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Визначеш параметри електропривода стр^ лочного переводу на базi двох лтшних двигутв та проведений аналiз отриманих результатiв. Об'ект дослидження — процеси в електромеха-шчнш системi стршочного переводу. Предмет дослиджень — лтшш електродвигуни рiзних кон-фиурацш. Розрахована конструкция лтшного електромагттного перетворювача i електро-приводу. Знайдено техшчне ршення створення безредукторного стршочного переводу. Аналiз дослидження впливу характеристики тертя та марки переводу геометричш параметри лтшного двигуна дозволив обрати найкращий варiант з урахуванням марки рельсу
Ключовi слова: стршочний перевiд, електро-приви), лтшний тдукторний двигун, електро-
магшт, методи оптимiзацii
□-□
Определены параметры электропривода стрелочного перевода на базе двух линейных двигателей и проведен анализ полученных результатов. Объект исследования — процессы в электромеханической системе стрелочного перевода. Предмет исследования — линейные электродвигатели различных конфигураций. Рассчитана конструкция линейного электромагнитного преобразователя и электропривода. Найдено техническое решение создания безредукторного стрелочного перевода. Анализ исследования влияния характеристики трения и марки перевода на геометрические параметры линейного двигателя позволил выбрать наилучший вариант с учетом марки рельса
Ключевые слова: стрелочный перевод, электропривод, линейный индукторный двигатель, электромагнит, методы оптимизации -□ □-
1. Introduction
One of the ways of increasing traffic intensity of trains is the creation of turnouts, which are able to reduce the time of switch of the rail points [1-3]. Another important aspect of traffic intensification is the automation of the ballast tamping process by special automated complexes, which work in continuous mode of motion along the main road. The shortest way of solving this problem in connection to a turnout is the introduction of sleeper-type electric drives [1]. The most promising electric drive is the drive with electromagnet or inductor type linear electric motor. They consist of a special electrical machine, electronic commutator on the power transistor modules and a microprocessor control unit.
At present, electromechanical transducers of inductor type [4] are widely used in various types of transport due to their high reliability, simple design and manufactura-bility. This makes it possible to use it as a motor for the turnouts that essentially simplifies their design.
UDC 621.313.33
|DOI: 10.15587/1729-4061.2016.75860]
DETERMINING PARAMETERS OF ELECTRIC DRIVE OF A SLEEPER-TYPE
turnout BASED ON
ELECTROMAGNET AND LINEAR INDuCTOR ELECTRIC MOTOR
S. Buriakovskyi
PhD, Professor* Е-mail: sergbyr@i.ua Ar. M as l i i
PhD, Senior Lecturer* Е-mail: a.masliy@ukr.net An. M a s l i i
Engineer LTD «Ukrtranssignal» Lui Pastera str., 2, Kharkiv, Ukraine, 61075 Е-mail: an_com@ukr.net *Department of energy savings, electrical engineering and electromechanics Ukrainian state university of railway transport Feuerbach sq., 7, Kharkiv, Ukraine, 61050
One more benefit of applying linear motors in the turnout is exclusion of a reducer, which considerably increases the performance efficiency of the turnout as a whole.
In many countries of the world, the turnouts are complex electromechanical devices. The application of linear motors will not only make it possible to considerably simplify the design of a turnout, but also to increase its reliability essentially, while at the same time cutting cost of regular maintenance and repair.
2. Literature review and problem statement
The performed survey shows that, along with the improvement of the existing turnouts by replacing unreliable elements, global companies are working to create their new types, hydraulic, pneumatic or electromechanical, with the purpose to increase reliability, performance speed and achieve high velocities of the motion along the switches. At present,
© S. Buriakovskyi, fir. Maslii, fin Maslii, 2016
to compensate for the indicated deficiencies, a number of papers [5-7] examine various possibilities. Some [8] work on a distance computerized control of the turnout and on monitoring their condition, others [9] study a possibility of introducing to the market of turnouts drives with electric power supply from solar batteries, some [1, 10] are testing turning mechanisms, built in the sleepers. Specialized constructions are also created, intended for application on the main and station, including sorting, ways. But in this case, all efforts are mostly directed toward the turnouts with electric drives, which use rotary elements. Consequently, all this reduces reliability and service period of an electric drive, leads to high operational costs and requires conducting large volume of repair work. The drawbacks of the known sleeper-type electric drives [10] include a single-stage reducer, which leads to additional losses and necessitates its constant maintenance. There is also complexity of the control system, made in the form of a frequency converter [2]. Taken together, it all leads to the increase in the operating costs and rises its price. Furthermore, the development of microcircuitry makes it possible to design the microprocessor control systems, and to expand functional possibilities of electric drive, to use contactless sensors of new generation [5, 6], to apply electronic converting technology, electronic protection of the motor during switching. Mono-sleeper systems, in turn, will make it possible to reduce their price and prolong the life cycle of operation. One of the most successful solutions for the sleeper design of the turnout is application of the linear motors, actively implemented lately in railway transport [11]. Despite the development of the methods of control of linear motors [12] and mathematical simulation of their different types [13], there is no practice of using such motors in the turnouts in the world yet. Such devices will help not only to simplify the mechanical part of the drive and the system of the rail points control, but also to increase its performance speed.
— multicriterion optimization of geometric dimensions of the electromechanical converter;
— conducting of comparative analysis of the obtained results for both proposed types of a linear electric motor.
4. selection of design of the linear electromechanical converter for the turnout
The main task in the development of design was the exclusion of rotating elements of the turnout and subsequent significant simplification of its kinematic line. Fig. 1 presents transverse and longitudinal sections of the proposed unit, placed in a sleep, and the proposed design of an electric drive is represented in Fig. 2.
Such a design of the electric motor in the form of an electromagnet is characterized by its simplicity and reliability.
Fig. 1. Design of a linear motor in the sleep
3. The purpose and objectives
The purpose of this work is to determine parameters of electric drive of a sleeper-type turnout based on two linear motors by using various methods of optimization.
To achieve the goal, the following tasks were set:
— selection of design of a linear electromechanical converter and an electric drive of a turnout;
Fig. 2. Arrangement of equipment in a mono-sleeper type turnout with electromagnets: 1 — housing; 2 — cover; 3 — transverse thrusts; 4 — articulated joints; 5 — longitudinal thrust; 6 — linear electric motor; 7 — control unit; 8 — cable; 9 — stock rail; 10 — rail points; 11 — position sensors of rail points; 12 — electric motor coil; 13 — anchor of electric motor; 14 — stator of electric motor; 15 — spring; 16 — guide
In this case, linear electric motor (6) consists of stator (14), made of charged electrical steel, coil (12) and anchor (13). Depending on the signal of sensor of the rail points (11), the power converter, located in the control unit (7) and made on the base of field or IGB transistors, connects the coil of the stator (12) to the power source. In this case, the electric motor converts electrical energy to mechanical, setting in motion the anchor (13). In its turn, the anchor, moving along the guide (16), transmits the force through transverse (3) and longitudinal (5) thrusts to the rail points (10). Electric drive of the turnout consists of two electromagnets for reverse work. The application of springs (15) is predetermined by insufficient value of electromagnetic force in the beginning of the switch, as well as by the provision of the necessary force in the case of rail point freezing to the stock rail. The control unit (7) is equipped with different types of speed regulators. Contactless sensors (11) are placed on the outer side of the stock rail (9) and provide control of the tight fit of a rail point to it.
In order to conduct a comparative analysis of the work of linear motor in the turnout, it is proposed to use one more type of electromechanical converter — induction (Fig. 3).
Fig. 4. Arrangement of equipment in a mono-sleeper type turnout with the induction motor: 1 — housing; 2 — cover; 3 — transverse thrusts; 4 — articulated joints; 5 — longitudinal thrust; 6 — linear electric motor; 7 — control unit; 8 — cable; 9 — stock rail; 10 — rail points; 11 — position sensors of rail points; 12 — the coil of electric motor; 13 — the anchor of electric motor; 14 — the stator of electric motor
A four-phase electromechanical converter (6) consists of two stators (14) (internal and external) that makes it possible to obtain maximum air gap in the intertooth zone at minimum dimensions of the unit, concentrating the magnetic flux in the tooth zone. The alternating start of the phases (12) of electric motor (A, B, C, D) ensures uniform distribution of electromagnetic force during anchor motion (13). With the increase in the number of coils (phases), it is possible, if need be, to substantially decrease the fluctuations of the force, acting on the anchor, during its motion.
Fig. 3. Design of inductor type motor: 1 — internal stator; 2 — pole pieces of external stator; 3 — poles; 4 — anchor; 5 — the coil of phases; 6 — housing
5. Diagrams of force distribution in the proposed electric drive of a turnout on the example of an electromagnet
The force of a turnout switch depends on the weight of its moving parts, the type of rails, the joints of switching thrusts and the coefficient of friction of rail points against the pillows. All indicated magnitudes, with exception of the latter, are known. The magnitude of the coefficient of friction depends on the condition of a switcher, quality of the lubricant of the switching pillows, quality of their surfaces treatment, as well on the soles of the rail points, and other factors [14, 15].
Considering the foregoing, the diagram of force distribution in the examined system is represented in Fig. 5.
At the beginning of switch, the distance between the anchor and the stator corresponds to the distance between the rail point and the stock rail (X1) and is 152 mm. In line with the D'Alembert's principle, to perform the switch of rail points, it is necessary that the sum of three of those acting in the system forces would satisfy the following inequality:
I
F = Fel + 2 ■ Fsp + Fc > 0,
(1)
Such a linear motor requires implementation of a more complex system of control, compared to the electromagnet, and, consequently, a more complex engineering solution, but it ensures reverse work without the use of additional springs. The proposed design of electric drive with induction machine is represented in Fig. 4.
where Fel is the force of electromagnet (electric motor); Fsp is the force of spring; Fc is the resistance force.
The electromagnetic force of linear motor depends on the anchor's movement and can be described by the following expression:
dW
where x is the anchor's movement; W is the energy of electromagnet, mostly concentrated in the magnetic gap, without regard to saturation, it is possible to approximately determine it as follows
W = j^di = ] BSdi = j|i0HSdi =
= j
^oiS
di =
^oi2S
(X1 - x) 2(X1 - x)'
Let us determine maximum magnetomotive force:
i = J ■ SL, (6)
where J is the current density; SL is the longitudinal section of the coil.
The longitudinal section of the coil can be expressed through the expression:
SL =
(3)
D Dn
L ,
k 7
(7)
where Y is the flux linkage of the coil of linear motor; i is the magnetomotive force of the coil of linear motor; B is the magnetic induction in the air gap; S is the cross section of the anchor of linear motor; is the magnetic permeability of air; H is the magnetic field strength in the air gap.
where DK is the coil's outer diameter; Dp is the outside anchor diameter; LK is the length of the coil.
Assuming current density equal to J = 5 106 A/m2, the formula for finding magnetomotive force will take the following form:
i=2 (D - DP )
(8)
An important component of electric drive is the pair of springs, which balance each other in the mid-position of the anchor and which create additional force on it in the moment of start, when resistance force provides maximum resistance. The force of the spring depends on the degree of its compression (anchor's movement) and on the coefficient of rigidity:
F.. = K|x - f
(9)
where K is coefficient of rigidity of the spring; X1 is the maximum distance between the rail point and the stock rail.
With the accepted approximation (Fig. 3), the resistance force can be described by the following system of equations
F =
-br,
-k4x - b2;
0 < x < x1, x4 < x < x2,
- b3;
(10)
k2x - b4;
Fig. 5. Interaction of forces of electric drive
After substituting formula (3) to the formula (2), we will obtain the expression for electromagnetic force in the final form:
The last design parameter, necessary for calculating the spring, is the coefficient of rigidity, computed by the expression:
K=GD
8 d3F n'
(11)
F -A Fel" dx
w2s
2(X1 - x)
^ci2S
2(X1 - x)2
(4)
Let us express the cross section of the anchor through the anchor and guide diameters:
S =
Dp + D„10-3 ^2 n _ n(Dp + 5 10-3)
16
(5)
where Dp is the anchor diameter; DH is the guide diameter.
where G is the shear modulus (for steel — 8 1010 H/m); dD is the wire diameter; dF is the diameter of coil; n is the quantity of turns of the spring.
With the use of previously obtained expressions, the program for calculating the electromagnetic force, as well as coefficient of rigidity of the spring, was written in the MATLAB package. The 1/22 type of the turnout with the maximum weight of rail points was used as the load. Based on this program, we obtained the characteristic of force distribution of electric drive from the gap S between the rail point and the stock rail (Fig. 6).
F, Il
0 02
0.04
0.06
0 08
0 1
0 12
0 14
Fig 1
3 —
6. Characteristic of force distribution of the linear drive of a turnout: — resistance force; 2 — electromagnetic force of the linear motor; the force of the spring; 4 — the force, applied to the rail points from the side of the linear drive
of the lower and upper boundaries of the variable parameters, respectively. Such constraints in the space of the variable parameters determine the hyperparallelpiped D={x| a<x<bj.
In the selection of the sleeper design of a turnout, the objective function, on the one hand, must connect by mathematical dependencies geometric dimensions of electric drive, and, on the other hand, the forces that interact in the process of the turnout switch. By using a mathematical description of these forces [17], the objective function must take a rather simple form and short computer time of calculation (for example, with the use of the MATLAB environment). Considering the foregoing, it is expedient to accept, as the objective function, the mean-square deviation of the total traction force of the proposed electric drive relative to resistance force, since minimization of this magnitude in a general case contributes to the decrease of metal consumption in the creation of the drive, as well as to obtaining higher performance efficiency both of the motor and the drive as a whole. The mean-square deviation of forces can be written down in the following form
This approach to development of the mathematical model, based on the simplified determination of electromechanical force, allows us to proceed to implementation of the turnout design.
The proposed design of a turnout (Fig. 2) has a large number of parameters: the diameters of stator and anchor, the sectional area of the coil or dimensions of the spring, etc. Their values can change in a sufficiently wide range. This requires applying optimization, which makes it possible, from the one hand, to minimize the cost of manufacturing the drive itself, and from the other hand, to ensure the necessary traction effort at the switch of a rail point.
The important benefit of such an approach is the fact that all arguments of objective function are calculated for the specific turnout.
Optimization is proposed to perform for the turnout with the rail of the P65 type, 1/11, the commonest one used on the railroads of Ukraine. This will make it possible in the future to optimize parameters of new electric drives on the stage of their development.
The formal formulation of the problem of conditional optimization [16] in a general form comes down to minimization of the objective function f(x), where x = (x4,x2,...,xN) is the vector of variable parameters, with constraints in the form of the equalities hj(x) = 0, i = 1,m and the inequalities gj(x) < 0, j = 1,p, which determine the permissible area
D = {x| hi(x) = 0,i = 1,m;gj(x)<0, j = 1,p}.
(12)
Mathematically, the task of conditional optimization is determined as follows:
minf(x).
(13)
Most frequently, the constraints in the form of inequalities take the form a < x < b, where a and b are the vectors
K - Fc
o = l
(14)
where FTi is the i-th summary traction force of electric drive; FCi is the i-th resistance force; n is the number of calculations.
The projections of the vector of the variable parameters for the examined optimization problem are geometric dimensions of the drive:
Hdk Lk dn HSp KpR)
(15)
where DK is the diameter of the coil; LK is the length of the coil; Dn is the diameter of the guide; HSP is the width of the back of the stator; KPR is the rigidity coefficient of the spring. The diameter of the stator can be determined as follows
Ds = 2HSp + DK.
(16)
The problem of minimization of the mean-square deviation will be represented as the problem of multi-criteria optimization [18, 19]. For this purpose, at solving the problem of selection of optimal geometric dimensions, we will form a hierarchical sequence of criteria.
The highest priority will be assigned to the criterion, which combines parametric constraints and which characterizes the degree of violation of the hyperparallelpiped D of the permissible area of change in the vector of variable parameters:
5
U4(x) = £ (max {0; a, - x,} + max{0; x, - b J), (17)
i=i
where ai, bi are the limiting values of geometric parameters of the motor.
As the problem of optimization calculation is determining geometric dimensions for the purpose of obtaining summary traction force of the drive FT, the next must be the equality
u
of summary traction force FT and the set value of resistance force FC. However, for simplification of the work of optimization procedure, it is more expedient to proceed to the constraints
1.01FC < F(x) (18)
and to write down this criterion in the form of penalty function for the violation of this constraint:
U2(X ) = max {0;F(x ) - 1.01FC}. (19)
This function evaluates the degree of violation of the assigned resistance force. It is accepted here that the constraint is satisfied if the summary traction force is larger than the assigned resistance force by not less than 1 %.
We assume the last criterion to be the objective function — the mean-square deviation:
U3(x) = o(X). (20)
The three set criteria U4(x), U2(x), U3(x) with regard to their priority are necessary to minimize. The vector function is formed for this
F = (U4(x), U2(x), U3(x)).
When selecting the range of variation of the parameters, it is necessary to obey design peculiarities of the proposed drive. On the one hand, they must be limited in the permissible dimensions by strength, on the other hand, by dimensions of the hollow sleep for the elements of the drive. It is also necessary, after performing optimization, to conduct a draft study with the purpose of determining the axial length of the motor and, consequently, the capacity of its fitting into the assigned assembly volume. Considering the foregoing, the range of variation of the parameters is given in Table 1.
points (maximum, minimum and average values). The results of the search solution are given in Table 2.
Table 2
Result of the search solution for optimization
Table 1
Range of variation of the parameters
Parameter Range of variation
Coil diameter, m DK 0,1...0,25
Coil length, m LK 0,2...0,7
Guide diameter, m Dn 0,01.0,03
Stator's back width, m HSP 0,005.0,015
Spring's coefficient of rigidity, N/m KPR 10000.600000
No. of Starting Geometry of motor
method point DK LK Dn HSP KPR
1 0.1 0.2 0.02 0.015 10000
1 2 0.1995 0.4993 0.0195 0.0145 300000
3 0.2353 0.6853 0.0153 0.0053 600000
1 0.1 0.2 0.02 0.015 10000
2 2 0.1999 0.5005 0.0198 0.0138 300000
3 0.2469 0.6958 0.0168 0.005 600000
1 0.1 0.2 0.02 0.015 10000
3 2 0.1995 0.5 0.0196 0.0143 300000
3 0.2283 0.6828 0.0157 0.00791 600000
1 0.1 0.2 0.02 0.015 10000
4 2 0.1995 0.5 0.0196 0.0143 300000
3 0.2253 0.6798 0.0143 0.0878 600000
1 0.1 0.2 0.02 0.015 10000
5 2 0.1995 0.5 0.0196 0.0143 300000
3 0.2131 0.6661 0.01 0.0186 600000
1 0.1 0.2 0.02 0.015 10000
6 2 0.1995 0.5 0.0196 0.0143 300000
3 0.2131 0.6661 0.01 0.0186 600000
1 0.1 0.2 0.02 0.015 10000
7 2 0.1989 0.498 0.0194 0.0142 300000
3 0.2286 0.6812 0.0168 0.0105 600000
1 0.1654 0.5068 0.01371 0.01176 44782
8 2 0.1654 0.5068 0.01371 0.01176 44782
3 0.1654 0.5068 0.01371 0.01176 44782
1 — — — — —
9 2 0.1393 0.5327 0.01247 0.01169 47333
3 0.25 0.2595 0.01 0.00633 68471
1 0.1 0.2 0.02 0.015 10000
10 2 0.1958 0.2888 0.02 0.015 68475
3 0.1848 0.288 0.03 0.02 68491
1 0.1 0.2 0.02 0.015 10000
11 2 0.16 0.5 0.02 0.005 67213
3 0.1083 0.7 0.03 0.02 42413
Thus, we selected the parameters and criteria, as well as defined their hierarchy, for solving optimization problem of geometric dimensions of the turnout. The problem is posed of the global multi-criteria optimization of the functions of five real variables [20].
The set problem was solved by different methods: the Hook-Jeeves method (1), the Nelder-Mead method (2), the method of steepest descent (3), the Fletcher-Reeves method (4), the Polak-Ribiere method (5), the Newton-Raph-son method (6), the Newton method (7), the Weyl method (8), the method of cyclic minimum (9), the Gauss-Seidel method (10), the Powell method (11).
For finding the optimal solution, all the methods indicated above were used with the use of different starting
As the results demonstrate, obtaining optimal solution largely depends on the starting point. It was noted earlier that reaching any magnitude of the traction force of the motor is possible at different combinations of geometric dimensions. There are cases when the solution was not found at all. This testifies to the set of local minimums, i. e., to the fact that the objective function is multi-extremal. Therefore, the operators of optimization procedure must contain, along with the determined, the stochastic components, capable of reviving the search process with its dying down in the local minimums of relief of the objective function. The trajectories of the search process for optimum point for three variable parameters (DK, HSP, KPR), with the use of the method of cyclic minimum and the Weyl method, are presented in
Fig. 7, 8, respectively, where a circle designates a starting point and rhombs display optimal solution.
F, H
Fig. 7. Trajectories of the search process for optimum point by the method of cyclic minimum
Fig. 8. Trajectories of the search process for optimum point by the Weyl method
The evaluation of optimization solution may be conducted with the aid of the curves of force distribution of the drive at its optimized parameters. In this case, the most appropriate are those parameters, at which the mean-square deviation of the forces c(X) will be minimal, i. e., the summary traction force will as closely as possible skirt the load curve.
The obtained values of the mean-square deviation of forces at optimization parameters of the linear electric drive are given in Table 3 and the characteristics of force distribution for particular methods are presented in Fig. 9.
Table 3
Values of mean-square deviation of the forces
Optimization method Mean-square deviation, c, N
The Hook-Jeeves method 20868
The Nelder-Mead method 20863
The Fletcher-Reeves method 20842
The Newton-Raphson method 20806
The Gauss-Seidel method 2497,2
The Powell method 2450,9
The Weyl method 680,9
The method of cyclic minimum 959
20000 18000 16000 14000 12000 10000 eooo 6000 4000 2000 0
\ 2
3 /
41
1
S, m
F, H
20000 18000 16000 14000 12000 10000 8000 6000 4000 2000 0
20000 16000 16000 14000 12000 10000 eooo 6000 4000 2000 0
4\ \ 2
1
3 --- S, m
i
0.1 0.12 0.14
4 V V2
1
3_
- i
Fig. 9. Characteristic of force distribution of the linear drive: a — the Newton-Raphson method; b — the method of cyclic minimum; c — the Weyl method
In the graphs Fig. 9: 1 — resistance force; 2 — electromagnetic force of the linear motor; 3 — the force of the spring; 4 — the force, applied to the rail points from the side of linear drive.
Table 3 clearly demonstrates that the best results in solving the set optimization problem were displayed by the method of cyclic minimum and the Weyl method.
a
b
Thus, the conducted optimization of geometric dimensions of electric drive by the method of cyclic minimum and by the Weyl method made it possible to obtain the required form of the traction characteristic, to decrease expenses for the materials, which, in turn, leads to obtaining the higher performance efficiency of both the motor and the drive as a whole.
The force of the turnout switch depends on the weight of the moving parts of the turnout, the type of rail, the place of fixing conversion thrusts and the coefficient of friction of rail points against the pillows. All the indicated magnitudes, with one exception for the latter, are known, and they are presented in Table 4 for all common types of turnouts.
Dk, m
Table 4
Basic data of switching masses
Rail type Switching type Rail point length, m Rail point weight, N Number of pillows
P75 1/11 8.3 4150 16
P65 1/9 7 3000 12
P65 1/11 8.3 3600 16
P65 1/18 15.5 6700 28
P65 1/22 18.5 8000 34
Coefficient of friction is a rather uncertain magnitude. It may vary in the range from 0.05 to 0.8 and it depends on various factors, such as: condition of the switcher, quality of the lubricant of the switching pillows, quality of their surfaces treatment, as well as the soles of the rail points, etc.
With the purpose of determining the influence of characteristic of friction and the type of turnout on parameters of the linear electric drive, the optimization study was carried out by the method of cyclic minimum, in the course of which the rigidity of load characteristic and the type of turnout changed. As a result of this study, we obtained characteristics of the change in the optimized parameters, depending on the condition and the type of a turnout in the form of the three-dimensional surfaces, which are shown in Fig. 10.
The graphs show that the result of optimization search for geometric dimensions of the motor, in particular, of dimensions of the coil, depends on the type of a turnout. They change within considerably wide range, especially so with different types of the switcher: diameter of the coil varies from 150 mm to 210 mm and its length — from 300 mm to 600 mm. In this case, the thickness of the stator's back remains practically unchanged, in the range of 11-16 mm. In its turn, coefficient of the spring changes quite strongly in connection to both rigidity of the friction characteristic and to the type of the switcher, and it can accept values from 5-104 N/m to 12-104 N/m.
Similarly, we carried out multicriterion optimization of geometric dimensions of induction machine (Fig. 3). The following variable magnitudes were accepted as the input data for various methods of optimization: Dd — motor diameter (limits from 190 mm to 210 mm); Lf — length of each coil (limits from 100 mm to 300 mm); Dr — anchor diameter (limits from 50 mm to 100 mm); Hr — anchor walls thickness (limits from 3 mm to 10 mm); HZ — stator tooth height (limits from 2 mm to 15 mm). A number of teeth NZ in each section of stator was also different but it depended on the coil length Lf and the anchor walls thickness Hr. The width of the stator tooth WZ, as well as the width of the in-tertooth area Wb, were accepted as equal to the anchor walls thickness during calculations.
0.190.18
0.160 15
P, Hc/m
Fm, H
Kpr, H/m
P, Hc/m
Fm, H
Hsp, m
0 0140.013 -0 012 -0 011 0.01 -
P, Hc/m
Lk, m
0.50.450 4 -
P, Hc/m
Fm, H
Fig. 10. Surfaces that reflect changes in the optimized parameters: a — coil diameter; b — coil length; c — stator's back width; d — rigidity coefficient of the spring
a
b
c
As earlier, the evaluation of results of different methods was performed by the value of the mean-square deviation of forces at optimization parameters of the linear electric drive (Table 5). In contrast to the electromagnet, the best results of optimization were displayed by the method of cyclic minimum.
Table 5
Values of the mean-square deviation of the forces
Optimization method Mean-square deviation, c, N
The Nelder-Mead method 18144
The Powell method 1544,9
The Weyl method 1108,2
The method of cyclic minimum 1052,3
As can be seen in Fig. 11, the result of optimization search for geometric dimensions of the motor, as earlier, strongly depends on the type of the turnout and characteristic of friction.
Thus, there is no unique solution of optimization problem of geometric dimensions of a linear electric motor for the existing turnouts, and, therefore, further research and design should be based on the switcher with the P65 type of rail as the most common.
6. conclusions
1. A fundamentally new design solution of the drive based on two types of the linear electric motor was represented, traction calculation of the acting electromagnetic forces was carried out and the graphs of the distribution of forces in the turnout were built.
Based on the obtained results, we confirmed the possibility of using the proposed types of linear motors in the turnouts, since they provide the required forces on the thrust in the range up to 20 KN. Due to significant simplification of the turnout design, it is possible to reduce the cost of its maintenance during operation, while applying microprocessor technology will make it possible to attain the required traction characteristic.
2. The problem of multicriterion optimization of geometric parameters of the linear motors of a drive was compiled, the special feature of which is the use, as the objective function, of the criterion of mean-square deviation of the summary traction power. The rational method of solving the problem of multicriterion optimization of parameters of motors is determined. The best result in the search for global optimum was demonstrated by the Weyl method (for electromagnet) and the method of cyclic minimum (for induction motor). The estimation was conducted according to results of the optimal (minimal) value of the mean-square deviation of electromagnetic force from the resistance force.
Dd,
Hz, mm
P, Hc/m
P, Hc/m
0 12 4000
Fm, H
Dr, m
Lf,M
P, Hc/m
Fm, H
P, Hc/m
Fm, H
Fig. 11. Surfaces that reflect changes in the optimized parameters: a — motor diameter; b — anchor diameter; c — stator's tooth height; d — coil length
b
a
c
The optimum traction characteristics of the electromagnet were determined based on the simplified model for determining the electromagnetic force, which make it possible to provide the required force at working traction of 20 KN.
3. We obtained results of optimization search for geometric dimensions of the motor, in particular, sizes of the coils, which strongly depend on the type of a turnout. They change within quite a wide range, especially so with different types of the switcher. Diameter of a magnet coil varies
from 150 mm to 210 mm, and its length — from 300 mm to 600 mm. In this case, thickness of the stator's back remains practically unchanged, in the range of 11-16 mm. In its turn, coefficient of the spring quite strongly changes in relation to both the rigidity of the friction characteristic and to the type of a switcher, and it can accept values from 5 104 N/m to 12 104 N/m. It should be noted for the induction motor that at sufficiently wide range of the stator's teeth heights, its optimum value is within the limits from 3.5 to 6.5 mm.
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