? ?????????,
????????? ???????? ?????????? ???????? ? ? ???? ???????? ??????? ?????? 4 ? ???????????
???????? ????? ?????? (??. ???????????? ?? ??????? ???????? ???????);
?
;
(4)
? ? ?????????? (1) ? (2) ?????????? ???????? D P D C E D ???
?
? ? ????????? (3) ?????????? ???????? 2 · ? ? = D ??? .
(5)
???????? ???????????? ??????????????, ??? ???? ????? ??????????? ????????,
??????????? ????? ???????? ???????? 4 (??????) ? 5 (???????), ???????????? ????? ????,
# 701 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ?????????. ???????? ??????? ?????????? ????? ??????????? ????? ??? ??????????????
X
? ?? ???????? ?? ???, D ??? ?? ?????? ????????? ??????? ???? ?????? ????????? ? ?? ???
X
d 2M [2, 3]. ??????? ?????????, ????????????? ? ???, ??? ????????????
??????, ?.?. D ???
???? ???????????
X
D ???
2M .
(6)
????? ????????, ??? ??? ???????? ????? ??????????? Ax ?? ?????????? ???????? ??????
X
6 ? ???????????? ?????? ????? ???????? ???? ??????????? D ??? ?????????? ???????????
[1, 4-6]. ? ???? ????? ?????????? ?????????, ??? ?????????? 1 ?????????????? ?????????
????????????? ??????????? ?? ??? ????:
? 2, ???????????? ?????????? ???????? ??????? 6 ????? ? ??????????? 1;
? 3, ???????????? ??????????? 1 ? ???????????? ???????? ??????? ?????.
??????????????, ??????? ?????? 4 (A'BP') ???? ?????? ????? ??????? ??????????? 1 ??
??? ???????:
? A'Ax, ????????????? ? ???? 2;
? AxBP', ????????????? ? ???? 3.
X
??? ???????? ?????? ? ?????????? ????????????? ??, ??? ???????? D ???
? ??????:
X
? ???? 2 ????????? ??????? ???? ?????? ????????? ? ??????, ?. ?. D ??? І 2M (?? ???? ????? ??????????? ????????, ???????? ?? ??????? ???????, ?? ????????????? ????? ????, ?
???????? ?? ??? ?? ?????? ? ????? ? ??? ?????????);
? ?????????? 1 ? ???????????? ???????? rx ????? ???????? ???? ?????? ????????? ?
X
??????, ?. ?. D ???
2M (?? ???? ????? ??????????? ????????, ???????? ?? ??????? ???????,
????????????? ????? ????);
X
І 2M (?? ???? ????
? ???? 3 ?????? ???????? ???? ?????? ????????? ? ??????, ?.?. D ???
??????????? ????????, ???????? ?? ??????? ???????, ??? ??????? ????????????? ?????
????).
? ?????? ?????? ???????????? ??????? ???? 2 ?????????, ? ???? 3, ??????? ??????????
1, ????????.
?????????? ??????????????? ?????????? ?????????
??? ???????????????? ?????????? ?????????? ????????????????? ?????????? ?????????.
??? ????? ???????????, ??????? ???????? ? ???? ?????????? ???????? ? ????? ??????? (??????????) ????????.
X
????????, ????? ?????????? ???????? ???????????? ???? ??????????? D ??? . ??????, ???????? ????????? ???? ?????????, ????? 2?.
????? ?????????? ?????????, ?????????? ???? ???????? ? ? ???????? ? ??????????? (1),
(2), ????? ??????????? ? ???? ????????????????? (????????????) ??????????:
E D p D c 2M ???????? ???????????? (4) ? (6);
(7)
? ? p + ? c ? 2?
???????? ??????????? (7);
=
2
2
?p ?
? ? p ? ? c + 2?
???????? ??????????? (7);
=
2
2
# 702 #
(8)
(9)
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ?????????. ???????? ??????? ?????????? ????? ??????????? ????? ??? ??????????????
?c ?
? ? c ? ? p + 2?
???????? ??????????? (7).
=
2
2
(10)
??????? ????? ????? (7)(10), ???????? ? (1) ? (3) ?? ??????, ??????? ????? ????????????????? (????????????) ?????????:
??? ?????? rx = r ? sin 2 ? p + [
sin(? p + ? c ? 2?) ? cos(
cos
??? ??????? rx = r ? sin 2 ? c + [
? c ? ? p + 2?
? p + ? c ? 2?
2
2
? p ? ? c + 2?
? p + ? c ? 2?
2
+ cos ? p ]2 .
(11)
? sin 2?
sin(? p + ? c ? 2?) ? cos(
cos
)
2
)
+ cos ? c ] 2 .
(12)
? sin 2?
?????????? ?????????, ?????????? ???? ???????? ? ? ???????? ? ??????????? (3), ????? ???? ??????????? ? ???? ????????????????? (????????????) ??????????:
? = 2 ? (? ? ?) ???????? ???????????? (5) ? (6);
(13)
?
= ? ? ? ???????? ??????????? (13);
2
(14)
?
= ? ???????? ??????????? (13);
2
(15)
??
2 ? ? ? ? = 2 ? ? ???????? ??????????? (13).
(16)
??????? ????? ????? ?????? ????????, ???????? ? ??????????? (3), ?? ??????, ???????
????? ????????????????? (????????????) ????????
rx = r ? sin 2 ? + [
sin 2 ? (? ? ?) ? cos ?
+ cos ?]2 .
cos(? ? ?) ? sin 2?
(17)
?????????? ???????????
??????????????????? ?????????? ????? ??????????????? ?????????? (11), (12) ? (17) ??????????? ???, ??? ??? ???????? ?????? ???????, ?????????? ?? ????????, ??????????????
?????????.
?????????? ??????? ? ??????????????? ????????? ?????????? (1), (2) ? (3):
? ????????? ??????????? ?????? ?? ???????????? ???????;
? ??????? ??????? ??????????? ??? ?????? ????????????? ????????????, ??????????????? ???????? ????? ????? ??????? ?????? ?????.
??????????
????? ????????????, ??? ??? ?????????? ???????????? ??????????? ???????? ?????????????? ?????????????? ???? ? ???????, ????????????, ? ?????????, ?? ??????? ?????????
?????:
# 703 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ?????????. ???????? ??????? ?????????? ????? ??????????? ????? ??? ??????????????
? ?????????? ?????????? ???????? ??????????????? ?????????? ? ?????? ???????? ???????? ????? ????? ??????? ?????? ?????;
? ????????? ??????????????? ??????? ???????? ????? ????? ????????????? ???????
?????? ????? ?? ???????? ???????????????? ???????? ?????????, ??????-???????????? ?????????? ???????, ? ????? ?? ??????????????? ? ????????????? ?????????????? ?????? ??????? ????????????? ?????;
? ????????? ???????? ??????????? ???????? ???????? ????? ????? ?????????????
??????? ?????? ????? ??? ????????? ??????????????????? ?????????????? ? ?????? ??
??????-???????????? ????????????? ? ???????.
?????? ??????????
[1] ??????? ?.?., ????????? ?.?. // ?????? ?????????? ???????????????? ???????????????? ????????????. ??????? ?????????? ????. 2011. ?. ??I?. ? 3-4. ?. 333-337.
[2] ??????? ?.?. ???. ... ????. ????. ????. ??????????, 2007. ?. 64-65, 92.
[3] ???????? ?. ?. ???????? ?????????: ? 3 ?. ?. 3. ?.: ?????, 1968. 384 ?.
[4] ??????????????. ????????????????? ???????. ???.: ??????????????? ?. ?. ??????.
?. XVI ?, ??. 32, 1895. ?. 854-857.
[5] ????????? ?. ?. ???? ??????????? ???????. ???., 1876.
[6] ????????? ?. ?. ??????????? ????????. ???., 1883.
The Algorithm of the Radius of the Circle
the Crossing Point of Knives the Performance
of A two-Way Headset
Valeury I. Kovaliev and Yury D. Alashkevich
Siberian State Technological University
82 Mira, Krasnoyarsk, 660049 Russia
Stated fact transcendence (uncertainty) the radius of the circle, a well-known algorithm passing
through point crossing straight cutting edges of knives sets of circular mills. Are algorithms for
rotation of the rotor disc, comprising only input parameters. To correct a transcendence was
adapting a known algorithm.
Keywords: input, output, parameters, headset, a knife, a two-way design, ring, cutting edge, angle, the
angle of the crossing.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 6 (2013 6) 705-711
~~~
??? 624.21:001.891
?????? ?????????????? ????????????
????????? ?????????? ??????????????? ???
??? ???????? ????????????? ??????????
?.?. ?????????*, ?.?. ??????????
?????????? ????????????-???????? ???????????????
??????????? ??????????? (????). ????????? ??????
?????? 354024, ????????????? ????, ????, ??. ?????????, 5
Received 09.12.2011, received in revised form 10.08.2013, accepted 10.09.2013
???????????? ? ??????????? ??????? ????????? ???????????? ?????????????? ???? (??)
???????????? ? ????????-???????????? ?????, ???????????? ? ?????????????, ? ??????????
?? ??????????? ???????????? ??????? ????????????? ?????????? ?? ??, ?????? ??
????????????? ??? ?? ?????, ????, ??????, ??????, ????? ? ???????? ????? ????? ? ?????????
???????????????? ?? ?? ?????????? ?????????? ???????? ? ????????? ? ????? ?????????
????????.
???????? ?????: ?????????????? ???, ?????????, ???????????, ?????, ??????, ??????????
??????????? ??????, ??????? ??????????? ????????.
???????? ??????????? ?????????????? ???? (??) [1-3] ?? ??????????? ???????????? ??????? (?????? US2008196183, 21.08.2008), ???????????? ????, ? ??????????? ????????
??????????? ???? (?????? EP1359254(?2), 05.11.2003, REISNER & WOLFF ENGINEERING),
????????-???????????? ?? (?????? ?105309, 31.01.2011). ??????????? ???? ??????????? ???????? ???????? ??????????? ? ??????????? ?????? ????? ???????????? ???????? ??? ????????? ??, ??????? ????? ???? ???????????? ??? ???????? ????????????? ??????????. ? ????
????? ??? ??????????? ?? ?????????? ??????? ??????????, ?????????????? ????????????
?????????? ????? ???????????? ????????. ??? ??????????? ? ?????-?? ??????? ????????? ???????? ???????????? ???????????? ?? ??? ??????? ??????????????, ?? ???????????? ???????????? ??? ??????????? ???????????? ?????????? ???????? ? ???????? ? ????? ?????????
????????, ??? ??????????? ? ???????????????? ? ????????? ?????????? ??????????? ???????
? ?????????????? ????????? (????? 100) ? ??????? ???????? ? ?? ????????????, ??? ????? ?
????????? ??????? ??????? ? ???????????? ????????????? ??? ????? ??.
???????? ??????????? ?????????? ??? ???????????? ?? (?????? EP1033442(?2), 06.09.2000,
REISNER & WOLFF ENGINEERING), ? ??????? ???? ?????????? ???????? ????????? ?????????
????? ???????????? ???????? ??????? ??????????? ????????, ??????????? ????? ????????
???????? ??????????? ? ??????? ?????? ??????????? ?????.
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: qwer63@bk.ru
# 705 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ??????????. ?????? ?????????????? ???????????? ????????? ???????????
??????????? ???? ??????????? ????????? ??????? ?????????????? ???????? ?????????? (??? ??????? ??? ????? ?? ?????? ??????? ??????????? ????????), ?????????????
??????????? ?? ????????????????? ????????????? ? ???????? ???????????? ??? ?????????
?????????? ???????? ?, ?????????????, ????????? ??????? ???????????? ??? ??????? ??
???????????? ? ??????? ?????? ??????????. ????? ??????????? ????????????????? ????????????? ???? ???????? ?????????? ?????????? ? ??-?? ????????????? ??????????? ???????????? ??????? ??????? ?????????? ?????????? ??-?? ?????????? ?????? ?????? ???????? ?????
????? ?????? ??????? ??????????? ????????.
????? ???????????? ??????? [5, 6] ???????? ????????? ???????????? ??? ????????
?????????? ?? ???????????? ????? (????????? ??????????) ?? ?? ???? ??????????? ?????????? ???????? ?????????? ???????? ?????????? ? ??????????? ???????????? ??????? ??????? ?? ????????? ?????????? ??? ?????????????? ????????????????? ????????????? ??? ???????????? ??.
??????????? ????????? ??????????? ?? ???? ????, ??? ?????????? ??????? ???????
??????????? ??????? ????? ??????????? ??? ??????????? ???????????-??????????? ?????? (?????????) ?????, ??? ???????????? ??????? ??????????? ?? ?????? ?????? ? ???????? ??? ?????????????? ???????? ??????? ??? ??????????????, ? ??? ?????? ???
????????????? ???????? ?????????? ????? ????? ???????? ??????? ? ????????????
???????? (??????????? ??????). ? ???? ???????? ??????????, ??? ???????, ???????????
????????????? ?????, ??????? ??????????? ??????? ??? ???????? ????????? ????????
???????? ??????? ??????? ??? ?????????????? ?? ????????????????? ????????????? ???
????????????.
??????? ??????????? ???????? ????????????? ?????????? ??? ?????? ????? ???????
???????? ? ?????? ?? ?????, ??????????????? ???????????? ??? ??? ?????? ???????????
????? ??? ????? ???????? ?????????? ???????????? ?????????? ????? ????? ? ??? ????????
??????? ? ?????????. ??? ????????????? ??????????? ? ?? ?? ??????????? ????????????
??????? ? ???????? ??????????? ????? ?????????? ??????????? ????????? ?? ?????? ? ?????????? ??????? ??????????? ??????? ??????? ??????????? ????? ? ??????, ??????????? ???
?? ?????????????????? ???????? ? ???? ??????????, ??? ?????????? ????????? ???????????????? ??????? ??.
?? ???????? ???????????? ???????? ?????????? ??????????? ?? ? ??????? ??????????? ???????: ?? ???. 1 ????; ?? ???. 2 ? 3 ? ?????????? ??????? ? ??????? ????????? ??????
?? ? ???????????? ??????? ? ???????????? ????????????? ???????? 1 ? ? ????????????
??????? ? ??????????? ????????????? ???????? 2, ???. 3 [4]; ??????? ??????????? ???????? 3, ?????? ????? 4, ??????? ??????????? ??????? 3, ????????? ??????? ??????? ?????
5 ? ????????????? ??????? ????? 6, ???. 3, ???????? ?????????? 7, ??????? ???????? 8; ??
???. 4 ? ????; ?? ???. 5 ? ?????????? ??????? ???. 4 ? ???????; ?? ???. 6 ? ???????? ???????????
??????? ???. 4, ?????? ????? 4 ? ??????? ???????? 8, ????????? ?????? ??????? ???????????
??????? 3, ?? ??????????? ??????; ?? ???. 7 ? ????; ?? ???. 8 ? ?????????? ???????, ???. 7 ?
???????; ?? ???. 6 ???????? ??????????? ???????, ???. 7 ?????? ????? 4 ? ??????? ???????? 8,
????????? ?????? ??????? ??????????? ??????? 3, ? ??????????? ???????????-???????????
??????. ??? ??????????? ?? ???. 9 ? 10 ????????? ???????? ??????????? ???????????? ??.
# 706 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
???. 1. ???????? ?????? ???????????? ?? ? ???????? ???????????? ?????????? (????)
???. 2. ???????? ?????? ???????????? ?? ? ???????? ???????????? ?????????? (?????????? ???????
? ???????)
???. 3. ???????? ?????? ????????-???????????? ?? ? ???????? ???????????? ?????????? (??????????
??????? ? ???????)
???. 4. ???????? ?????? ??????? ??????????? ??????? ?? ??????????? ?????? (????)
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
???. 5. ???????? ?????? ??????? ???????????
??????? ?? ??????????? ?????? (??????????
??????? ? ???????)
???. 6. ???????? ?????? ??????? ???????????
??????? (?????????? ???????)
???. 7. ???????? ?????? ??????? ??????????? ??????? ? ??????????? ???????????-??????????? ??????
(????)
???. 8. ???????? ?????? ??????? ??????????? ??????? ? ??????????? ???????????-??????????? ??????
(?????????? ??????? ? ???????)
???. 9. ???????? ?????? ???????????? ?? ? ???????? ???????????? ?????????? (3D)
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
)LJ
?.?. ?????????, ?.?. ??????????. ?????? ?????????????? ???????????? ????????? ???????????
???. 10. ???????? ?????? ???????????? ?? ? ???????? ???????????? ?????????? (3D)
)LJ
?? ???????????? ??? ????????-???????????? ????, ????????????? ? ??????????????? ?????? ???????????? ????????????? ???????????? ???????? (???????????? ???????
? ???????????? ????????????? ????????) 1 ??? ?????????? ??? ? ??????????? ???????????? ??????????? ?????? (??? ??????? ???? ??????????? ????? ? ??????????? ????????????? ????????) 2, ????? ???????? ??????????? ??????? ??????????? ???????? 3,
??????? ??????????? (? ?????????? ?? ? ???????????? ????????????? ????????????
???????? 1) ??? ??????????? ???????????-??????????? (? ?????????? ?? ? ???????????
????????????? ???????????? ???????? 2) ?????, ? ????? ???????? ??????????? ??????
?????? 4, ??????? ??????????? ??????? 3, ????? ??????? ??????? ?????? 5 ? ????????????
????????????? ???????????? ???????? (???????????? ??????? ? ???????????? ????????????? ????????) 1, ??? ????? ????????????? ??????? ?????? 6 ? ??????????? ????????????? ???????????? ???????? (???????????? ??????? ? ??????????? ?????????????
????????) 2, ??? ?????? ??? ?????????????? ????????? ?????????? 7. ??????? ??????????? ???????? 3 ?????????? ? ?????? ??? ?????? ??????? ???????? 8, ?????????? ?????? ????? 4 ??????? ??????????? ??????? 3. ??? ????? ???????????????? ????????? ??
?????????????? ????? ??????? ??????????? ??????? 3 ?????? ????????????? ?????????????? ???????? ? ??? ????? ????????? ???? ????? ?????????????? ???????? ? ?????????
???????????? ????????????? ???????????? ???????? 1 ? (???) ??????????? ????????????? ???????????? ???????? 2.
??????? ??????????? ???????? 3 ? ??????????? ???????????-??????????? ?????? ?????
????? ?????? ??? ????????? ????? ???????????? ??????????? ??? ????????? (???. 8,9), ? ??????????? ?? ?????????? ??????? ??????????.
?????? ??????? ??????????? ??????? 3 ?????? ???? ????? ?????? ????? ?????????
???????????? ????????????? ???????? 1 ??? ????????? ??????????? ????????????? ???????? 2, ? ????? ????? ????? ? ? ?????? ?? ?????????? ? ??????? ??????? ?????? 5 ??? ? ????????????? ??????? ?????? 6, ? ????????? ??????????? ????? ? ???????????? ????????????? ???????? 1 ??? ? ??????????? ????????????? ???????? 2. ????? ??????? ???????????
??????? 3 ?????? ????????????? ????????? ????? ???????????? ????????????? ????????????
?????? 1 (??????????? ????????????? ???????????? ?????? 2) ? ????? ?? ?????????? ??? ???????????? ????????? ??. ??????? ??????? ??????????? ??????? 3 ???????????? ????????
?????????? ????????? ? ?????????? ??????????, ??????? ??? ?????? ??????????? ? ???????
?????????? ????? ????????????.
# 709 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ??????????. ?????? ?????????????? ???????????? ????????? ???????????
??? ?????????? ????????? ??????? ??????????? ??????? 3 ?? ??????? ????? ???? ????????? ?? ???? ?????????? ?????????? ????? ??? ?????? ????????? ?????? ??????? ??????????? ??????? 3 ? ???? ?? ??????. ??????????????? ?????? ??????? ??????????? ??????? 3 ??
????????? ????? ????? ??????? ???????????? ?????????? ? ????????? ?????????????? ???
???????? ????????? ? ??????? ? ??????? ?? ???????.
????? ???????? ??????? ??????????? ??????????? ???????? ????????????? ??????????
??????????? ???????????? ?????? ?? ????????????? ??? ?? ?????, ????, ??????, ?????? ?
????? ? ???????? ????? ?????, ??? ????? ???????????? ????????? ? ??????????? ??????????? ???????, ????????????? ????????? ???????, ????????? ??????? ?????????? ???????????? ??? ??? ???????????? ?? ????? ??????? ?????. ?????????????? ????????? ? ???????????
??????????? ??????? ?? ??????????? ??? ? ???, ??? ???????? ?????????? ?????? ?????????
??? ????????? ???????????? ????????? ???????????? ????????, ????????????? ?????????
? ?????? ???????????, ?????????? ?????????? ????????? ????????, ????????? ?? ????????, ???????? ? ???????? ? ????????? ????????????, ??????? ? ???????????? ?????????? ?
?? ??????? ??????????? ????????, ??????? ?? ????????? (????????), ??? ? ????? ?????????????? ?????????????? ????? ??? ????????????? ???????????? ? ???????? ?????????? ????,
????????? ?? ?? ? ???????? ?????.
? ???? ????? ????????????? ?????????? ??????????? ?? ???? ????? ?? ??? ????????
????? ???????????? ??????? ??? ???????? ???????????? ???????, ??? ??? ???????? ????? ???
???? ?? ??????????. ? ???? ??, ??????????? ?????????? ?? ???????????? ? ??????? ???????
??????????? ??????? ?? ???? ????? ???????????? ??, ????? ???????????? ????? ?? ??????????? ????????????? ?????????? ????? ???????????? ???????? ? ??? ????? ???????????
???????? ???????????????? ?? ?? ?????????? ?????????? ???????? ? ????????? ? ?????
????????? ????????.
?????? ??????????
[1] ?????????? ?.?., ?????? ?.?., ?????????? ?.?., ????????? ?.?. ?????????????
?????????????? ??? ???????? ??????????//????????-?????? «????????????». 2012 ?3
(12) ? ?. 1-17. [??????????? ??????]. ? ?. 2012 ? ??. ????? ???? ??? «?????????????» ?
????? ???????: http://naukovedenie.ru/sbornik12/12-41.pdf.
[2] ?????????? ?.?., ?????? ?.?., ?????????? ?.?., ????????? ?.?. ?????????????
??????????? ?????????????? ???? ???????? ?????????? ? ???????????? ??????? ??
??????????//????????-?????? «????????????». 2012 ?3 (12) ? ?. 1-7. [??????????? ??????]. ?
?. 2012 ? ??. ????? ???? ??? «?????????????» ? ????? ???????: http://naukovedenie.ru/
sbornik12/12-42.pdf.2
[3] ?????????? ?.?., ?????? ?.?., ?????????? ?.?., ????????? ?.?. ?????????? ?
?????????????? ???? ???????? ??????????//????????-?????? «????????????». 2012 ?3
(12) ? ?. 1-6. [??????????? ??????].-?. 2012 ? ??. ????? ???? ??? «?????????????» ? ?????
???????: http://naukovedenie.ru/sbornik12/12-43.pdf.
[4] ????????? ?.?. ?????? ??????????????? ???????????? ?????????????? ????
?????????? ? ???????????? ?????// ?????? ? ?????. ???. ?????????, 2012. ? 27.
? 155-165.
# 710 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ??????????. ?????? ?????????????? ???????????? ????????? ???????????
[5] Kozlachkov S.W. The expansion joint // PCT/RU2011/000269 ?? 26.04.2011. ??????:
??????????? ????????? ?? ???? ? WO 2011126413 ?? 13.10.2011 ? 21 ?.
[6] ????????? ?.?. ?????????????? ??? // ?????? ?? ??????????? ? 2461680 ?? 09.03.2011.
??????: ??????????? ????????? ??????????? ?????? ?? ???????????????? ?????????????
? 26 ?? 20.09.2012 ? 9 ?.
Analysis of Design Features of The Protective
the Device of the Of Expansion Joint
for Bicycle Movement
Sergey V. Kozlachkov and Iliya I. Owchinnikow,
Moscow Automobile and Road State
Technical University (MADI), Sochi Branch
5 Chekmeneva Str., Sochi, Krasnodar, 354024 Russia
Research and technical solution is devoted to construction of expansion joints (DS) comb and modular
comb types used in bridge engineering, and is aimed at ensuring the security of travel cycling on the
DS, protection from penetration under QUI snow, ice, dirt, gravel, crushed stone, on the carriageway
of the bridge, and improving the functionality of the DS in the perception of transverse displacements
and rotations in terms of steel structures.
Keywords: expansion joints, modular, comb, review, analysis, shell comb fingers, elastic comb
plates.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 6 (2013 6) 712-720
~~~
??? 623.6
?????????? ????? ???????????????? ???????
??? ??????? ?????? ????????? ???????????
????????????? ??????? ????????????????????? ???????????
?????? ???????? ??????? ???
?.?. ????????*, ?.?. ??????????, ?.?. ????????
?
???? ??? «??????-????????? ????????
??. ?????????? ?.?. ?????????? ? ?.?. ????????»
?????? 394064, ???????, ??. ?????? ???????????, 54?
?
??????? ???????? ????????-??????????? ???????
????? ?.?. ??????
?????? 170022, ?????, ??. ????????, 50
Received 10.06.2013, received in revised form 26.07.2013, accepted 30.08.2013
? ?????? ??????????? ???? ?? ?????????? ??????? ????????????? ????????? ? ??????
??????? ?????????-???????????? ??????????? ?????? ???????? ??????? ???, ???????????
????????? ????????? ?? ???? ???????????? ??????? ?????????? ??? ?????? ????????
???????????????? ???????????? ?? ???????? ?????????? ???????????? ??????????? ??
?????? ???????????, ??? ??????? ?????? ?????????????????? ??????????? ?????????????
??????? ?????????-???????????? ??????????? ?????? ???????? ??????? ?? ??????????
?????????? ???.
???????? ?????: ????????????, ?????????, ????????????,
?????????????, ?????????, ????????????? ? ?????????? ??????.
???????
??????????,
? ?????????? ?????????? ?????????????? ???????????? ??????? ?????????-????????????
??????????? (????) ?????? ???????? ??????? ??? ????????? ??????????? ???????????
????????? ??????? ????? ??????????? ?????????? ? ??????????????? ???????????? ?? ?????????. ??????? ?????????????? ???????????? ??????? ???? ?????? ???????? ??????? ?
????? ????? ?? ???????????? ? ????????? ??????? ?? ?????????? ? ????? ??????? ?????????? ?? ???. 1.
?? ??????? 1 ???????????? ??? ???? ??????. ????????????????? ??????? ???????? ????? ????????????? ???????? ?????? ? ????? ?????, ??????????????? ???????? ?? ?????????????? ????????? ??????? ????, ??????? ?????? ??????????? ??? ??????????? ??????????
???? ?????????. ??????????????? ??????? ? ????? ????????????? ???????? ??????, ???????
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: borodin.aleksei@mail.ru
# 712 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ?????????? ?????????? ????? ???????????????? ??????? ??? ??????? ?????? ??????????
???????? ??????
?????????????? ??????????
X 2 (X 2.1 , X 2.2 ) Џ : X 2
??????? ???? ?????? ???????? ???????
?? ?????????? ?????????? ??? X1(G1, G2 , G3 , G4 , G5 , G6 ) Џ:X1
??????????
??????????
?????????????? ?????????
?????????? ?????? ???
?????????? ?? ?????????? X2.1
??????????? ?????????
??????????? ???????
??????????
??????????????
??????????
??????? ?????????? ??????????
????????? ??????????? ??????????? ???????
(??????????? ???? ??????????? ???)
??? ???, ??????????? ??
???????? ???????????
??????????? ??????? X2.2
?????????????? ????? ?????
X 3 (X 3.1 , X 3.2 , X 3.3 , X 3.4 , X 3.5 , X 3.6 ) Џ : X 3
?????????????? ?????? ????????
?? ? ??, ???????????? ???????
??????????? ???? X3.1
??????? ??????????
?? ?? ??, ????????
??????? ?? ? ??? G1
??????? ??????????
????????? ???????
???? (???, ??, ???) G2
??????? ??????????? ?????????
??????????? ??????? ?? ?????????? ??????????
????????? ??????????? ??????????? ???????
(??????????? ???? ??????????? ???)
?????? ? ?????????????????????????? ?????????
???????? ????????? ??????????
??????????? ???? X3.2
??? ? ??? ???????????? ??
?????????? ??????? X3.3
??????? ??? ?
???????????? ???
????????? ????????????????
???????????? ???. ???????
??????? ?????????????? ?? X3.4
G3
??????? ????????
??????? ?? G4
??????? ??????????? ??????????????
??????????
????????? ??????????? ??????????? ???????
(??????????? ???? ??????????? ???)
?????????????? ??????????? ???
?????????????? ???????????
??????????? ???????? X3.5
????????? ????????????????
???????????? ?????????
??????? ??????? ???????????
?????????????? ?????????? X3.6
??????? ?????????????????????????
??? ? ??????? G5
???????
?????????????? ?
?????????? ??? G6
???. 1. ??????? ?????????????? ???????????? ??????? ???? ?????? ???????? ??????? ???
????????? ??????????????????? ??????? ???? ?? ????? ? ??????? ?????? ????????????????
?????????.
?????????? ??????????, ???????? ???????? ?????? ?????? ?????????-????????????
??????????? ?????? ???????? ??????? ?? ?????????? ?????????? ???. ? ????? ???????????,
?????????????? ??????? ?????????? ??????????????, ????????? ?????????? ?????????? ??????????; ?????????? ??????????? ????????? ??????????? ???????; ?????????? ???????????
?????????????? ?????????? ? ???? ?????? ????????.
???????????? ??????? ???? ? ?????? ???????? ???????? ? ????????? ??????? ????????, ??? ??? ????? ???????????? ???????? ?????????? ?????, ? ?????????????? ?????? ??
??? ????????? ??????? ?? ??????????????? ?????????????? ?????? ??????????. ????????, ?????????? ?????????? ?????????? ? ?????????? ??????????? ????????? ????????????
??????? ????? ????? ???? ? ???????? ?????????? ??????????? ??????? ? ????????? ??????????? (???, ???????????? ???, ???????? ???????, ??? ???????????????). ???, ???
??????????? ?????????? ? ??????????????? ?????????? ????????? ??????????? ???????
?? ?????????? ?????????? ??? (????? ?????? ?????? ?????????????) ?????????????? ?????????????? ?????????-????????????? ? ?????? ??????????? ??????????? ???????, ?
????? ?????????????? ? ???????????? ????????? ???, ??? ? ???????? ??????? ??. ?????? ? ??? ??? ??????????? ????????????? ?????????? ?????????? ?????????? ??????????
??? ????? ?????????????? ?????????? ? ????????? ????????????? ????????? ??????????
???????.
# 713 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ?????????? ?????????? ????? ???????????????? ??????? ??? ??????? ?????? ??????????
??? ??????????? ?????????? ? ??????????????? ?????????? ??????????? ??????????????
?????????? ????? ?????????????, ???????????? ???????? ??????????????, ???????????????
?????????? ? ????????? ????????????? ?????????-????????????? ? ?????? ???????????
???????? ????????? ??????? ???? ?????????? (???, ?? ? ??), ??????? ????? ???????? ???????????? ??????????? ??????? ?????????? ??????????. ?????????? ?????????? ?????????? ????????? ??????? ?? ?????? ?????????? ???????? ????????? ??????? ???? (???, ??,
??), ????????????????? ??????????? ??????????? ?????????????? ? ???? ?????? ????????, ?
??????? ?? ??????????? ?? ????????? ???? ? ????? ?? ?????? ???? ????????? ? ????????.
?????????????? ??????? ??????????? ????????? ??????????? ??????? ?????? ???? «???????????» ? ??????????? ?????????? ??????????? ?????????????? ??????????, ????????
???????? ???????????? ? ???????? ? ?.?.
?????? ??? ?? ???????????? ??????????????? ?? ???. 1 ???????? ????????????, ??? ???
??????????? ????????? ????? ???? ?????? ??? ??????? ?????????? ? ??????????????? ?????? ?? ???. ??? ?????????????? ????? ????????? ????? ????????? ? ??????????????? ?????????? ? ?????????? ?? ?? ????????????????? ????????? ? ?????????? ?????? ????? ?????????????? ??? ?????????? ?????? ????????????? ????????? ? ?????? ??????? ???? ??????
???????? ???????.
????? ???????, ???????????? ? ???????? ???????????? ????????????? ??????? ???? ?
????? ???????? ?????????? ?????????? ??????? ??????? ??????????????? ????? ??????.
??? ??????????? ???, ??? ? ?????????? ???????????? ??????? ????????????, ???? ? ????????? ??????????? ????????? ???????????? ???????????????? ?????????, ?????? ?? ?????????
??? ???????????? ?????????? ?????? ????? ????. ???????? ??????????????? ?????????,
??????????????? ? ??????? ?????, ???????? ???????????? ???????????? ????????????
?????????, ????????? ????? ?? ????????? ????? ??????????? ??????? ???? ?????. ???????
?????????????? ????????? ??????? ???? ?????? ???? ??????????????? ??????? ??????????????.
?????????????, ??? ??????? ????????????? ?????????, ?????????? ? ?????????? ???????
??????? ?????, ????????? ?? ??? ??? ????????? ????????? ???????? ??????????? ??? ???????????? ????????????? ??????? ???? ? ?????.
??? ?????????????? ????? ???????? ? ??????? ??????? ???????? ?? ?????? ??????????
???????? ?????. ?????????? ????????? ?????????? ? ????????? ????????? ?? 2n ????? ? ??????? n ????????? ?????, ??????????????? ????????? ??????????, ?????????? ???????
????????? ???????? ???????? ????????????? ??????????? ????????? ??????? ????????????????????? ??????????? ?????? ???????? ??????? ?? ?????????? ?????????? ??? ? ??????????? ? ?????? ???????????? ???????????. ???????????? ???? ???????? ???????? ??,
??? ?????? ??????????? ??????, ??????????????? ????????????? ????????? ?????????????,
????? ???? ? ?????? ???? ????? ??????? ? ?????? ?? ????? ??????????? ?????. ????????? ?
????????????? ???????? ???????????? ??????? ???? ???????? ??? ??????????, ????? ?????
????????????? ????????? ?? ????????????? A1, A 2, A3. ?????? ????? ??? n = 3, ???????????
????????? ?? 8 ?????, ??????????? ?? ???. 2.
?? ??????? 2 ????????? ?1 ???????? ???????????? ????????????? ??????? ?????????? ?????????? ?????????? ???, ????????? ? 2 ? ??????? ??????????? ????????? ??????# 714 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ?????????? ?????????? ????? ???????????????? ??????? ??? ??????? ?????? ??????????
?1
?12
?2
?123
?13
?23
?3
???. 2. ?????? ????? ??? n = 3
????? ??????? ? ?3 ? ??????? ??????????? ?????????????? ?????????? ? ???? ?????? ????????. ???????????? ??? ??????????? ???????? A1, A 2, A3 ???????????? A123 = A1?A 2?A3,
?13 ?1 ?3 ?2 , ? 23 ? 2 ?3 ?1 ???????? ????????? ????????????? ?????????, ??????????? ???? ?????, ???????????? A123 ????????????? ???????? ?????????? ???????? ????????????? ?????????. ??? ?????????? ???????????? ????????????? ??????? ???? ? ?????
?????????? ???????? ???????? ??????????? ????????, ? ?????????? ???????? ??????? ???3
?????? ? ? n , ?????????? ??? ?????????????? ??????? ?????????-???????????? ????????n 1
??? ?????? ???????? ???????. ??????? ????????, ??? ????????? ????????????? ????????? ?1,
? 2 , ?3 ?????????? ????? ?????, ?? ???? ?1 ? ? 2, ?1 ? ?3, ? 2 ? ?3, ??? ??? ?1 ? 2 z 0 , ?1 ?3 z 0 ,
? 2 ?3 z 0 ??????????????. ????? ?????? ????????? B = {B1, B2,?Bm}. ?????? ????????? ????????? P = {p1, p2,?pn} , ?????? ??????? ???????? ????????????? ?????????????? ??????????????? ????????????? ?? ????????? ? ??????????? ?????????-???????????? ???????????
? ???????????? ?? ????????????????.
????? ???????, ??????? ???????? pi?P ????????????? ????????? ???????????? ????????????? ?? ?, ??????? ???????????? ???? ????????? ? ???????? ?????? ?????????????
{K1, K 2,?K L}. ????????? ?????? ????????????? ????? ????????? ?????????? ???????? ?,
?????????????, ???????? ??????????????? ???????????, ? ?? ??????????? ????? ????????? ?, ?? ???? K1 U K1 U K U K L = B . ? ?????????? ????? ???????? ??????? ????????? ?
4 ???????????? mЧn, ???????? ??????? ????? ???????, ?? ???? ?ij = 1, ???? ??????????????
??????? bi , i ?1, m ???????????? ????????? p j , j ?1, n , ? ?ij = 0 ? ????????? ??????. ???,
??? ?????????? ?????????? ?????????? ????? ???????????? ????????? ?1, ??? ??????????
??????????? ????????? ??????????? ??????? ????????? ?2 ??????????????, ??? ??????????
??????????? ?????????????? ?????????? ? ????????? ?3. ? ???? ?????? ????????? A1 = K1,
A 2 = K 2, A3 = K 3.
????????? ????????? ?? ?????? ????? ??????? ? ???????????? f : B ? ?, ????????
????????? ?? ? ???? ? ?????? ???? ??????? ?? ? (????????? ??????? ???????? ?????????????? ???????????????? ?????????). ????????, ??? ????? ??????????? f : B ? ? ?????????
????????? ??????????????? ?? ????????? ?. ?????? ?i ??????? ??????????????? ????????
? ???????????? ??????? ?????????????? ?? ?. ????????? ????? ????????????????? ??????????. ?? ??????? 3 ???????????? ??????????? f : B ? ?, ??????????? ????????? ??????????????? ?? ?.
# 715 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ?????????? ?????????? ????? ???????????????? ??????? ??? ??????? ?????? ??????????
f :B o?
?1
?2
?1
?2
?3
?3
???. 3. ??????????? f : B ? ?
?????????? ???????? ??????????? f2 : B ? C, ??? ? ? ????????? ?????????? ?????????
??????? ?????????-???????????? ???????????, ????? ??? f 2 (bi ? A n ) = Cn , n = 1,3 .
? ?????????? ??????? ??????? ??????????????? ????? ??? ????????? ????????? ??????? ??????????? ????????????? ???????????????? ????????? ??????? ???? ?n, n = 1,3
???????? ???????????? ??????????? ?? ?????? ???????????. ??? ????????, ??? ?? ????????? ????????? ??????????? ?????????? ????????? ??????? ???? ? ????????????????
bi ? A n , n = 1,3 , ?????????? ????????? ??????? Cn (bi ? A n ) ? ?n bi Џ A n . ??? ???? ?????
(1)
(2 ) (1)
(2 )
????????, ??? ???????????? bi ?????????? ?? ?????? ??? ????????????? bi bi f bi
,
???? ? b 1 d ? b 2 ? ? b 1 t ? b 2 ??? ???? ?? ???? ?? ?????????? ???????? ???????. ??-
(
i
i
i
)
i
????? ????????? ????????? ?????? Fn , n = 1,3 ? ????????? «???????????????????????» ????????, ???????????? ? ?????????, ??? ?? ???????????? ?????? ??????????????? ???????, ????? ???????? ??????????? ????????????? ???????????. ?? ??????? 4 ???????
???????????? ????????? ??????????? ? ????????? «???????????????????????» ??? ????????? ????????? ??????? ????.
?? ???? ??????? ??????? ??????? ???????? ??????? ????????????? ??????????? ??
?????? ??????????? ?Fn , n = 1,3 . ??????????? ???? ???????? ??????????? ??????? ????? ????? ?????????? ???????????? ???????????, ?? ?? ????????? ????? ????????????, ?????? ?
?????-???? ?????? ????????????. ? ???? ?????? ?? ????? ?????? ?????????????????? ???????????.
???????? [1, 2], ??? ????????? ???????? ??????? ??? ?????? ????????? ???????
????? ????????? ?? ?????????, ????????????? ? ??????????. ????????? ????????? ??
?????????? ??????? ?????????????? ?????????? ????? ????????? ??????? ???????
fi ( x) ? F . ??? ?????? ????????? ???????????? ? ???? ?????? ????????? ??????????
??????? ????????, ? ??????????? ?? ?? ???? ????????? ???????? ?????????????. ???,
??????? ????
n
? ( x) = ? fi ( x) ,
(1)
i =1
??? ?????????? ???????? ???????????? ????? ????? ????????? ???????, ????????????? ???????
??????????? ?????????????.
? ???? ??????? ????????? ??????? ????????????? ???????????, ??? ???? ??????????
??????? ???????? ????? ???
# 716 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ?????????? ?????????? ????? ???????????????? ??????? ??? ??????? ?????? ??????????
?1
F1
?2
F(?,?)
F2
F(?,?)
SF1
F3
F(?,?)
SF2
?1
?3
SF3
?2
?3
???. 4. ????????? ??????????? ?????????? ????????? ????
n
? ( x) = ? fi ( x) .
(2)
i =1
?????? ?????????? ?????????? ??????? ???????? ? ???????????? ? ????????? ???????????????? ??????????. ??? ????????? ????????????? ????? ???????? ??????????? ??????????????? ?????????? ???? ?? ????????? ???????????, ??? ???? ?? ????? ??????????????
????? ??????? ?????? ????
? ( x) = max
i ?i < n
fi ( x)
,
fi max
(3)
max
??? fi ? ???????????? ???????? ???????? fi (x) .
??????? ??????????????? ??? ????????? ????? ????? ????? ????????? ????? ? ???????????? ????????? [3], ?????????????? ??????????? ??????? ? ???????????? ????????? ??????
????? ????????? ????????? ??????, ?????, ??? ? = {?1,??n}, ??? ? i = min f i ( x) ? ??????? ???x?X
??????????.
?????????? ???????? ?????????? ???? ? ??????????? ?????? ???????? ????????????
?????????. ???, ????????????? ?????????? ??????? ???????? (1) ????????, ????? ?????????
???????? ????? ????? ??? ????? ????? ?????????? ??????????? ???????. ???? ????????
fi (x) ????? ????????? ??????? ?????????, ?????????? ????????? ???? ? ??????????
??????? (1) ? ????????????? ????, ?? ??? ????????? ? ?????????????? ?????? ????????????? ? ???????????? ???????? fi (x) ? ??? ???? ????? «?????????? ????????» ? «??????????
????????» ??????? ?? ????????? ????????? ???????? ????????. ?????????? ??????? (2, 3)
??? ??????? ???????????? ?????? ????? ?????????? ????? ???????????????? ????? ????????? ? ?????????? ???????? ???????, ??? ????? ???????? ? ???????????????????? ????????????? ????????? ????????? ??????? ?????????-???????????? ??????????? ?????? ????????
???????. ????? ????, ? ??????? (3) ?????????? ?????? ????????????? ???????? ???????
????????. ????????????? ?????? «????????? ????? ? ????????????» ??????? ???????? ????????? ???????, ?????? ??? ?????? ???????? ?????????? ????? ?????? ????????????.
??????? ????? ??????????? ??????? ?????? ?? ????? ???????, ??? ????? ????????? ????????????.
????????? ?????????????? ???? ???????????? ???????????? ??????? ??????????, ??????????? ???????????? ????, ???????????? ???????. ?????? ????? ???? ???? ??????? ?????? ? ????????????? ??????????? ??? ????????????, ??? ? ????????????? ?????????. ??????
# 717 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ?????????? ?????????? ????? ???????????????? ??????? ??? ??????? ?????? ??????????
???????? ??????????? ??????? ? ?????? ????? ???????????? ????, ???????????? ???????.
??? ???????????? ?????????????? ?? ???? ???????????? ??????? ??????????.
??? ???????????? ???? ??????? ?????????? ????????? ???????? ???????? ?? ????????????? ?? ??????????. ???? ?????? ????, ???????????? ???????, ????????? ??????? ?????,
??? ????????????? ????????????? ????? ?????, ?? ?? ???????? ??????? ????????????????? ???
????????, ??????????? ??? ????????????? ??????? ??????? ??????????.
? [1] ?????????? ????????????? ????????? ????, ?????????? ?? ??????? «????????????? ?? ??????????». ????? ?????????? ????????? ?????? f? = ( f1 , f 2 ,..., f m ,..., f n ) . ?????????? ??
? ???? f? = (? , v) , ??? ?=(f1, ..., fm) ? v=(fm+1, ..., fn), ?????? ??Y, v?Z, F=YЧZ. ?????????? ?????
??????????? ??????? ?????????? u(?,v). ?? ????? ?????????????? ????? ???????? ???????
??????????. ???????? ??????? ?????????? ?? ????????? Y ?????????? ????? ???????? ?=?0,
?.?. u(?0,v), ? ?? ????????? Z ????? ???????? v=v0, ?.?. v(?,v0). ?????????, ??? Y ?? ??????? ??
?????????? ?? Z, ???? ???????????? ????, ???????????? ??????? ?? Y ??? ?????????????
v0?Z, ?? ??????? ?? ?????? v0. ??? ????????, ??? ?? u(??,v0) > u(???,v0) ??? ??,???? Y ? ???????? v0?Z
???????? u(??,?) > u(???,?) ??? ?????? v??. ? [105] ??????? ?????????? ??????? ? ????
u (? , v) =
u (? 0 , v)?u (? 0 , v0 )
,
1+k u (? 0 , v0 )
(4)
??? u(?0,v0) = u(?,v(?)) = 0 ? ?????? ?????? ???????????; k ? ??????????? ??????????? ?????????.
??? ???????????? ??????? (4) ?????????? ????????? ???????? ???????? ?? ????????????? ?? ??????????. ???? ?????? ????, ???????????? ???????, ????????? ??????? ?????,
??? ????????????? ????????????? ????? ?????, ?? ?? ???????? ??????? ????????????????? ???
????????, ??????????? ??? ????????????? ??????? ??????? ??????????.
?? ???????? ????? ?????? ????????????? ?? ???????????? ?????????, ????????? ? ?????????????? ????? ??????????? ???????? ?????????? ??????????, ? ????? ? ???, ??? ????,
??????????? ???????, ???? ?? ????? ???? ??????????, ??????????? ??? ?????????? ?????????, ???? ???? ?? ? ???????? ????????. ????? ????, ????????? ????????? ? ??????????
???????? ??????????? ??????????? ????????? k. ?????? ??????????, ??????????? ???
?????????? ????????????? ????????, ?????????? ?? ?????????? ?? ????????. ???????????
?????????, ? ? ???? ??????? ? ????????? ????????? ?? ???? ???????????? ??????? ?????????? ??? ?????? ???????? ???????????????? ???????????? ?????, ?? ??????????????
??????? ?????????? ? ????? ????. ?????????, ??????????? ??? ????, ?????????? ??????????? [4].
????? ?????????? ???????? ?????? ?????????????? ???? ????? ???????????????? ??????? [5], ???????? ???????? ??????? ? ?????????. ??????? ??? ??????? ?????????? f i , i ?1, n
??????????? ?? ???????? ? ??????? ?? ????????: f1 > f 2 > K f n , ????? ??????????????? ?????? ?? ???????? ?????????? f1 ( x) ? ???????????? ??? ???????????? ???????? f1max . ?????
????? ??????????? ???????? ??? ??????????? ???????? (???????) ?1 ? ? ??????? ???????????
max
?????? ?????????? ???????? f 2
??????? ?? ???????? ?????????? f 2 ( x) ??? ???????, ???
max
? ?1 . ????? ??????????? ???????
???????? ??????? ?????????? ?????? ???? ?? ????? ??? f1
f
?2 ??????? ?????????? ? ??????????????? ?????? ?????????? 3 ( x) ? ?. ?.
# 718 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ?????????? ?????????? ????? ???????????????? ??????? ??? ??????? ?????? ??????????
?????????????????? ???????? ??? ??????? ???????? ?????? ????????? ??????????? ????? ???? ???????????? ? ????
f1max = sup f1 ( x) ,
(5)
x?X
f 2max =
f nmax =
sup
x?X
f1 ( x )? f1max ??1
sup
f 2 ( x) ,
x?X
f n ?1 ( x )? f nmax ? ? n ?1
(6)
f n ( x) .
(7)
??????? ????????? ?????? ??????????? (7) ????????? ??????????? ???????? ??????
????????? ???????????.
???????? ??????? ?1 , ? 2 ,K ? n ?1 ??????????????? ??????????? ? ?????????? ????????
??????????? ??????? ??????????? ????????? ???????. ??????? ???????? ?????? ? ?????????? ???????? ??????????? ???????? ?1 ??????? ?????????? ?? ??? ??????????? ?????max
??? f1 . ??? ????? ?????? ????????? ??????? ??????? ?11, ?21, ?31? ? ????? ??????? (5)
max c 2
max c 3
max c 1
(' 1), f 2
(' 1), f 2
(' 1)
?????????? ??????????????? ???????????? ???????? f 2
??????? ??????????. ?????????? ??? ???????? ?? ???. 5. ?? ??????? ???????, ??? ??????? ????
????????? ???????? ??????? ???????? ??????? ?????????? ????????? ???????? ???????????? ??????? ?? ??????? ??????????, ? ?????????? ??????????? ??????? ??????? ??????
?????????. ?? ?????? ??????? ?????????? ?????? ??????????? ???????? ??????? ?1, ? ?????
??????? f2(?1).
????? ????????????? ???? ??????????? f2, f3 ? ????? ????????? «???????» ???????? ??????? f2 (?12), f2 (?22), ... ? ???????? ????????? (6) ??????? ?????????? ???????? ???????? ?????????? f3 (?12), f3 (?22),... ?????????? ?????? ???????????, ????????? ?2, ????????? ? ?????????
???? ??????????? f3, f4 ? ?. ?. ???????, ? ?????????? ??????? ????????? ??????? ??????????? fn?1
? fn ?????????? ???????? ????????? ??????? ?n?1, ? ? ???????????? ? ?????????? (7) ???????????? ??????????? ??????? ??????.
f1
f1
max?
max
f1 ?'11
f1max??'21
f1max??'31
f1max??'1
f2 *
f 2maxc ('11)
f 2maxc ('31)
f2max
???. 5. ????????? ??????????? ???????? ??????????? ?? ???????? ???????
# 719 #
f2
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ?????????? ?????????? ????? ???????????????? ??????? ??? ??????? ?????? ??????????
????? ???????, ????????????? ? ??????????????? ??????? ???? ?????? ????? ?????
???????????? ?? ????? ????????????? ?? ????????? ? ?????? ??????? ????. ? ???????? ??????? ??????????? ?????????? ????????????? ?????????? ????????????? ????????? ???????
????.
?????? ??????????
[1] ???? ?. ??????? ?????????? ??????????? ???????????. ?.: ???, 1976.
[2] ??????? ?.?., ??????? ?.?. // ????????? ? ?????????????? ??????. 1980. ?. ?VI.
???. 1.
[3] ?????????? ?.?. // ?????????? ? ????????????. 1972. ? 5.
[4] ??? ?. // ??????? ??????? ? ????????? ???????? ???????. ?.: ???, 1976.
[5] ???????? ?., ????? ??., ???????? ?. // ??????? ??????? ? ????????? ???????? ???????. ?.: ???, 1976.
Adaptive Method of Consecutive Concessions
at the Solution to the Problem of Vector Optimization
of Characteristics of System of Engineering ?
Air Field Maintenance of Operations
of Aircraft of the Air Forces
Alexey A. Borodina,
Vladimir N. Samusenko and Victor V. Lazukina
a
VUNTs Air Force ?Military and Air Academy of a Name of Professor
N.E. Zhukovskogo and Yu.A. Gagarin?
54a Starykh Bolshevikov Str., Voronezh, 394064 Russia
b
Military Academy of Aerospace Defense of a Name G.K. Zhukov
Tver 170022 Zhigarevs St. of 50
b
In article one of adaptive methods of aggregation of subsystems is presented to uniform system of
engineering-air field maintenance of operations of aircraft of the Air Forces, allowing to simplify
required on behalf of making a decision the information, by search of the most preferential alternative
from areas a subject consideration optimum on Pareto alternatives, at the solution to the problem It
is a lot of criteria optimization of characteristics of system of engineering-air field maintenance of
operations of aircraft in constant air stations of the Air Forces.
Keywords: decomposition, the set, the alternative utility function, aggregation, a priori, a posteriori,
and adaptive methods.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 6 (2013 6) 721-736
~~~
??? 711.1
???????????????? ?????????
??????????????? ???????
????????????? ????
?.?. ???????
????????? ??????????? ???????????,
?????? 660041, ??????????, ??. ?????????, 79
Received 26.03.2013, received in revised form 23.08.2013, accepted 30.08.2013
? ?????? ??? ?????? ?????????????? ??????????????? ???????, ?? ?????? ???????
?????????????? ??????????? ?????? ?????????? ????????????? ???? ??? ???????? ???????,
??????????? ??? ?????????? ??? ???????????????? ?????????. ?????????? ??????????
??????, ??????????? ? ???????? ????????? ?????????. ? ?????? ????????? ?? ?????????
????????.
???????? ?????: ?????????? ???????????, ?????????????? ??????, ?????????-????????????
??????, ???-?????????? ??????, ????????-?????????? ????????? ???????, ???????? ?????
???????????????? ???????????, ???????? ????? ???????????????? ???????????, ?????????
????? ???????????????? ???????????.
????????????, ??? ????? ?. ?. ??????????, ????????? ?? ??????????? ????? ??????????????, ??????? ?????????????? ? ????????????? ??????????? ?????? ????????, ? ??? ??? ??????????? ? ???????????? ?????. ?? ???? ??????? ?????? ?????????? ?????????, ?????????
???????? ??????????? ????? ??????????.
??????? ?????????? ????????????? ??????????? ????????????? ?????????, ?? ???? ????????, ???????????????, ??????? ? ???????????? ?????????? ? ????????? ????????.
?????? ????????????? ? ???? ????????. ??????? ??? ?????? ???????, ????????,
??????? ? ?????? ????? ????????????????? ??????? ???????, ??? ????? ? ???? ???????
???????????? ?????????. ?????? ????????????? ?????????? ? ????????, ????????????
????????? ???????????? ???????, ???????????? ?? ????? ???????, ??????????? ???????? ????????, ??? ??????????? ??????????, ?????????? ????????? ??????. ???????
?????????????? ?????? ? ??? ?????? ??????? ? ??????????? ????, ????????? ????????
???????? ? ??????? ???????????? ?? ???????????, ?????????? ????????????? ??????????? ????????.
????????-?????????? ????????? ??????? ? ?????? ??????????????? ???????. ?? ??????? ?? ???????? ??????????? ???????? (?????????? ???????, ???????????, ?????????? ? ?.?.),
?????????? ?????????-???????????? ? ????????? ??????????. ??? ?????????? ????????, ???*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: astanin_d@incom.ru
# 721 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
?????? ? ?????????????? ????????, ?????????? ????????? ???????? ?????????????? ??????????????? ???????:
1. ?? ?????? ???????????????? ??????????? ? ?????????????? ?? ??????????.
2. ?? ???? ????????? ? ?????????????? ?? ??????? ??????? ? ????????? ?????????????????????? ? ?????????? ???????? (?????????????? ?? ????????? ?????????? ? ????????????).
3. ?? ??????? ?????????????? ? ?????????????? ?? ??????? ????????.
??????? ??????????? ???????? ????? ????? ????????? ????? ???????????????? ???????????:
1. ???????? ? ????????? ???????????? ? ????????????? ?????????.
2. ???????? ? ??????? ???????? ????, ????????? ??????.
3. ????????? ? ???? ??????????????? ?????????? ????????, ???????????? ???? ??????????????????, ???????? ???????????? ?????.
? ??????????? ????? ?????????? ???????? ????????-?????????? ???????, ?? ??????????? ???????? ????????? ?????????????? ???????? ????????? ? ???????? ????????. ?? ?????? ????????? ???????? ??????????? ???????? ???????? ???????? ????????-????????????
??????, ??????? ????? ????? ??????? ??????? ??????????, ??????????? ? ?????????????
??????????? ????????. ???????, ??????? ??????, ???????????? ??? ??????????????? ????? ?
????????? ? ??????????, ????????, ????????????? ????????????? ? ?????????? ????????.
???????? ?? ??????? ??????????? ???????? ?????? ????? ??????? ??? ??????????? ????????????? ?????????.
?? ?????? ????????, ????????? ? ???????? ???????? ????????? ???????????????? ????????? ??????????????? ???????, ???, ??-??????, ?????????? ???? ? ??????, ???????????
??????? ?????????, ????????, ?????????? ? ??????????? ???????? ????????-??????????? ????????, ???????? ???????????? ? ????????????? ???????? ????????. ??-??????, ??? ???????
????????, ??????? ???????????? ???????, ????????-?????????? ??????????, ??? ??????????
?? ?????????-???????????? ???????, ?????????? ? ????????? ?????????, ????????????
????????? ? ????????, ??????? ????? ?????. ????? ?????? ??????????? ? ?????????????? ????????? ? ?? ???????????? ?????, ????????????????? ???????????? ??????????????????, ???
??? ????????? ????????? ???????????? ?????? ?? ????????????????? ??????????? ???????.
?-???????, ???????????? ???????? ???????, ???????? ????????? ???? [5].
???????? ???????? ????????? ?????????? ??? ?????????? ?????? ?????????? ? ????????????? ?? ??? ??????????. ????????? ?? ???????? ?????????? ? ?? ??????????????? ???????????? ??????? ? ????????????????? ????????-?????????? ??????????, ? ??????????? ??
?????????????, ? ????????????? ????????????? ???????, ? ??????????? ????????? ? ????????????? ?????????????? ???????. ?????? ?????? ?????? ?????????? ? ?????? ???????????
????????? ? ???????, ??? ??????? ????????? ??????????? ???????? ???? ???????, ????????
?????????? ?? ?????? ????????? ???? ?? ????, ?? ? ?????????? ?????, ?????????? ? ????????? ????????, ??????????? ????????? ? ?????????? ???????. ????? ???????, ???????
??????? ?? ????????? ? ?????????-????????????? ???????? ????? ?????????????? ?????? ??
?????? ????????, ??? ?????????-???????????? ??????, ? ?????? ??????????? ? ?????????????
??????.
# 722 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
?????????-???????????? ?????? ?????????????? ? ???????? ?????? ??????????????????????? ?????????????? ???????. ?????? ????????? ? ???? ???????????, ??????????? ????????????? ????????, ???????????? ??????????????? ?? ???????????? ? ???????????
??????????, ???????????????? ? ????????????? ???????????, ?????????????? ??????????,
???????. ? ????????????? ???????, ??? ??????? ???????????, ?? ??????????? ? ?????????
????????, ????????? ? ?????????? ????????, ????????? ????? ??????, ?????? ? ??????.
??????????????, ??? ???? ??????????????? ??????? ?????????? ? ?????????? ????????????, ? ?????????? ????????. ???? ?????????-???????????? ?????? ?????????? ????????????
???????? ?????????? (?????????, ???? ??????) ? ???????????? (??????????, ???????????
????), ?? ????????????? ?????? ?????????? ???????? ? ???????? ??????? ?????????? ????????, ????, ??????????? ????, ?????????? ???????, ?????????, ? ? ???????? ??????? ???????????? ???????? ??????? ? ?????? ???????, ?????? ???????, ?? ???? ???????? ????????????,
??????????????? ????????? ????????.
????????????? ?????? ?????????? ????????? ? ?????????? ????????, ????????? ???????? ??????? ???? ?? ????? ????????? ??????????, ???? ?????????????????? ? ???????? ????? ??????. ?????????????, ???????????????, ????????????? ? ?????????????-????????????
?????? ? ???? ???-??????????? ???????. ? ????????? ????? ?????? ??????? ? ???????? ??????
? ?????????? ????????? ???????? ? ??????? ??????? ??? ????????????, ???????? ? ???????? ????????? ? ???????? ? ????????? ?????????? ?????????. ? ???? ?????? ????????????? ??????, ? ???????????? ??? ?????????, ?????????? ??????????????. ???????? ??????? ?
???????? ????? ??????????? ?? ????? ?????????? ????????? ???????????. ?? ???????????
????????????? ??????????? ??????????, «????????????? ?????? ? ??? ????????????? ??????????? ? ????????? ????, ???????, ??????????? ?????????? ????? ? ??????????????
?????????????? ??????? ???????». ????? ???????, ????????? ????????? ? ???????????????
????????, ???? ???????? ??????? ? ????????? ???? ?????????? ????? ???????????, ????????
?? ????????, ????????, ???? ? ???????? ?????, ??????? ? ??????????.
?? ????? ????????? ??????????? ????? ? ??????????? ????????????? ?????. ?????? ?????????? ? ?????????? ???????????? ? ?????? ? ???????? ????????????, ??????? ? ?????????? ?????????? ????????? ????????????? ??????????????? ?????.
?????? ?????????? ? ???????? ?????? ??????????? ? ????????? ????????????? ?????.
??????????? ??? ? ??????????, ?????????? ????????, ??????, ???? ????? ???????, ????? ??
???????, ?????? ??? ???? ????????????? ? ?????????? ?????????? ????????????? ??????????, ?????????? ??? ????????? ????????.
??????????? ? ???????? ?????? ?????????? ???????????? ? ???????????? ?????????????? ??????. ??????? ???????? ?????????? ????????? ????????????????, ?????????? ??????????, ????????? ?? ???? ??? ????????? ???????????????? ??????? ??? ??? ???????? ?????? ? ???????.
?????? ???????? ??????????????? ???????
???????? ?????????? ???????????? ??????? ????????????? ?????????? ????????, ??
????????????????, ????????????? ????????????????? ? ????????????? ????????, ??????????????? ??????????. ??????????? ? ???????????? ?????? ???????? ??????????????? ???????
# 723 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
???????? ???????? ????????? ??? ????????????, ??????? ??????? ???????? ????????? ?????? ?? ??????????? ???????? ??????? ? ????????, ??????? ?????????? ??? ??? ???? ????????
???????? ? ?????????? ?????????? ??? ??????????? ?????????? ????????????, ??????????
???????? ????????????? ??????, ???? ? ????????. ???? ???? ????????? ???????? ??????????. ??????? ???????? ?????????? ? ??????? ? ?????? ?????????? ??????????????? ???????:
? ?????????? ?????????????? ?????? (??????????? ??????????? ????????? ??????????,
????????? ??????? ?? ????????? ?? ???? ??????????? ??????);
? ????????????? ?????????????? ?????? (3?5 ??????), ??? ??????????? ???????????? ????? ????????;
? ??????????? ?????????????? ?????? ???????? ?????????-????????????? ???????? ?????????? ?????? ????? ?????????? ????????, ??????? ?? ??????????????? ??????;
? ?? ??????????? ?????????? ?????????;
? ??????????? ???????? ???????? ???????????????? ?????, ??? ??? ????????????? ????,
??? ???????????????? ?????? ????? ??????? ??????????? ?????????? ? ??????????
??????? ????????????? ????????????, ?? ????? ???? ??????????? ???????????;
? ???????????? ????????????? ??????? ?????? ????????????? ?????????, ??? ?????????
?? ?????????????? ??? ?? ??????????? ????????????? ????????? ???????? ??? ??????????? (?????? ?????????? ?????????? ????????).
?????? ??? ??????????????? ??????? ????? ???? ???????? ??? ?????? ?????????? ????????. ?????? ???????? ??????? ?? ??????? ?????????????? ???????????? ??? ?????? ????????? ???????????? ???????:
1. ???????????? ???????????? ????????????? ???????? ??????????? ? ?????????? ???????? (?? ???????? ? ??????? ? ????????????? ????????) [5].
2. ??????????? ??????? ???????????? ???????? ????????.
3. ??????????? ??????????? ???????????? ?? ?????????? ? ????? (??????? ??????????
???????? ????????? ???????????? ????, ????????????????? ??????, ???????, ????? ??????????? ????????????? ????????????????? ??????????).
?????? ??????? ?? ???????? ?????, ?????? ??? ?????? ???????? ???????????????? ?????????? ????????, ??? ???? ??? ????????? ????. ???????????? ?????? ???? ???????????
?????? ?????? ?????????? ? ????? ?????? ????????????? ?????????????????, ?????????? ??
?????????? ?? ?????????? ?????, ???????? ?????????? ??????, ???? ??????????? ?????????
????????? ?????????? ?? ?????????? ????????? ??????. ?? ????, ?????????? ????? ????????
?????????? ?????? ?????????? ????????, ?? ??? ?????? ???????? ?????? ??? ?????????? ?
?????? ???????????. ??? ????????? ???????? ?????? ????????????? ?????????? ????????
?????? ? ????????????, ???????? ????????? ???????? ???????????? ?????: ??????????????;
????????????????; ???????????? ????????????; ????????????; ????? ????????????.
??? ???? ?????? «????? ????????????» ??????? ? ??????????? ??????????? ???????????????????? ??????????? ??????, «????????????» ? ? ???????? ??????????????????? ?????????? ????, «???????????? ????????????» ? ? ???????? ????????????? ???? ???????, ??????????? ?????????? ??????.
??? ??????????? ?????? ?????????? ????????????? ???? ?? ???????? ???????????????
??????? ????????????? ???????????????? ?????, ??????? ?????????? ?? ???? ?????? ???# 724 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
????????????? ??????????? ??? ???? ????? ????????? ???????? ? ?????????????? ???????.
??? ?????? ????????? ???????? ???????????? ?????????? ??????????????? ???????????????
???????, ???????????? ???????, ?????????? ???????? ????????????? ???????????, ??? ?????? ???????? ???????? ? ???? ??????????????? ???????, ???? ???????????? ??? ?????????
???????????? ????????. ??????? ????????? ?????-????? ?? ??????? ???? ???????. ??? ??
??????????? ???????????? ???????? ???????????? ?????-?????, ??????????? ??????????
????????????-?????????????? ???????? ????????? ??????????, ???????????????? ?? ?????????????? ???????? (???. 1, 2). ??????????????? ??, ????? ??????? ????????? ??????:
? ?????????? ?????? ????????????? ?????? (????. 1)
? ?? ?? ?????? ?????????? ?????? ?????????? ???????????: ?????, ???????????, ?????????? ? ????????.
????????? ???? ????? ?????????????? ???????? ?????? ??????? ???? ?????????????
???? ? ??????. ?????? ?? ?????? ? ??? ???????? (??????, ?????? ? ??????????? ????????)
??????????? ???????? ??????????? ?????? ? ???????, ????????????? ????????, ??????????????? ????????.
????? ???????, ??????, ??????????? ???????????? ???????????? ???? ? ??? ?? ?????,
???????? ????????? ???????? ?????????? 1-?? ???????.
?????? ??????????? ??????? ?? ?????????? ????????????? ???, ??????? ???? ????. ???
??????? ? ??????? ??????????? ????????? ??????????? 2-?? ???????. ? ??????????? ?????????? ??????????? ?????????? ? ??????? ? ???????? ????????? ?????????????? ??????????,
? ?????????? ????????????? ??????? ??? ?????? ? ???????? ????????. ? ????? ???????????
???. 1. ??????????? ?????? ?????????-????????????? ??????? ????????????? ????
# 725 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
???. 2. ??????????? ?????? ???-??????????? ??????? ????????????? ????
??????? 1. ????????????? ?????????????? ?????????? ??????? ????????????? ????
?????????????
?????
1. ??????????
?????
???????????????????????? ??????????
34
21
?????
??????
55
???-??
?????
???????
8
2?. ?????????
22
9
31
5
2?. ?????????
19
6
25
6
3. ????????
19
20
39
6
9
9
5
4. ????????
???????? ???????????
???????? ???????
????????????-????????????,
??????????, ?????????????
????????????, ??????????,
???????????????
????????????-????????????,
???????????????
????????????-????????????,
?????????????
???????-???????????????,
????????????
????? ???????? ?????????? ???????? ???????? ?????, ? ?????????? ? ??????, ???????? ? ??????, ???? ? ???????, ??? ???????? ?????-???????????? ?????.
????????? ??????????? ???????? ??????? ???????? ???????????????? ???????? ????????????? ???. ??? ? ????????? ??????????????, ? ?????????????????? ??????, ??????? ?????? ???????? ? ??????, ??? ? ?????????? ????? ? ?. ?.
????? ????????? ????????? ??????????? ???????? ???? ???????. ???????? ?????????
????????? ????????? ????????? ????????????? ? ?????? ???????? ?? ??? ???????????? ?
?????????? ??????????????.
# 726 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
?????????? ?????????? ??????????? (????. 2, ???. 3)
???????? ???????? ?????????????? ???? ?????????? ? ?????????. ???????? ? ????? ?????????? ????????? ????????? ???????? ? XVII-XVIII ??. ?? ???? ?????????? ? ??????????
?????? ?? ???????? ????? ??????. ? ????????? ????? 200 ?????????? ???????????. ?? ??????
??????? 2. ?????????? ?????????? ???????????.
?????
????????
?????????? ?????
??????????? ?????
??????????? ?????
???????????
??????????? ?????
??????-??????????
?????
?????????
???. ???
??????????? ?????
????????? ??????????
???????? ???????
1. ????????-?????????? ????? «???????
?????????????? ????»
2. ???????????? ???? «?????-??????????????
??????? ?????????»
3. ????????-???????????? ???????? «????????????
?????»
4. ????????? ???? ???????
?) ???-??????????
????? ? ??????
?) ??????????? ???????
???????? ? ???????? ??
????????? ?? ???????
5. ????-?????????? ????????? ????????
6. ??????????????? ???????? «????????? ?????»
(???????? ???????, ?????, ????????? ????????,
??????????? ???????? ????.
7. ????????????? ???????? «???????????
????????? ????? ?????? ?????? ? ?????? ????????
?????????????? ????????? ????? ? ?????»
8. ????????-??????????????? ???????? ????????
«??????? ?????»
9. ????? ????????????????????
?) ??????????????????
????? ?? ??????? ??????
??????? ?????????
10. ???????????? ???? ?????-????????? ?????????
(???? ??????? ?????????????.
11. ??????????????? ???????? «??? ??????» ?
????????? (???????, ??????, ??????????, ??????,
????????, ????????????, ???? ? ???????, ?????? ?
??????
12. ??????????????? ?????????? ??????????
«???????????????»
13. ?????????? ????????
- ?????? ? ??????
?) ???????? ??????
?????? ????? ??
????????? ?? ??????
????????
???????
14. ??????????????? ????????? ??????????
«??????????»
15. ?????????????? ???? ?? ???????? ???????????
?????????
16. ?????????? ?????????????
????????. ?????????????? ????????? ?????????
# 727 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
???. 3. ?????????? ?????????? ???????????
? ?????? ???????-?????????? ??????. ?? ????? ?????????? ????????????? ???? ??? ??????????? ? ?????????. ?????-?????????????? ?????????, ?????? ??????? ?????????, ???????????? ?????, ??????????? ????? ????????? ?????? ?????? (??????????) ????? ???? ??????? ???
??????????? ?????????????? ? ???????????? ??????, ??? ??????????? ?? ?????????????? ?
XVIII ? ???????? ????? ? ????? ?????????.
?????? ???????????? ?????? ???????? ???? ? ?????? ?????????. ? XVII ???? ????? ???,
??????????? ? ??????, ??????? ??????. ??????????? ??? ??????? ?????? ??????? ????? ?????????????? ????????????? ?? ????? ?????? ??????????? ? ?????????? ?????????? , ????????? ???? (?????-?????????). ?? ???????? ? ???????? ??????? ? ?????????? ? ????????? ?
??????????, ? ??????? ????? ? ???????????.
????????????? ?? ??? ???????????? ?????? ??????????-????????? ????????? ?????????? ??????????, ?????????? ??????????? ????????, ???-?????????? ?????, ???????????
????????? ???? ??????? ? ??????????? ?????????? ????????? ?????, ???????, ??????????
????? ????? ??????? ???- ? ??????????????? ???????. ?????????? ??? ????? ?????? ???????
??????????? ? ?????? ?????????? ??????? ?????????, ????????????? ? ?????????? ?????????????. ????? ????? ????? ?????? ???? ????? ? ??????????????? (???????), ??????????
(????) ? ???????-?????????? ?????? ????????? ????? (??????) ? ???????????? ?????? ????????? ??????? ???? ?? ????? ????????? ??????????, ???????? ????? ???????, ???? ??????????????????. ??????? ???????????? ?????????? ???????????? 30 ???? 1908 ?. ? ??????????
??????????? ???????? ? ?? ??????? ??????? ????, ? 70 ?? ? ??????-?????? ?? ??????? ????????, ??????????? (?? 40 ????????) ????? ???????????? ??????? ??????????????? ???????,
?????????? ??? ????????? «?????????? ????????». ?? ????? ??????? ??????????? ?????????
??????????? ?????????? ????????? ?????????? ??? ?????????? ????????????? ? ???? ??????,
# 728 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
?????? ??????????? ????????????????? ???????? ????????????? ??????????? ???????????
?????????.
??????????? ?????????? ??????????? (????. 3, ???. 4)
?? ?????????????? ?????????????? ?????????? ???????? ????????? ??????????? ? ??
?????? ???? ??????? ??????????, ????????????? ?? ??????????? ???????? ???????? ??????? ??????? (???????? ??? ?????????? ?????????) ? 1-?? ??????? ? ?. ??????. ??????????
????? ????????? ??????????? ????????. ????? ???????? ? ???? ????? ?????????? ???????
????????, ??? ???????? ?.?. ???????? ? ???????? ?.?. ???????. ? ??????????? ???????????
??????? 3. ??????????? ?????????? ???????????
?????
??????????
????????? ??????????
1. ??????????? ???????? ??????? ?????????
???????
2. ?????? ???????? ????????? ??????? ?
???????????? ????? ?????????
3. ????????????? ???????? «?????-?????????
??????? ?????????»
4. ????????????? ???????? ????????????? ??????
?. ???????????
5. ?????????? ??????
?????????????
?????
????????????????
?????
??????? ?????
??????
??????????? ?????
?????
?????????? ?????
??????????? ?????
???????? ?????
???????? ?????
???????? ???????
???????? ??? ? ??????
???????????? ????????
???????? ??? ?? ?.
???????
?) ?????????????
?????? ?????????? ?
????????.
?) ????? ?? ????
6. ????????? ???????? ?????
(???????, ?????????, ?????????, ??????????,
????????????, ???????
7. ????????? ??????
???? ???? ???????????????
8. ????????? ???????? ????? «??????????»
9. ????????-??????????? ???????? «???????» ?
????? ?????????? ??????? ????????? ? ??????
???????? (?????????? I)
10. ??????????????? ????? «??????????
?????????? ? ????? ???????» (???? ?????????,
?????? ? ??????????
11. ????????? ???? «??????? ????» (??????, ?????,
???????, ???????, ???????, ?????, ???????
12. ????????? ???????? ???????? (???????? ????,
???????
13. ???????????? ???????? «?????????????? ????
?????» ? ???????????????? ??????????.
????????? ? ?????????:
- ??????-??????? ????? ????????;
- ????????????? ???????????????????? ?????????
14. ????????? ???? «??????? ?????????»
# 729 #
?) ???? ????????????
???????????? ??????? ?
????? ???????
?) ????? ?? ????
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
???. 4. ??????????? ?????????? ???????????
????? 200 ?????????? ???????????, 22 ?????, ??????????????? ????????? ?????????? «??????». ???????? ?????????? ???? ??????????? ???????? ????? 200 ????? ???????. ????? ????????????? ???????? ?????????, ?????????? ? ???????????: ???? ?????????, ???? ??????,
?????????????? ???????????? ?? ????????????. ??????????? ??????? ????????????? ???????? ???????? ???????????? ??????. ????????? ??????????? ????? ???? ?? ????? ??????? ?
????. ? ?????-????????? ??????? ????????? ???? ???????????????, ????????? ? ????????
???????????.
? ??????? ?????? ?????????? ???????????? ??? ?????????? ?????? ???????? ?????????
????? ????????? ???? ? ??????. ? ?????-???????? ?????? ?. ?????? ????????? ??? ?????
??. ???????? ???????? ?????????. ? ?????? ???????? ???????? ????????????? ???????
??????????????.
?????????? ? ??????????? ????? ? ?????? ?????????????? ?????? ? ???????? ????????
?? ????? ??????????? ?????. ????? ???? ?????????? ???????????????? ?????????? ????????? ? ?????????, ??????-??????? ????? ????????, ????????? ????????????? ???????????????????? ?????????.
????? ? ???????? ????????? ??????? ???????, ??? ???? ????????? ?????? ?????? ???????? ? ????? ?????? ???????. ?????????, ?? ???????, ??? ????? ??????????? 1, ???????????? ???? ????????????. ???-???????? ??????? ?????????? ??????????? ?????, ???????
????? ??????? (??????, ???????, ???????, ?????, ???????), ???????????????? ???????????.
??????? ?????????? ?????????? ?????????, ???? ??????, ?????????? ? ?????? ??? ????????
???????????????? ????? ??? ???????? ?????.
# 730 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
????? ?????????? ??????????? (????. 4, ???. 5)
???????? ????? ?????????? ????????? ????? ?????????? ?????? XIX ????. ??????? ????????????????????? ?????? ? ??????????? ????????????? ????? ????? ?.?. ?????????? ? ?????? ????? ? ?????????? ????????. ?? ????????? ???????? ? ?????? (1900 ?.) ??????? ???????? ? ?????????? ???????. ????????? ????? ??????????? ? ???????????? ????? ? ????????
?.?. ?????????????? ? ?.?. ????????. ????????? ? ???? ?? ??????? ??????????? ??????????
?????????? ???????????????? ?? ????? ? ????????? ??????????? ? ???????? ? ???????????
???????? ??????? ????????? ??????????.
??????? 4. ????? ?????????? ???????????
?????
?????????
??????????? ?????
????????? ??????????
???????? ???????
1. ????????????? ????????
«?????? ?????????»
2. ??????????????? ????????
«??????? ???? ? ??????????? ? ?????????»
3. ?????????? ???????????? ??????
4. ???????????? ???? «????????? ???»
5. ????????? ? ?????????? ????
???????????????
?????
??????????? ?????
?????????
??????????? ?????
6. ??????????????? ????????
?????????? ?????????? ? ???????????? ??
????? ??????, ??????, ????
7. ???????????? ???????? «???? ????» ?
????????? ????? ?????? ???????? ???????
8. ??????????????? ????????
«?????????????????????»
9. ???????????? ???? ?????-????????????
??????? ????????? (?????????)
10. ????????????? ???????? ??????
?????????? (????????????? ? ??????????)
11. ????????? ???????? ???
(???????????, ??????, ???????) ? ???????? ?
??????????
12. ????????????-??????????????? ?????
«?????????»
13. ????????????? ?????????
«???????? ??????»
14. ????????? ???? «??????»
?) ?????? ???????? ?????
?????
???????? ??? ??????
????????
?) ?????? ?? ?????? ?
??????.
?) ?????????? ?????
????????? (1771 ? 1781)
????? ??????? (1830),
???????? ????????? (1938).
?) ?????????? ?? ?????????
?/? ?????? ?????? ?
??????????? (??????????),
1942 ?.
?????? ?? ??? ? ??
15. ????????? ????????, ?????????? ????? ????????? ???????? ?????
???????????? ? ?????????, ??????? ???????? (1910) ? ?????????? ?? ???
????????? (1889)
????? ? ?????????
# 731 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
???. 5. ????? ?????????? ???????????
?????? ?????? ?????? ??????????? ?????????? ???? ????. ???, ? ????????? ?????????
«?????????? ??????» ????? ????????? ???? ??????? ?????? ? ???????? ??????????, ?????????? ? ????????????. ? 60 ?? ?? ?????????? ????????? ???? ????????, ?????????? ??????????????? ?????????? ??????? ?.?. ????????. ? 1894 ?. ?? ????????????? ???????? ?
?????????? ????? ???????????? ?????? ???? ????????? ??????? ??????? ??????. ? ???????
????????? ??????? ?????????? ? ?????? ?? ???????. ??????????? ????? ??? ??????? ????????????? ???? ???????? ???????????? ?????????, ????? ?????????? ??????? ???????? ?
???? ???????????? ????????, ??? ????? ????? ??????? ??? ???????? ???????????.
??? ???? ????? ????? ?????????? ??????????? ? ????????? ? ???????? ???????
?.?. ?????? ? 1897 ?. ?? ???? ????? ??? ?????? ????????-??????????????? ????? ? ?????????? «?????????». ????? ?? ? 2003 ?. ?????????? ????????????? ????????? ??????????
?????? «???????? ??????». ? ??????????????? ?????? ?? ???? ???? ????? ????????? ?????
?????? ????? ???????? ???????, ???????, ???????? ??????? ??????, ????????? ? ???? ?
??????.
??????????? ????? ? ????? ?????????????? ???????. ? ???? ??????????? ?????????? ????? ???????, ??????????? ?? ?????????? ???????. ???? ????? ?? ????????? ??????, ?? ????? ?
???????? ???????? ????????? ????????? ???????? ?? 17 ???????????? ? ??????????? ? ?????????? ?? ??????????????? ?????? ?????????? ???????, ????? ??? ????????? ? ???????????? ?????, ??????? ???????? ????? ? ?????????. ????? ?????????? ????????? ???? «??????», ??????? ????????? ??-?? ?????????????? ????, ?????????, ??????????? ???????? ????
? ?????????? ?????????? ???????, ????? ??? ???????? ??????? ? ????? ??????. ?????????
???????? ?????, ??????????? ? 1910 ?. ?? ???????? ??????, ? ??????????, ?????????????? ??
??? ????????? ? 1889 ?., ???????? ?? ????????????? ?????? ????????? ?????.
?????????? ???????????? ? ??????????? ?????? ???????? ??????????????? ???????? ???????????? ???????? ????????????? ???????? ?????? 10 ?? , ????? ?? ????? ???????? ???????? ?????????? ? ?????????. ????????? ??? ?????? ????????????? ? ???????????? ??????? ?????? ??????????. ??????????? ? ?????? ?????? ????? ? ?????? ????????? ????? ??????????
?????????? ????????????, ????????? ????? ????????? ????????? ??????????? ? ?????????.
# 732 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
?????? ????????? ? ?????? ??????? ? ?????????. ???????????? ????????? ????? ????????
???????????? ??????? 1857 ?. ? ?????-???????????? ??????? ????????? ? ?????????. ???????? ????????????? ?????, ??????????? ?????????? ????????? ? ??????????? ????????????, ??????? ?? ??????????? ???????????? ???? ??????????????, ? ?????? ?????????????
???? ?? ???????????? ????????, ???????? ???????? ????????? ? ???????????? ???????
????????? ?????????. ? ???? ?????? ???????????? ???? ??? ?? ??????????????? ? ???????????
???????? ????????? ? ??????????? ??????????.
???????? ?????????? ????? ???????? ? XVIII ???? ? ????? ???????? ??????? ????????
?????? ??????????????. ??? ? 1771-1781 ??. ?????? ? ?? ????? ?????????? ?? ??????? ????????
???? ????????, ?????????? ??? ???? ???????? ????????? ?????????? ??????????????? ???????? ???? ??????, ????? ???? ? ????????? ????? ? ????????? ???????? ????????, ???????
???????? ?????? ???????????????? ????? ? ??????. ?????????? ??????????? ?????????? ??????????? ? 1942 ?. ?? ????????? ???????? ?????? ?????? ? ???????????. ??? ??? ????????
????? ????? ??????? ????????????? ??????????????? ???????.
???????? ?????????? ??????????? (????. 5, ???. 6)
????? ????????? ???????????? ???????, ???????? ?????????????? ??????? ? ??????? ??????????? ????????? ???????? ? ???????? ??????????????? ???????? ?????????? ???????????.
???????? ??????? ??????????? ?????????? ?????????. ??? ? ????????? «???????
?????», ????? ????, ????, ??????????, ??????????????? ????????? ?????????? «???????????», ?????????? ???????? ?????????? ????????. ???? ?? ?? ??????, ????? ????????? ??
???????????? ? ?????? (?????????? ? ?? 520 ?). ???????? ????? ?????????, ?????????? ?
??????????? ? ??????, ???? ? ????????? ??????? ???????? ?????? ????? 100 ?.
???? ?? ?????????? ?? ??????? (????-???????) ? ???? ?? ???????? ?????? ????????????? ? ???? ????? ?????????? ? ?????????? ?? ?????????? ??. ??????? ??????? ?????? ???????,
??? ????????????? ????????????? ?????? ???????????, ? ?? ?. ???????????? ? ??????????
??????. ???? ?? ?????????? ?? ?????????? ????? ????????, ????????? ?????? ???????? ?
???? ????????. ?????????? ?????????? ? ????????? ????? ??? ???????? ???????????? ????????? ?????????. ?????????? ??????????? ????? ?? ??????????? ?????????????? ???????????, ??? ?????????? ????????? ??????????? ? ???????????? ????. ?????? ????? ???????
??????????????? ????????. ?? ????? ???????? ?????? ? ?????????? ???? ????????? ?????, ?
???????? ????????? ? ???????? ? ????, ? ?????? ??????? (????-???? ? ?????????) ? ????????? ? ???????, ? ????? ??????? ? ???????? ???????? ? ???????, ????????? ? ?????. ????????
?????? ?????? ? ????????? ? ????????? ?????????? ???????, ??????? ?????????? ??????
????? ??????????? ??????? ???????????. ?? ?????????? ????? ??? ????????? ???????????
??????????, ?????????????? ? ????????????? ???????? ? ????????? ?????????? ??????????? ????????? ??????, ???????????? ???????? ?????????.
???????? ??????? ???????? ???????? ? 1610 ?. ????? ? ?????? ?? ???? ?????? ???????????
? ??????????? ???????? ?????? ?? ????? ? ?. ??????????, ????? ???? ??????? ???????? ?????????? 1733-1743 ??., ??????????? ?? ??? ??????? ?? ????? ??????? ???? ?? ????????? ?????????? ?????? ? ?????.
# 733 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
??????? 5. ???????? ?????????? ???????????
?????
????????
??????
???????????
?????
?????????, ????
?????? ??????
???????
?????
????????? ??????????
1. ????????-???????????? ????????
«????? ??????». ????????? ?????
??????????, ??????? ??????????
???????? ???????
?) ???? ?????? ? ?????? ? ???????????
???????? ?????? ?? ????? ? ?.
?????????? ?? ????????? ?? ??????;
????????? ??????? (1741), ???????? ?
????????? (1930-? ??.)
?????? ?? ????? ????? ????????
2. ??????????????? ?????????
?????????? ???????????
3. ????????? ???????? «??????????
??????? ?????»
4. ???????? «?????????? ???????»
5. ????????-??????????????? ????????
«?????????? ????????? ?????? ? ?????»
?) ?/? ?????? ???????? ? ??????
6. ????????-????????????? ????????
«503-? ???????
7. ????????-????????????? ????????
«????? ???????? ?. ?. ???????»
8. ????????-??????????????? ????????
«????? ? ??????????? ?????»
?) ????? ?????? ? ??????????
????????????
?) ???? ?????? ? ??????? ?
9. ?????????? ?????????????
?????????????????? ???????
??????????? ?????? ?????????????
??????????? ????????? ?. ?????? ??
?????????? ?? ?????? ? ???????
10. ??????????????? ?????????
?) ???? ??????? ? ??????? ?
?????????? ?????????? «??????????» ?????????? ??????? (1741)
11. ????????-???????????????
???????? «???????? ?????????»
?? ??????? ???????? ????? ?????????? ?????????? ???????, ???????????, ?????????,
??????????? ??????? ???????? ? ?????????, ????? ??????? ? ?????? ????.
???????? ??????? ?????? ??????? ???????? ??????? ? ???????? ???????? ?????? ????????? ? ?????????? (1935-1956 ??.), ????? ???????? ?????? ?. ???????, ?. ???????????.
????? ?? ?????????? ?????? ???????? ??????? ???????? ?????? ? 603 ?????? ? ????????.
? 1999 ?. ? ??????? ?? ???? ??????????? ??????????? ??? ?????? ???????????? ? ????
????? «??????? ? ???????? ??. ????. ?. ?. ??????????».
??????????
? ?????????? ??????????? ?????? ?????????-???????????? ? ????????? ????????
????????????? ???? ??????????? ???????????????? ????????? ??????????????? ???????
???????, ??? ?????? ???????? ????????? ???????????? ???????: ????????? ????????
???? ??????? ? ???????????? ???????? ?????????? ????? ? ?????????? ??????????.
?????? ????????? ???? ??????????? ?????? ?????????, ??? ??? ???????? ?????????
# 734 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
???. 6. ???????? ?????????? ???????????
???????? ???????? ????? ??????????? ??????. ??? ????? ???? ??????? ??? ????????
? ???????? ????????-???????????? ??????????: ?????? ??? ???????? ?????, ??????????????? ? ??????????????? ??????????, ???????????? ?????? ? ?. ?. ??? ?????????? ???
?????????? ? ???????????????? ?????????? ???????, ???????? ? ???????. ???????,
?????????????? ???????? ?? ????? ???? ???????????? ??????????. ?????????????
???????? ??????????? ? ?????????? ???????? ?????? ? ????????? ???????, ????????????
????????????? ?????????????????? ????? ?????????? ??????? ????????????? ????????
????????.
?????? ??????????
[1] ????????? ?. ?. ????? ????????? ??????. ???????????: ??????, 2008. 479 ?.
[2] ???????? ?. ?. ? ??. ?????????????????? ??????; ???. ?. ?. ?????. ???.: ????, 2011.
783 ?.
[3] ??????? ?. ?. , ??????? ?. ?. ??????? ? ???????? ??????? ?????????????? ???? ??????????: ???, 2007. 246 ?.
[4] ????????? ????????????? ????; ???. ?. ?. ???????. ??????????: ???????, 2006. 223 ?.
[5] ?????? ?. ?. ???????? ?. ?. , ???????? ?. ?. ????????????? ?????????: ?????????????????? ????????. ?. : ??????: ????, 2005. 493 ?.
[6] ?????? ?. ?. ??????????? ?????? ??????, ??????? ? ?????? ????????? ????? ?? ??????. ?. : ??????????, ??, 1981. 244 ?.
# 735 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
Spatial Pattern of Educational Tourism
of the Krasnoyarsk Region
Dmitry M. Astanin
Siberian Federal University
79 Svobodny, Krasnoyarsk, 660041 Russia
The article presents analysis of differentiations of educational tourism which was the basis of integrated
assessment of the territory of the Krasnoyarsk region for the development of tourism, needed for
the construction of its spatial pattern. It defines touristic centres, agglomerations and lineal linking
structures. The research gives their detailed description.
Keywords:Touristic agglomeration, educational tourism, cultural heritage tourism, ecological cultural
tourism, historical cultural potential of the region, dot forms of spatial localization, areal forms of
spatial localization, cores and centres of spatial localiz.
??????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 6 (2013 6) 721-736
~~~
??? 711.1
???????????????? ?????????
??????????????? ???????
????????????? ????
?.?. ???????
????????? ??????????? ???????????,
?????? 660041, ??????????, ??. ?????????, 79
Received 26.03.2013, received in revised form 23.08.2013, accepted 30.08.2013
? ?????? ??? ?????? ?????????????? ??????????????? ???????, ?? ?????? ???????
?????????????? ??????????? ?????? ?????????? ????????????? ???? ??? ???????? ???????,
??????????? ??? ?????????? ??? ???????????????? ?????????. ?????????? ??????????
??????, ??????????? ? ???????? ????????? ?????????. ? ?????? ????????? ?? ?????????
????????.
???????? ?????: ?????????? ???????????, ?????????????? ??????, ?????????-????????????
??????, ???-?????????? ??????, ????????-?????????? ????????? ???????, ???????? ?????
???????????????? ???????????, ???????? ????? ???????????????? ???????????, ?????????
????? ???????????????? ???????????.
????????????, ??? ????? ?. ?. ??????????, ????????? ?? ??????????? ????? ??????????????, ??????? ?????????????? ? ????????????? ??????????? ?????? ????????, ? ??? ??? ??????????? ? ???????????? ?????. ?? ???? ??????? ?????? ?????????? ?????????, ?????????
???????? ??????????? ????? ??????????.
??????? ?????????? ????????????? ??????????? ????????????? ?????????, ?? ???? ????????, ???????????????, ??????? ? ???????????? ?????????? ? ????????? ????????.
?????? ????????????? ? ???? ????????. ??????? ??? ?????? ???????, ????????,
??????? ? ?????? ????? ????????????????? ??????? ???????, ??? ????? ? ???? ???????
???????????? ?????????. ?????? ????????????? ?????????? ? ????????, ????????????
????????? ???????????? ???????, ???????????? ?? ????? ???????, ??????????? ???????? ????????, ??? ??????????? ??????????, ?????????? ????????? ??????. ???????
?????????????? ?????? ? ??? ?????? ??????? ? ??????????? ????, ????????? ????????
???????? ? ??????? ???????????? ?? ???????????, ?????????? ????????????? ??????????? ????????.
????????-?????????? ????????? ??????? ? ?????? ??????????????? ???????. ?? ??????? ?? ???????? ??????????? ???????? (?????????? ???????, ???????????, ?????????? ? ?.?.),
?????????? ?????????-???????????? ? ????????? ??????????. ??? ?????????? ????????, ???*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: astanin_d@incom.ru
# 721 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
?????? ? ?????????????? ????????, ?????????? ????????? ???????? ?????????????? ??????????????? ???????:
1. ?? ?????? ???????????????? ??????????? ? ?????????????? ?? ??????????.
2. ?? ???? ????????? ? ?????????????? ?? ??????? ??????? ? ????????? ?????????????????????? ? ?????????? ???????? (?????????????? ?? ????????? ?????????? ? ????????????).
3. ?? ??????? ?????????????? ? ?????????????? ?? ??????? ????????.
??????? ??????????? ???????? ????? ????? ????????? ????? ???????????????? ???????????:
1. ???????? ? ????????? ???????????? ? ????????????? ?????????.
2. ???????? ? ??????? ???????? ????, ????????? ??????.
3. ????????? ? ???? ??????????????? ?????????? ????????, ???????????? ???? ??????????????????, ???????? ???????????? ?????.
? ??????????? ????? ?????????? ???????? ????????-?????????? ???????, ?? ??????????? ???????? ????????? ?????????????? ???????? ????????? ? ???????? ????????. ?? ?????? ????????? ???????? ??????????? ???????? ???????? ???????? ????????-????????????
??????, ??????? ????? ????? ??????? ??????? ??????????, ??????????? ? ?????????????
??????????? ????????. ???????, ??????? ??????, ???????????? ??? ??????????????? ????? ?
????????? ? ??????????, ????????, ????????????? ????????????? ? ?????????? ????????.
???????? ?? ??????? ??????????? ???????? ?????? ????? ??????? ??? ??????????? ????????????? ?????????.
?? ?????? ????????, ????????? ? ???????? ???????? ????????? ???????????????? ????????? ??????????????? ???????, ???, ??-??????, ?????????? ???? ? ??????, ???????????
??????? ?????????, ????????, ?????????? ? ??????????? ???????? ????????-??????????? ????????, ???????? ???????????? ? ????????????? ???????? ????????. ??-??????, ??? ???????
????????, ??????? ???????????? ???????, ????????-?????????? ??????????, ??? ??????????
?? ?????????-???????????? ???????, ?????????? ? ????????? ?????????, ????????????
????????? ? ????????, ??????? ????? ?????. ????? ?????? ??????????? ? ?????????????? ????????? ? ?? ???????????? ?????, ????????????????? ???????????? ??????????????????, ???
??? ????????? ????????? ???????????? ?????? ?? ????????????????? ??????????? ???????.
?-???????, ???????????? ???????? ???????, ???????? ????????? ???? [5].
???????? ???????? ????????? ?????????? ??? ?????????? ?????? ?????????? ? ????????????? ?? ??? ??????????. ????????? ?? ???????? ?????????? ? ?? ??????????????? ???????????? ??????? ? ????????????????? ????????-?????????? ??????????, ? ??????????? ??
?????????????, ? ????????????? ????????????? ???????, ? ??????????? ????????? ? ????????????? ?????????????? ???????. ?????? ?????? ?????? ?????????? ? ?????? ???????????
????????? ? ???????, ??? ??????? ????????? ??????????? ???????? ???? ???????, ????????
?????????? ?? ?????? ????????? ???? ?? ????, ?? ? ?????????? ?????, ?????????? ? ????????? ????????, ??????????? ????????? ? ?????????? ???????. ????? ???????, ???????
??????? ?? ????????? ? ?????????-????????????? ???????? ????? ?????????????? ?????? ??
?????? ????????, ??? ?????????-???????????? ??????, ? ?????? ??????????? ? ?????????????
??????.
# 722 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
?????????-???????????? ?????? ?????????????? ? ???????? ?????? ??????????????????????? ?????????????? ???????. ?????? ????????? ? ???? ???????????, ??????????? ????????????? ????????, ???????????? ??????????????? ?? ???????????? ? ???????????
??????????, ???????????????? ? ????????????? ???????????, ?????????????? ??????????,
???????. ? ????????????? ???????, ??? ??????? ???????????, ?? ??????????? ? ?????????
????????, ????????? ? ?????????? ????????, ????????? ????? ??????, ?????? ? ??????.
??????????????, ??? ???? ??????????????? ??????? ?????????? ? ?????????? ????????????, ? ?????????? ????????. ???? ?????????-???????????? ?????? ?????????? ????????????
???????? ?????????? (?????????, ???? ??????) ? ???????????? (??????????, ???????????
????), ?? ????????????? ?????? ?????????? ???????? ? ???????? ??????? ?????????? ????????, ????, ??????????? ????, ?????????? ???????, ?????????, ? ? ???????? ??????? ???????????? ???????? ??????? ? ?????? ???????, ?????? ???????, ?? ???? ???????? ????????????,
??????????????? ????????? ????????.
????????????? ?????? ?????????? ????????? ? ?????????? ????????, ????????? ???????? ??????? ???? ?? ????? ????????? ??????????, ???? ?????????????????? ? ???????? ????? ??????. ?????????????, ???????????????, ????????????? ? ?????????????-????????????
?????? ? ???? ???-??????????? ???????. ? ????????? ????? ?????? ??????? ? ???????? ??????
? ?????????? ????????? ???????? ? ??????? ??????? ??? ????????????, ???????? ? ???????? ????????? ? ???????? ? ????????? ?????????? ?????????. ? ???? ?????? ????????????? ??????, ? ???????????? ??? ?????????, ?????????? ??????????????. ???????? ??????? ?
???????? ????? ??????????? ?? ????? ?????????? ????????? ???????????. ?? ???????????
????????????? ??????????? ??????????, «????????????? ?????? ? ??? ????????????? ??????????? ? ????????? ????, ???????, ??????????? ?????????? ????? ? ??????????????
?????????????? ??????? ???????». ????? ???????, ????????? ????????? ? ???????????????
????????, ???? ???????? ??????? ? ????????? ???? ?????????? ????? ???????????, ????????
?? ????????, ????????, ???? ? ???????? ?????, ??????? ? ??????????.
?? ????? ????????? ??????????? ????? ? ??????????? ????????????? ?????. ?????? ?????????? ? ?????????? ???????????? ? ?????? ? ???????? ????????????, ??????? ? ?????????? ?????????? ????????? ????????????? ??????????????? ?????.
?????? ?????????? ? ???????? ?????? ??????????? ? ????????? ????????????? ?????.
??????????? ??? ? ??????????, ?????????? ????????, ??????, ???? ????? ???????, ????? ??
???????, ?????? ??? ???? ????????????? ? ?????????? ?????????? ????????????? ??????????, ?????????? ??? ????????? ????????.
??????????? ? ???????? ?????? ?????????? ???????????? ? ???????????? ?????????????? ??????. ??????? ???????? ?????????? ????????? ????????????????, ?????????? ??????????, ????????? ?? ???? ??? ????????? ???????????????? ??????? ??? ??? ???????? ?????? ? ???????.
?????? ???????? ??????????????? ???????
???????? ?????????? ???????????? ??????? ????????????? ?????????? ????????, ??
????????????????, ????????????? ????????????????? ? ????????????? ????????, ??????????????? ??????????. ??????????? ? ???????????? ?????? ???????? ??????????????? ???????
# 723 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
???????? ???????? ????????? ??? ????????????, ??????? ??????? ???????? ????????? ?????? ?? ??????????? ???????? ??????? ? ????????, ??????? ?????????? ??? ??? ???? ????????
???????? ? ?????????? ?????????? ??? ??????????? ?????????? ????????????, ??????????
???????? ????????????? ??????, ???? ? ????????. ???? ???? ????????? ???????? ??????????. ??????? ???????? ?????????? ? ??????? ? ?????? ?????????? ??????????????? ???????:
? ?????????? ?????????????? ?????? (??????????? ??????????? ????????? ??????????,
????????? ??????? ?? ????????? ?? ???? ??????????? ??????);
? ????????????? ?????????????? ?????? (3?5 ??????), ??? ??????????? ???????????? ????? ????????;
? ??????????? ?????????????? ?????? ???????? ?????????-????????????? ???????? ?????????? ?????? ????? ?????????? ????????, ??????? ?? ??????????????? ??????;
? ?? ??????????? ?????????? ?????????;
? ??????????? ???????? ???????? ???????????????? ?????, ??? ??? ????????????? ????,
??? ???????????????? ?????? ????? ??????? ??????????? ?????????? ? ??????????
??????? ????????????? ????????????, ?? ????? ???? ??????????? ???????????;
? ???????????? ????????????? ??????? ?????? ????????????? ?????????, ??? ?????????
?? ?????????????? ??? ?? ??????????? ????????????? ????????? ???????? ??? ??????????? (?????? ?????????? ?????????? ????????).
?????? ??? ??????????????? ??????? ????? ???? ???????? ??? ?????? ?????????? ????????. ?????? ???????? ??????? ?? ??????? ?????????????? ???????????? ??? ?????? ????????? ???????????? ???????:
1. ???????????? ???????????? ????????????? ???????? ??????????? ? ?????????? ???????? (?? ???????? ? ??????? ? ????????????? ????????) [5].
2. ??????????? ??????? ???????????? ???????? ????????.
3. ??????????? ??????????? ???????????? ?? ?????????? ? ????? (??????? ??????????
???????? ????????? ???????????? ????, ????????????????? ??????, ???????, ????? ??????????? ????????????? ????????????????? ??????????).
?????? ??????? ?? ???????? ?????, ?????? ??? ?????? ???????? ???????????????? ?????????? ????????, ??? ???? ??? ????????? ????. ???????????? ?????? ???? ???????????
?????? ?????? ?????????? ? ????? ?????? ????????????? ?????????????????, ?????????? ??
?????????? ?? ?????????? ?????, ???????? ?????????? ??????, ???? ??????????? ?????????
????????? ?????????? ?? ?????????? ????????? ??????. ?? ????, ?????????? ????? ????????
?????????? ?????? ?????????? ????????, ?? ??? ?????? ???????? ?????? ??? ?????????? ?
?????? ???????????. ??? ????????? ???????? ?????? ????????????? ?????????? ????????
?????? ? ????????????, ???????? ????????? ???????? ???????????? ?????: ??????????????;
????????????????; ???????????? ????????????; ????????????; ????? ????????????.
??? ???? ?????? «????? ????????????» ??????? ? ??????????? ??????????? ???????????????????? ??????????? ??????, «????????????» ? ? ???????? ??????????????????? ?????????? ????, «???????????? ????????????» ? ? ???????? ????????????? ???? ???????, ??????????? ?????????? ??????.
??? ??????????? ?????? ?????????? ????????????? ???? ?? ???????? ???????????????
??????? ????????????? ???????????????? ?????, ??????? ?????????? ?? ???? ?????? ???# 724 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
????????????? ??????????? ??? ???? ????? ????????? ???????? ? ?????????????? ???????.
??? ?????? ????????? ???????? ???????????? ?????????? ??????????????? ???????????????
???????, ???????????? ???????, ?????????? ???????? ????????????? ???????????, ??? ?????? ???????? ???????? ? ???? ??????????????? ???????, ???? ???????????? ??? ?????????
???????????? ????????. ??????? ????????? ?????-????? ?? ??????? ???? ???????. ??? ??
??????????? ???????????? ???????? ???????????? ?????-?????, ??????????? ??????????
????????????-?????????????? ???????? ????????? ??????????, ???????????????? ?? ?????????????? ???????? (???. 1, 2). ??????????????? ??, ????? ??????? ????????? ??????:
? ?????????? ?????? ????????????? ?????? (????. 1)
? ?? ?? ?????? ?????????? ?????? ?????????? ???????????: ?????, ???????????, ?????????? ? ????????.
????????? ???? ????? ?????????????? ???????? ?????? ??????? ???? ?????????????
???? ? ??????. ?????? ?? ?????? ? ??? ???????? (??????, ?????? ? ??????????? ????????)
??????????? ???????? ??????????? ?????? ? ???????, ????????????? ????????, ??????????????? ????????.
????? ???????, ??????, ??????????? ???????????? ???????????? ???? ? ??? ?? ?????,
???????? ????????? ???????? ?????????? 1-?? ???????.
?????? ??????????? ??????? ?? ?????????? ????????????? ???, ??????? ???? ????. ???
??????? ? ??????? ??????????? ????????? ??????????? 2-?? ???????. ? ??????????? ?????????? ??????????? ?????????? ? ??????? ? ???????? ????????? ?????????????? ??????????,
? ?????????? ????????????? ??????? ??? ?????? ? ???????? ????????. ? ????? ???????????
???. 1. ??????????? ?????? ?????????-????????????? ??????? ????????????? ????
# 725 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
???. 2. ??????????? ?????? ???-??????????? ??????? ????????????? ????
??????? 1. ????????????? ?????????????? ?????????? ??????? ????????????? ????
?????????????
?????
1. ??????????
?????
???????????????????????? ??????????
34
21
?????
??????
55
???-??
?????
???????
8
2?. ?????????
22
9
31
5
2?. ?????????
19
6
25
6
3. ????????
19
20
39
6
9
9
5
4. ????????
???????? ???????????
???????? ???????
????????????-????????????,
??????????, ?????????????
????????????, ??????????,
???????????????
????????????-????????????,
???????????????
????????????-????????????,
?????????????
???????-???????????????,
????????????
????? ???????? ?????????? ???????? ???????? ?????, ? ?????????? ? ??????, ???????? ? ??????, ???? ? ???????, ??? ???????? ?????-???????????? ?????.
????????? ??????????? ???????? ??????? ???????? ???????????????? ???????? ????????????? ???. ??? ? ????????? ??????????????, ? ?????????????????? ??????, ??????? ?????? ???????? ? ??????, ??? ? ?????????? ????? ? ?. ?.
????? ????????? ????????? ??????????? ???????? ???? ???????. ???????? ?????????
????????? ????????? ????????? ????????????? ? ?????? ???????? ?? ??? ???????????? ?
?????????? ??????????????.
# 726 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
?????????? ?????????? ??????????? (????. 2, ???. 3)
???????? ???????? ?????????????? ???? ?????????? ? ?????????. ???????? ? ????? ?????????? ????????? ????????? ???????? ? XVII-XVIII ??. ?? ???? ?????????? ? ??????????
?????? ?? ???????? ????? ??????. ? ????????? ????? 200 ?????????? ???????????. ?? ??????
??????? 2. ?????????? ?????????? ???????????.
?????
????????
?????????? ?????
??????????? ?????
??????????? ?????
???????????
??????????? ?????
??????-??????????
?????
?????????
???. ???
??????????? ?????
????????? ??????????
???????? ???????
1. ????????-?????????? ????? «???????
?????????????? ????»
2. ???????????? ???? «?????-??????????????
??????? ?????????»
3. ????????-???????????? ???????? «????????????
?????»
4. ????????? ???? ???????
?) ???-??????????
????? ? ??????
?) ??????????? ???????
???????? ? ???????? ??
????????? ?? ???????
5. ????-?????????? ????????? ????????
6. ??????????????? ???????? «????????? ?????»
(???????? ???????, ?????, ????????? ????????,
??????????? ???????? ????.
7. ????????????? ???????? «???????????
????????? ????? ?????? ?????? ? ?????? ????????
?????????????? ????????? ????? ? ?????»
8. ????????-??????????????? ???????? ????????
«??????? ?????»
9. ????? ????????????????????
?) ??????????????????
????? ?? ??????? ??????
??????? ?????????
10. ???????????? ???? ?????-????????? ?????????
(???? ??????? ?????????????.
11. ??????????????? ???????? «??? ??????» ?
????????? (???????, ??????, ??????????, ??????,
????????, ????????????, ???? ? ???????, ?????? ?
??????
12. ??????????????? ?????????? ??????????
«???????????????»
13. ?????????? ????????
- ?????? ? ??????
?) ???????? ??????
?????? ????? ??
????????? ?? ??????
????????
???????
14. ??????????????? ????????? ??????????
«??????????»
15. ?????????????? ???? ?? ???????? ???????????
?????????
16. ?????????? ?????????????
????????. ?????????????? ????????? ?????????
# 727 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ???????????????? ????????? ??????????????? ??????? ????????????? ????
???. 3. ?????????? ?????????? ???????????
? ?????? ???????-?????
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