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UDC 656.259.12
A. YU. ZHURAVLEV1*
1 Dep. «Automation, Remote Control and Communication», Dnepropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipropetrovsk, Ukraine, 49010, tel +38 (067) 990 76 51, e-mail anton.zhuravlev@gmail.com, ORCID 0000-0001-6885-5177
ABOUT TRACK CIRCUIT CALCULATION METHOD DEPENDENT ON FERROMAGNET PROPERTIES IN CONDITIONS OF TRACTION CURRENT NOISE INFLUENCE
Purpose. The work is intended to investigate the electromagnetic processes in impedance bond in order to improve noise immunity of track circuits (TC) for safe railway operation. Methodology. To achieve this purpose the methods of scientific analysis, mathematical modelling, experimental study, a large-scale simulation were used. Findings. The work examined the interference affecting the normal performance of track circuits. To a large extent, part of track circuit damages account for failures in track circuit equipment. Track circuit equipment is connected directly to the track line susceptible to traction current interference, which causes changes in its electrical characteristics and electromagnetic properties. Normal operability, performance of the main operating modes of the track circuit is determined by previous calculation of its performance and compilation of regulatory tables. The classical method for determination of track circuit parameters was analysed. The classical calculation method assumes representation of individual sections of the electrical track circuit using the quadripole network with known coefficients, usually in the A-form. Determining the coefficients of linear element circuit creates no metrological or mathematical difficulties. However, in circuits containing nonlinear ferromagnets (FM), obtaining the coefficients on the entire induction change range in the cores is quite a difficult task because the classical methods of idling (I) and short circuit (SC) are not acceptable. This leads to complicated methods for determining both the module and the arguments of quadripole network coefficients. Instead of the classical method, the work proposed the method for calculating the track circuit dependent on nonlinear properties of ferromagnets. Originality. The article examines a new approach to the calculation of TC taking into account the losses in ferromagnets (FM), without determination of equivalent circuit quadripole network coefficients. When building the FM reversal model in parallel magnetic fields, the most accurate methods are the approximation ones that take into account not only the changes in values and over time, but also their derivatives. The development of computer hardware and software makes real the mathematical methods for calculating TC with significant change in ferromagnetic inductance, including the saturation areas. Herewith, it is important to search for approximating analytical expression that describes the dynamic limit hysteresis loop (HL). Practical value. The changes in the electrical parameters of the same TC were analysed using the classical and the new calculation methods, the difference made less than 10%. The work introduced some measures to increase operational noise immunity of TC.
Keywords: track circuit; impedance bond; quadripole network; ferromagnet; hysteresis; spectrum; vortical currents; magnetic viscosity; magnetizing curve; simulation
Introduction
Experience has shown that certain conditions and operating modes of the power network create a powerful influence of the traction current noise on the work of electric track circuits (TC). Such exposure results in magnetization of nonlinear ferro-magnets (transformers, impedance bonds and components containing ferromagnetic core) in track circuits and, consequently, in failure of TC and signalling systems. Adverse conditions [11, 12, 13] for TC operation are created in the following cases:
1) At a certain switching circuit of DC traction network of splicing stations the level of permanent traction current potentials «rail-to-earth» in the rail network increases. It results in increased leakage currents into the open-line track of AC electric traction lines, causing magnetization of impedance bonds and track transformers, and disruption of short (less than 500 m) track circuits;
2) In the areas of AC electrified railroads the ice on the contact network collectors creates an electric arc, accompanied by electrical transients in the power circuit of an electric locomotive. Con-
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stant component of this current at the rail line asymmetry also causes saturation of ferromagnets;
3) Switching on the locomotive main switch in a certain voltage phase of the circuit power line also leads to transition process with the consequences given above;
4) When a laden electric locomotive enters the neutral section on the current collectors there are several electric arcs repeated aperiodically; this leads, as mentioned above, to the occurrence of transients and failures of TC. From the above it follows that improvement of track circuit noise immunity in the signalling systems in conditions of permanent reverse traction current influence is an actual scientific and technical problem.
Purpose
The purpose of this work is to examine the causes of traction current harmful influence on TC operation, to create the calculation method for TC
with nonlinear ferromagnets (FM) and to propose technical solutions to improve the reliability of TC and railway automation systems.
Methodology
Disruption of TC operation. Let's consider one of the causes of TC operation disruption - longitudinal asymmetry of track lines. Measurements show that the asymmetry coefficient is higher in winter than in summer due to increased insulation resistance. It is established that the best way to approximate the conductive joint resistance distribution is asymmetric Weibull law, resistance variation reaches 1.8 ... 15 m.e.r. (meters of entire rail); longitudinal asymmetry coefficient ranges from 10% to 12% - in summer, up to 18% - in winter [1, 6].
Fig. 1. Equivalent circuit of track lines
The EMF equation for equivalent circuit contour of the track (Figure 1) consisting of two rails, equipment impedance Z igo, Z ire and choke cables,
for the difference in currents can result in the following expression:
winding resistance DT.1, Ohm; R
CHC1(2)
- choke
AI =
where IE
AZ + 2 (Rchci RCHC2 )
Z + Z
IGO
JIRE
+2 (RCHC1 + RCHC2 ) + Zi
'MWR
(1)
cable resistance, Ohm.
It follows from (1) that Z igo, Z ire perform the
symmetric action, but their impedance for the signal current under the track integrity monitoring conditions is small and can be neglected. For DC the equation (1) can be written as:
AI =-
AR,
CC
2 ( rдп1 rдп 2 )
RP
- electric locomotive current; AZ = Zj - Z2 - difference in rail resistance, Ohm; Z - rail loop resistance, Ohm/km; ZMW
2 (R
дп1 + rfln 2
)+R
1эл ■>
■др
or
AI = Ka • 4л ,
(2)
main
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Thus, the longitudinal asymmetry coefficient of track line is:
Ka =
ARRC + 2 (RCHC1 RCHC 2 ) RP + 2 (RCHC1 + RCHC 2 ) + AR1
(3)
MWR
where ARrc - difference in track resistance due to resistance of connectors.
In short TC (less than 500 m) longitudinal asymmetry is one of the main causes of traction
current asymmetry Ka = I-- , where Il2 -
I\ — 12
traction currents in the rails 1 and 2.
Measurements show that the resistance of the steel DC rail connector is distributed among its components, so [4, 3]:
2 3
Rrc = Rsc +{rn + Rws ) = 5 Rrc + 5 Rrc ,
where Rm - resistance of nipple - rope junction; Rsc - resistance of steel cable; Rws - resistance
of weld seam.
For steel connector with 100 mm2 cross-section, which is widely used in practice, it appears that averages Rsc = 295 mcOhm; Rn + Rws = 437
mcOhm; Rrc = 232 mcOhm; for the connector with 90 mm2 cross-section - Rrc = 770 mcOhm [8].
Rules for protection of metallic structures from stray-current corrosion allow increasing rail resistance through the joints by max 20%, while the DC
AR
asymmetry coefficient is Ka =-=0,12...0,13.
Rp
Approximate calculation of asymmetry for alternate traction current is performed with the following assumptions [3, 8]:
- Resistance of rails differ among themselves by the amount of resistance of connectors;
- Connector losses do not depend on the frequency;
- Resistance in points of welding and junctions cable - nipple - plug - rail depends on the frequency as much as the internal resistance of the rails.
- Herewith, the minimum coefficient of longitudinal asymmetry:
|Kz| = Ka
( rn + RWS ) Zi
Rc - Z
<
Rc • Z
< 0,008%, or 8.0%, (4)
where Zi - internal resistance of rails, 0.35ej35 Ohm/km; rail loop resistance Rp = 0.1 Ohm; Z = 0.8ej65 Ohm/km - rail resistance to 50 Hz current. For higher frequency the coefficient |KZ| is reduced to 1.608% for 420 Hz frequency and 1.376% for 780 Hz.
Let's assess the numerator of the fraction (3) for TC that most often fail with length of 0.25 ... 0.5 km. We assume that Rrc = 770 • 10-6 Ohm,
RCHC1 = 8000 -10-
RCHC2
=3076-10
6 Ohm 6 Ohm (й
(1CHC = 3.25 m), CHC = 1.25 m), rail link
t
nc =■
TC
--2.
25m, rail resistance 0.10hm/km,
0,025
It turned out that AR = 0.026...0.056 Q, and the value Ka is in the range of 30.2% ... 38.6%. We
should note here that the resistance of 300 m long line to 50 Hz current does not exceed 0.1 Ohm/km and is compared to the total impedance of contact connectors «cable - plug - nipple -wing IB» (normative 60 ... 80).
Let us consider the proposed TC calculation method for nonlinear FM modes of TC circuits, based on the mathematical model of ferromagnet reversal magnetization [2, 4].
Originality and practical value
Mathematical description of model. We assume that ferromagnetic saturation leads to changes in induction (intensity) of the magnetic field of DT.1.150 core according to the complex law
b = b + z
k=1
bksin sin (kat ) + +bkcos cos (kat)
(5)
where k = 1, 2, . , m , nd measuring of quadripole network using the known methods of idling and short circuit is too complicated [2].
It is known that when there is cyclical change in the external magnetic field the ferromagnetic induction retards in phase from the tension and enables the cycle of dynamic hysteresis loop (HL)
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(Fig. 2 (a)). HL area defined the power losses caused by reversal magnetization, vortical currents and magnetic viscosity [3].
The mathematical model that accurately describes the research HL is as follows:
h =
(AeVbm2 ) a, sinh (ßb) + a2 ddb cosh (ß2b)
b = b0 + bm sin (cot) ( b = bm sin (cot)), (6)
( Ae- bm - makes sense when building the specific loop exits and depends on constructive features of the subject) and allows taking into account the influence of harmonic spectrum for ferromag-net reversal input current. The values A, y, a1, P1, a2, P2 - approximation coefficients of the function (6), are determined using numerical methods by HL experimental end value and magnetization curve, taken at the maximum values of induction and signal frequency. The first term (6) describes the basic magnetization curve (BMC), the second one describes dissipative processes both for hysteresis and vortical currents, and depends on the magnetic viscosity.
Coefficients a1 and P1 of anhysteretic component (6) are determined by the selected points on the BMC curve, the values A and y are determined by expressions [1]
ln(A) = yb max ;
2 = !n ( v a1 •sinh (ß1b0 ))
bm max - b,
2
Herewith, we take the points b0, h0 close to the maximum induction bm , and induction bm max corresponds to the maximum operating value. The coefficients a2 h P2 are calculated by the formulas:
K
ß2 = ^
where hc - coercive force, A/m.
Let us consider the ferromagnetic reversal process affected by induction core created b = b0 + bm sin (Qt) by direct current field and signal current field of 25 Hz (Fig. 2 (b)). We substi-
tute this expression as an argument in the formula (6) and turn it omitting the exponential factor
bm , which does not affect the quantitative result of the first term. As the argument b changes according to the periodic law, then the functions sinh (Pjb) and cosh (P2b) are also periodic and
can be represented by Fourier series [10], in which the coefficients in the trigonometric functions are Bessel functions of different orders of imaginary argument jxm . The result is:
h = a1 sinh (P1b0) • cosh (Pjbm sin (ra t)) +
+a1 cosh (P1b0) • sinh (Pjbm sin (rat)) +
+a 2 -rabm cos (rat )x
cosh (P2b0) • cosh (P2bm sin (ra t)) + +sinh (P2b0) • sinh (P2bm sin (rat))
(7)
We present the hyperbolic functions in (7) by rows:
Sh (Xm sin (ra t)) = 2 [- jJ1 ( jXm )] • sin (ra t) -
-2 [ jJ3 (jXm ) sin (3rat)-Ch (Xm sin (rat)) = [ J0 ( jXm )] +
+2 [J2 (jXm )]• cos ( 2rat)+ ...
and keeping harmonics no higher than the second one, after transformations we obtain:
h = h0 + m1 sin (rat) + n2 sin (2rat) +
+m2cos(rat) + n1 cos(2rat), (8)
where
h0 =a1 • sinh (P1b0 ) • [ J0 ( jP1bm )] ; m1 =a1 •cosh (P1b0) 2 [-J1 (P1bm ;
n1 =a1 •sinh (P1b0 )^2 [ J2 (jP1bm )] ;
m2 =a 2rabm • cosh (P2b0 )• J0 ( jP2bm ) +
+a2ra bm • sinh (P2b0 ) • [-J0 ( jP2bm )] ^ n2 =a2rabm • sinh (P2b0 ) J1 (jP2bm )] ;
m
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We examine the term h0 in the formula (8), since this is the component of the magnetic field strength that leads to the choke core saturation and, ultimately, to failure of TC receiver.
When applying the numerical estimate for field intensity dependence on induction in the formulas (6) and (8), the following parameters are used:
a2 = 0.26:
ß2 = 0.77
A 1
ai = 2.1 -, Pi = 4.5 -
ml m i
Y = 0.92i, A = 5.92 (steel grade 2412), cross-
sectional area of the DT. 1.150 choke core is 29.2.10-4 m2, average length of the magnetic power line I = 0.58 m, number of operating winding turns W0= 16. Maximum values of induction bm for different lengths of TC are calculated by the for-
Uch~" where Uchmax - voltage on
mula bm =-
Chmax
4.44 fWS
the choke primary winding, taken according to the reference data and the regulatory tables of phase-
sensitive TC as 25 Hz [10]. For TC of 250 ... 500
m long U,
Chmax
= 1.45 ... 2.5 V bm = 0.28 ... 0.42
T; marginal field voltage hf is in the range of 240
... 280 A/m, bias current I0 = hv • 0.036 = 8.5 ...
9.5 A, and asymmetry current 17 ... 19 A.
TC bench tests showed that the limiting current for choke magnetizing, in which the receiver transits to zero state, reaches 8.4 ... 9.25 A.
Figure 2 (b) shows the BMC curve, approximated by the expression (6), and the hysteresis loop at constant field induction (displacement) b0 = 1.1 T; it also represents reversible permeability curve, (h0), calculated by the formula
, , Ab0 mh <tan(a) = —0•—-, where Ab0, Ah0 - incre-
Ah0 mb
mental induction and field intensity in i -th point of the curve b0(h0); mb, mh - axis scales.
Fig. 2. Dependence of field intensity on induction at 25 Hz frequency:
a - harmonic signal; b - harmonic signal with bias
b
а
Coercive force hc of HL is determined taking into account the fact that anhysteretic component (6) is zero, then 62.2 A/m, and maximum loop induction corresponds to bm = b0 + bc = 1.4 T. The given value allows easy determination of inductance L0 and impedance Z0 of the main winding, and BMC - magnetization current.
The impedance argument Z0 can be determined by the value of power losses for vortical currents and hysteresis [5]:
2n
Pb.t= Vfc f HdB , (9)
0
where V - core volume. Phase shift between first EMF harmonics and winding current is determined at the intensity u = Um sin Qt, if induction and intensity are the given functions:
O)
B(t) = 1 Bmn sin(nQt-Yn),
n=1
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i(t) = Z^r, sin(nQt + vn ).
(10)
n=1
From (10) and the equation of magnetized winding circuit of the choke DT.1 with the resistance r :
ri + W0 S— = u
(11)
we obtain EMF and phase for the first harmonic:
n
E1 =QW00 ; y1 =y1 + — . Substituting intensity iW
H0 =~y~ and core volume V = S • l into (9) we determine that
PBJ =QW0S[[sm^ -V1)]. (12) If induction
b1 = b0 + b1m sin(Qt -Y1) =
= 1.1 + 0.38 •V2sin(157t - Y1),
current iQ = 2.6 A adopted by BMC for b0 = 1.1 T, b1m = 0.521 T, r = 0.003 Ohm, then from (11) we find that E1m = 2.174 V; voltage losses for circuit resistance 7.810-3 V, voltage u =2.7178 B, V, and full power S = 2.7178 • 2.6= 7.066 VA, where we get that PBT= 7.0563 W.
The impedance argument Z0
is
P ,
9 = arcsin BT-= 86057 . The argument Z0 can be S
found in another way. Magnetic flow (11), passing through the core sheet bands,
2ßbh0
d
Ф = tanh| ß(1 + j)- I, (13)
(1 + j)ßd 1 V 1
iW
0,2 ^AZ =
2 j •vSn QW2 (1 + j ) ß-1 • d
x tanh |ß(1 + j)d
(14)
where Sn = a • b - flowed cross-section area of the package; a = 0.175m m - steel package height. For low frequencies (below 900 Hz)
^ rSW2
L0 =
l
where L0 - winding DC induc-
tance; S = 29.2 • 10-4 m2 - cross-sectional area of the magnetic core covered with windings; l = 0.58m -average length of the magnetic line for flows. Then (14) can be written as
L0
AZ =
2 j • Q (1 + j)ß-d
xtanh| (1 + j)-
and decomposed into real and imaginary parts. As a result we will get the formula for inductance evalua-
tion AL = L0
1 sh ( x ) + sin ( x ) x sh (x) + cos (x)
and active resis-
where h0 =—, , y - steel conduc-
tivity (7 •103 yOhm • mm), ^r - magnetic permeability of steel is taken 500, d = 0.055m, b = 0.18m -thickness and width of the package of core plates [6].
Calculation of complex impedance growth of DT.1.150 core winding due to vertical current effect is possible thanks to (13):
1 sh ( x )- sin ( x )
tance of winding AR = raL0----- .
x sh(x) + cos(x)
Complete winding inductance L = L0 + AL, and
I
impedance R = R0 +AR, where R0 = p—^-, In, Sn
Sn
- wire length and cross section.
Let us consider the peculiarities of calculation of the track circuit with nonlinear ferromagnets.
Findings
Calculation of TC operation modes are conducted using the structural equivalent circuit (Fig. 3) of impedance bond, presented by the circuit of L-shaped quadripole network and ideal transformer.
Determination of quadripole network coefficients (usually in A-form) on the entire change range in the induction cores, which exceeds the saturation limit, is quite a difficult task because the classical methods of idling and short circuit are not acceptable. The proposed method of TC calculation facilitates the solution of the above problem.
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The calculations require the FM hysteresis loop (Fig. 2 (a)), taken at maximum induction, and the
magnet permeability dependence (h()) on the current (intensity) of magnetization. Then taking
into account (8) we determine the intensityh,
Z
impedance 0 of magnetization needles at a given induction and A-matrix coefficients of the
quadripole networks of DT. 1.150 estimated equivalent circuit (Fig. 3):
AT = n
1
BT = nrx.
0 ;
nzn
DT =
(15)
Fig. 3. Impedance bond equivalent circuit:
a - real; b -design
The design equivalent circuit of choke excludes the leak inductance of windings and the given additional winding resistance that affects the calculation accuracy to a small extent.
The calculation results for phase-sensitive twin TC at 25 Hz using the coefficients (15) with choke bias at the ends of TC showed coincidence with those obtained by conventional methods.
Table 1 shows comparative design parameters for the same TC, obtained by two calculation methods - classic and new, using a mathematical
model of ferromagnet reversal magnetization.
Figure 4 shows the dependence of voltage at the receiver input resistance on the impedance module Z0. It can be seen that the end value of resistance at saturation of both chokes reaches 0.44 Ohms, which is 1.6 times less than the nominal value. Switch of the receiver to zero state is possible at saturation of one choke up to resistance Z0 = 0.2 Ohm (Fig. 4).
Table 1
TC calculations results
Calculation meth- U BB Bbb U sc S ßP Notes
ods В А В ВА grad
The difference in results is caused
Classic 3.75ej95'5° 0.82ej60° 5.1ej78'6° 4.58 6032' mainly by accounting resistances of steel ChC. Values are given without correction
New 4.1ej89° 0.77 eJ 540 5.5ej780 4.23 60 for angle PP
Difference in calculations, % 9.3 9.3 7.8 7.64 -
1
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Conclusions
To solve the problem of providing TC noise immunity under the influence of powerful noise of traction current, several solutions were proposed.
The first solution is to use DT.06.500S type, used for splicing stations, at the stations of impedance bonds with air gap [2, 3].
The second solution is to use switching units [9], which excludes spreading of traction DC out of the splicing station rail network towards the range of electric traction AC that, beside IB saturation, eliminates electric corrosion of supports and metal elements at a distance of 30 km from the source of noise. The device is tested in the laboratory of DNUZT and in the field of Pyatikhatky splicing station of Prydniprovs'ka railway.
The third solution is to install symmetric resistive (RCHC1 or RCHC 2) units [2, 8] in short TC at AC electric traction. The impedance values of unit resistors are designed to exceed substantially the sum of all resistances in the rail line bridge circuit (Fig. 1). The unit resistors (Fig. 1) are switched on in series with choke cables at one end of the rail line, which is much cheaper than in the case of choke replacement.
The conclusion should emphasize the following: it is found that the cause of TC failures is ferromagnetic core saturation under conditions of rail line asymmetry, herewith the asymmetry of direct current magnetizing FM is 4 ... 5 times higher than the asymmetry of alternating current.
The new method of TC calculation using the mathematical model of ferromagnet reversal magnetization allowed obtaining the numerical evaluation of maximum allowable asymmetry currents and input impedances at the circuit ends, which cause failure of signalling system devices.
The work formulated the technical measures for improvement of noise immunity and TC protection under conditions of powerful traction current noise.
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Наука та прогрес транспорту. Вкник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2016, № 1 (61)
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А. Ю. ЖУРАВЛЬОВ1*
1 Каф. «Автоматика, телемеханжа та зв'язок», Дшпропетровський нацюнальний ушверситет затзничного транспорту iменi академжа В. Лазаряна, вул. Лазаряна, 2, Дтпропетровськ, Украша, 49010, тел. +38 (067) 990 76 51, ел. пошта anton.zhuravlev@gmail.com, ОЯСГО 0000-0001-6885-5177
ПРО МЕТОД РОЗРАХУНКУ РЕЙКОВИХ К1Л 13 УРАХУВАННЯМ ВЛАСТИВОСТЕЙ ФЕРОМАГНЕТИК1В В УМОВАХ ВПЛИВУ ЗАВАД ТЯГОВОГО СТРУМУ
Мета. У робот необхвдно дослвдити електромагнггш процеси в дросель-трансформаторi з метою тдвищення завадостшкосп рейкових кш (РК) та, як наслвдок, тдвищення безпеки руху на залiзницi. Методика. Для досягнення поставлено! мети застосовано методи наукового аналiзу, математичного моделювання, експериментального дослвдження, масштабного моделювання. Результата. Розглянуто перешкоди, що впливають на нормальну працездатнiсть рейкових кш. Значною мiрою частина пошкоджень у рейковому колi доводиться на ввдмову в його апаратурi. Апаратура рейкового кола тдключена безпосередньо до рейково! Мни, схильно! до впливу перешкод тягового струму, яш викликають у них змiну електричних характеристик та електромагштних властивостей. Нормальна працездатшсть при виконаннi основних режимiв роботи рейкового кола визначаеться попередшм розрахунком И характеристик та складанням регулювальних нормативних таблиць. Проаналiзовано класичний метод визначення параметрiв рейкового ланцюга. Класичний метод розрахунку передбачае подання окремих дмнок електрично! схеми рейкових кш чотириполюсниками з ввдомими коефiцiентами, зазвичай в А-формi. Вiдшукування коефiцiентiв схем iз лiнiйними елементами не представляе метрологiчних та математичних труднощiв. Разом iз тим, у ланцюгах, що мютять нелiнiйнi феромагнетики (ФМ), отримання коефiцiентiв на всьому дiапазонi змши iндукцiй у сердечниках - досить важке завдання, оск1льки класичнi методи холостого ходу (ХХ) та короткого замикання (КЗ) стають неприйнятними. Це призводить до ускладнення методiв визначення, як модуля, так i аргумента коефiцiентiв чотириполюснишв. Замiсть класичного методу запропонований метод розрахунку рейкового кола з урахуванням неМтйно! характеристики феромагнетишв. Наукова новизна. У статтi розглянуто новий щдхщ до розрахунку рейкового кола з урахуванням втрат у феромагнетиках без пошуку коефiцiентiв чотириполюснишв схеми замiщення. При побудовi моделi перемагнiчування ФМ у паралельних магттних полях найбiльш точними е апроксимацшш
и с соединителями / А. П. Разгонов, M. А. Кав-ригин // Автоматика, тeлeмexaникa и связь. -1994. - № 8. - С. 32-34.
10. Рельсовые цепи магистралью« железный дорог : справочник / под ред. B. С. Аркатова. -Mосквa : Mиссия-M, 2006. - 496 с.
11. Щека, B. I. ДосМдження впливу зворотного тягового струму на режими роботи тональ-ниx рейковт шл / B. I. Щека, I. О. Романцев, К. I. Ящук // Bi^. Днiпpопeтp. нац. ун-ту за-лiзн. трансп iм. акад. B. Лазаряна. - Дншропетровськ, 2012. - Bип. 42. - С. 24-28.
12. Ogunsola, A. Electromagnetic Compatibility in Railways: Analysis and Management / A. Ogunsola, A. Mariscotti // Berlin : SpringerVerlag, 2013. - 528 p.
13. Rhee, E. Electromagnetic Compatibility Analysis for the Railway Telecommu-nication Intrasubsystem / E. Rhee, C. Kim // Intern. J. of Software Engineering & Its Applications. - 2014. - Vol. 8, № 5. - P. 115-126. doi: 10.14257/ijs-eia.2014.8.5.10.
Наука та прогрес транспорту. Вкник Дншропетровського нащонального ушверситету залiзничного транспорту, 2016, № 1 (61)
методи, що враховують не тiльки змши величин i у часi, а ще й !х похiднi. З розвитком обчислювально! технiки та програмного забезпечення математичнi методи розрахунку РК при значнш змiнi iндуктивностi феромагнетишв, включаючи дiлянки насичення, стають реальними. При цьому важливим е пошук апроксимуючого аналiтичного виразу, що описуе динамiчну граничну петлю гiстерезису (ПГ). Практична значимкть. Проведено аналiз змши електричних параметрiв одного й того ж РК при розрахунку класичним i новим методом: рiзниця склала не бiльше 10 %. Наведено деяш заходи з пвдвищення експлуатацшно! завадостiйкостi РК.
Ключовi слова: рейкове коло; дросель-трансформатор; чотириполюсник; феромагнетик; гiстерезис; спектр; вихровi струми; магнггна в'язкiсть; крива намагнiчення; моделювання
А. Ю. ЖУРАВЛЕВ1*
1 Каф. «Автоматика, телемеханика и связь», Днепропетровский национальный университет железнодорожного транспорта имени академика В. Лазаряна, ул. Лазаряна, 2, Днепропетровск, Украина, 49010, тел. +38 (067) 990 76 51, эл. почта anton.zhuravlev@gmail.com, ОЯСГО 0000-0001-6885-5177
О МЕТОДАХ РАСЧЕТА РЕЛЬСОВЫХ ЦЕПЕЙ С УЧЕТОМ СВОЙСТВ ФЕРРОМАГНЕТИКОВ В УСЛОВИЯХ ВЛИЯНИЯ ПОМЕХ ТЯГОВОГО ТОКА
Цель. В работе необходимо исследовать электромагнитные процессы в дроссель-трансформаторе с целью повышения помехоустойчивости рельсовых цепей (РЦ) и, как следствие, повышения безопасности движения на железной дороге. Методика. Для достижения поставленной цели применены методы научного анализа, математического моделирования, экспериментального исследования, масштабного моделирования. Результаты. Рассмотрены помехи, влияющие на нормальную работоспособность рельсовых цепей. В значительной мере часть повреждений в рельсовой цепи приходится на отказ в его аппаратуре. Аппаратура рельсовой цепи подключена непосредственно к рельсовой линии, подверженной влиянию помех тягового тока, что вызывает в них изменение электрических характеристик и электромагнитных свойств. Нормальная работоспособность при выполнении основных режимов работы рельсовой цепи определяется предварительным расчетом ее характеристик и составлением регулировочных нормативных таблиц. Проанализирован классический метод определения параметров рельсовой цепи. Классический метод расчета предполагает представление отдельных участков электрической схемы рельсовых цепей четырехполюсниками с известными коэффициентами, обычно в А-форме. Поиск коэффициентов схем с линейными элементами не представляет метрологических и математических затруднений. Вместе с тем, в цепях, содержащих нелинейные ферромагнетики (ФМ), получение коэффициентов на всем диапазоне изменения индукций в сердечниках - довольно трудная задача, поскольку классические методы холостого хода (ХХ) и короткого замыкания (КЗ) становятся неприемлемыми. Это приводит к усложнению методов определения, как модуля, так и аргументов коэффициентов четырехполюсников. Вместо классического метода предложен метод расчета рельсовой цепи с учетом нелинейной характеристики ферромагнетиков. Научная новизна. В статье рассмотрен новый подход к расчету РЦ с учетом потерь в ферромагнетиках, без поиска коэффициентов четырехполюсников схемы замещения. При построении модели перемагничивания ФМ в параллельных магнитных полях наиболее точными являются аппроксимационные методы, учитывающие не только изменения величин и во времени, но и их производные. С развитием вычислительной техники и программного обеспечения математические методы расчета РЦ при значительном изменении индуктивности ферромагнетиков, включая участки насыщения, становятся реальными. При этом важным является поиск аппроксимирующего аналитического выражения, описывающего динамическую предельную петлю гистерезиса (ПГ). Практическая значимость. Проведен анализ изменения электрических параметров одной и той же РЦ при расчете классическим и новым методом: разница составила не более 10 %. Приведены некоторые мероприя-тия по повышению эксплуатационной помехоустойчивости РЦ.
Ключевые слова: рельсовая цепь; дроссель-трансформатор; четырехполюсник; ферромагнетик; гистерезис; спектр; вихревые токи; магнитная вязкость; кривая намагничивания; моделирование
Наука та прогрес транспорту. Вкник Дншропетровського нащонального ушверситету залiзничного транспорту, 2016, № 1 (61)
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Prof. V. I. Havryliuk, Dr. Sc. (Phys.-Math.) (Ukraine); Prof. M. M. Babaiev, Dr. Sc. (Tech.) (Ukraine)
recommended this article to be published
Received: Dec. 05, 2015
Accepted: Feb. 04, 2016
