CC BY
37
Electrical Machines and Apparatus
UDC 621.313:536.2.24:539.2 doi: 10.20998/2074-272X.2019.3.02
V.F. Bolyukh, Yu.V. Kashanskij, I.S. Schukin
INFLUENCE OF GEOMETRICAL PARAMETERS OF THE INDUCTOR AND ARMATURE ON THE INDICATORS OF A LINEAR PULSE ELECTROMECHANICAL CONVERTER OF AN ELECTRODYNAMIC TYPE
Purpose. The aim of the paper is to study the influence of geometrical parameters, namely, the number of layers and the cross section of the copper tire of the inductor and the armature coils on the power and speed indicators of a linear pulse electromechanical converter (LPEC) of an electrodynamic type. Methodology. On the basis of the developed chain mathematical model, recurrent relations are obtained for the calculation of interconnected electromagnetic, mechanical and thermal processes of LPEC of an electrodynamic type. The effect of the thickness of a square copper tire and the number of its layers in the inductor and armature coils on the characteristics and characteristics of electrodynamic LPEC is investigated. It is these parameters that determine the number of turns and the axial height of the coils with limited radial dimensions. Results. The influence of the geometrical parameters of the inductor and the armature coils with limited radial dimensions on the electrical and mechanical characteristics of LPEC of an electrodynamic type is established. It has been established that with an increase in the thickness of a rectangular cross-section of copper tire from 1 to 2.5 mm, an increase in the amplitude and pulse of electrodynamic forces (EF) occurs. However, the maximum speed of the armature is the highest at LPEC wound with a 1.5 mm thick tire. The highest efficiency value is demonstrated by LPEC, in which the inductor and armature coils are wound with a 2 mm thick tire. With an increase in the number of layers of the inductor coil tire, the amplitude of the EF decreases significantly, and the magnitude of the EF pulse decreases slightly. As a result, the maximum armature speed, efficiency and temperature rise of the coils are reduced. Originality. It is established that the largest amplitude of the EF is realized in LPEC with the minimum number of layers of tires of the inductor and armature coils. The largest value of the pulse EF occurs when the maximum number of layers of the inductor and the armature. In this case, the largest values of the amplitude and pulse of the EF occur under the condition that the number of tire layers of the inductor and the armature coils are the same. Practical value. It has been established that the greatest efficiency 21.82 % is realized in LPEC, in which the number of tire layers is 2 mm thick with inductor and armature coils are 4. A catapult model for launching an unmanned aerial vehicle was made and tested on the basis of LPEC of an electrodynamic type. References 12, figures 6.
Key words: linear pulse electromechanical converter of electrodynamic type, chain mathematical model, recurrent relations, geometrical parameters of inductor and armature coils, electrodynamic forces, efficiency.
Розроблена ланцюгова математична модель лiнiйного мпульсного електромехатчного перетворювача (Л1ЕП) електродинамiчного типу. Отриманорекурентнi спiввiдношення длярозрахунку взаемопов'язаних електромагттних, механiчних i теплових процеав. Встановлено, що при збшъшеиш товщини квадратноi мiдноí шини котушок тдуктора i якоря вiд 1,0 до 2,5 мм збтьшуються амплтуда i величина Шпульсу електродинамiчних зусилъ (ЕДЗ). Максимальна швидксть якоря найбтьша у Л1ЕП, котушки тдуктора i якоря якого намотан шиною товщиною 1,5 мм. Найбтьше значення ККДу Л1ЕП, котушки якого намотан шиною товщиною 2,0 мм При збтьшент ктько<т шири; шини котушки тдуктора амплтуда ЕДЗ знижуетъся ктотно, а величина мпульсу ЕДЗ - незначно. Вналдок цъого знижуються максимальна швидмсть якоря, ККД i перевищення температури котушок. Найбтъша амплтуда ЕДЗ реатзуеться в Л1ЕП при мЫмальнш кiлъкостi шары шин котушок тдуктора i якоря, а найбтьша величина мпульсу ЕДЗ виникае при максимальнш 1х кшькости При цьому найбiлъшi значення амплтуди i мпульсу ЕДЗ виникають за умови, коли число шарiв шини котушок однаковь Найбтьший ККД (21,82 %) реалзуеться в Л1ЕП, у якого котушки тдуктора i якоря намотан в чотири шари квадратно1 шини товщиною 2,0 мм На базi Л1ЕП електродинамiчного типу була виготовлена i випробувана модель катапульти для запуску безптотного лтального апарату. Бiбл. 12, рис. 6.
Ключовi слова: лшшний iмпульсний електромехашчний перетворювач електродинамiчного типу, ланцюгова математична модель, рекурентш ствввдношення, геометричш параметри котушок вдуктора i якоря, електродинамiчнi зусилля, ККД.
Разработана цепная математическая модель линейного импульсного электромеханического преобразователя (ЛИЭП) электродинамического типа. Получены рекуррентные соотношения для расчета взаимосвязанных электромагнитных, механических и тепловых процессов. Установлено, что при увеличении толщины квадратной медной шины катушек индуктора и якоря от 1,0 до 2,5 мм увеличиваются амплитуда и величина импульса электродинамических усилий (ЭДУ). Максимальная скорость якоря наибольшая у ЛИЭП, катушки индуктора и якоря которого намотаны шиной толщиной 1,5 мм Наибольшее значение КПД у ЛИЭП, катушки которого намотаны шиной толщиной 2,0 мм При увеличении количества слоев шины катушки индуктора амплитуда ЭДУ уменьшается существенно, а величина импульса ЭДУ - незначительно. Вследствие этого снижаются максимальная скорость якоря, КПД и превышения температуры катушек. Наибольшая амплитуда ЭДУ реализуется в ЛИЭП при минимальном количестве слоев шин катушек индуктора и якоря, а наибольшая величина импульса ЭДУ возникает при максимальном их количестве. При этом наибольшие значения амплитуды и импульса ЭДУ возникают при условии, когда количество слоев шины катушек одинаковы. Наибольший КПД (21,82 %) реализуется в ЛИЭП, у которого катушки индуктора и якоря намотаны в четыре слоя квадратной шины толщиной 2,0 мм На базе ЛИЭП электродинамического типа была изготовлена и испытана модель катапульты для запуска беспилотного летательного аппарата. Библ. 12, рис. 6.
Ключевые слова: линейный импульсный электромеханический преобразователь электродинамического типа, цепная математическая модель, рекуррентные соотношения, геометрические параметры катушек индуктора и якоря, электродинамические усилия, КПД.
© V.F. Bolyukh, Yu.V. Kashanskij, I.S. Schukin
Introduction. Linear pulse electromechanical converters (LPEC) allow to provide a high speed of the actuator (A) in the short active area and/or to create powerful force pulses at its slight displacement [1-3]. Such converters are used in many branches of science and technology as electromechanical accelerators and shock-power devices [4, 5]. One of the most promising is LPEC of electrodynamic type [6, 7]. In this converter, which has a coaxial configuration, the fixed inductor and accelerated armature are made in the form of monolithic disk coils, which are impregnated with epoxy resin. Serially connected the inductor and the armature are tightly wound with the same copper tire. The current from a pulsed power source containing a capacitive energy storage (CES) is excited in them [4, 8]. The armature is connected to the inductor and to the power source using movable (flexible or sliding) current leads. The inductor and the armature are connected in opposite directions by the magnetic field, as a result of which electrodynamic forces (EFs) of repulsion act between it. These EFs cause axial displacement of the armature relative to the fixed inductor (Fig. 1,a).
number of nonlinear dependencies, the solutions of the equations describing the indicated processes will be presented in recurrent form [10].
When a starting pulse is applied to the thyristor VS, the inductor and the armature are excited by an aperiodic polar pulse from the CES C, shunted by a reverse diode VD (Fig. 1,b). We believe that in a pulsed power supply the resistance of the diode VD and thyristor VS in the forward direction is negligible, and in the opposite direction their conductivity is just as small.
Electrical processes in LPEC of an electrodynamic type on the time interval {0, t1}, where t1 is the time at which the CES voltage is uC = 0, can be described by the equation:
fa (Ti ) + R2(T2)\ i + ^ +1 f idt = 0, «c(0) = U o, (1) dt C 0
where n = 1, 2 are the inductor and armature indexes, respectively; Rn, Tn, Ln are the active resistance, temperature and inductance of the n-th element; M12 is the mutual inductance between the inductor and the armature, moving along the z axis with speed vz;
-\t 2M (z) , T ld' 2iv (t)12
^ = [¿1 - 2M12( z) + L21 - 2ivz (t )dM dt dt dz
Substituting equation (2) into (1) we obtain:
(2)
R1T1) + R2(T2) - 2vz(t) t
^ ]• i + [A -2M12(z) + L21 + dz I dt
(3)
a b
Fig. 1. Constructive (a) and electric (b) circuits of LPEC of electrodynamic type: 1 - inductor; 2 - armature; 3 - actuator; 4 - return spring; 5 - power supply; a, b - flexible current leads
In the process of LPEC operation, a change in the magnetic coupling between the armature and the inductor occurs. In addition, their resistances increase due to heating with high-density pulsed current. These features of the operating process must be taken into account in the mathematical model of LPEC of electrodynamic type [9]. When operating in a dynamic mode with a rapid change of electromagnetic, mechanical and thermal parameters, the efficiency of LPEC is not high enough, which is due, in particular, to the lack of justification for choosing the geometric parameters of active elements - inductor and armature coils.
The goal of the paper is the study of the influence of geometrical parameters, namely, the number of layers and the cross section of the copper tire of the inductor and the armature coils on the power and speed indicators of LPEC of electrodynamic type.
Mathematical model. Consider a mathematical model of LPEC of electrodynamic type, which uses the concentrated parameters of the inductor and the armature. We will assume that the fixed inductor and the accelerated armature are made in the form of coaxially mounted circular multi-turn disk coils that are tightly wound with the same square-section copper tire.
To take into account the interconnected electrical, magnetic, mechanical and thermal processes, as well as a
+ — f idt = cJ
0.
The solution of equation (3) can be represented as:
i = A1 exp(a1/) + A2 exp(«2t), (4)
where Ab A2 are the arbitrary constants,
\2
a12 = -0,5—+
0,25
0
1
~3C
0,5
are the roots of the
characteristic equation; ^ = L1 - 2M12 (z) + L2 ;
dM12
0 = R1T1) + R2T2) - 2vz(t )-
dz
To represent the solution in a recurrent form, we define the values of arbitrary constants at the time tk.
then after a series of
If 0> 2yJ30_1 transformations we get:
A = uC(tk) + ®' i(tk) + a2,13 • i(tk) (5)
1,2 3exp(«1,2tk \ci21 -«1,2) '
Substituting expressions (5) into equation (4), we obtain the expression for the current:
"C(y + i(!k) [exp(a1At) -exp(a2At)]-+
i(tk+1) =--
(a2 -a1 )
+—i(tk ) exp(a1At)- a1 exp(a2At)
a2 -a1
where At = tk+1 - tk . Voltage on the CES:
(6)
"c(tk+1 ) = Uc(tk) + &'l(tk) [ ехрЦДГ)-exp(«2At)]-л
a 2 -«i
+ д l(tk) la| exp(a1At)-a12 exp(a2At)l
a2 -a1
(7)
If © < 2^3C 1 , then the roots of the characteristic equation can be represented as:
«1,2 = ~s ± j W = «0 expjj + 9)), (8)
-1
where 8 = Q,50^_1 ; 6 = arctg (4S0~2C-1 -1
(4S0~2C-1 - ^ ;
(9)
(1Q)
®0 = (-C)"0'5; w = (c-1 - 0,25©2 - "2 ).
Substituting the values of the roots (8) into equations (6), (7) and taking into account that
2j sinjw At) = expjj w At) - expj- j w At),
we get:
%+1) = -W-1 expj- SAt ){a [ (tk) + ©■ i(tk )]sin(w At) + a>0i(tk) sin j At - &)). Voltage on the CES:
uc (tk+1) = -WW-1 expj- SAt )[ (tk) + © ■ i(tk)] x x sinjAt - 6) + i(tk )®0— sinj At - 20)
If © = 2V—C-1 , then S = ®0 and current is:
i(tk+1) = expj- SAt )t )S - [uc (tk) + © ■ i(tk )]).(11) Voltage on the CES: uc (tk+1) = [uc (tk) - i(tk )—& + ©■ i(tk )](SAt +1) x (12) x expj-SAt) + i(tk )(SS-©).
current in LPEc in the time interval {ti, <» } varies according to the law:
i(tk+1) = i(tk )exp(-©--1At). (13)
Mechanical processes in LIEP can be described by the equation:
i2 (t)^- = (ma + m2 )— + K PAz(t ) + K T vz (t) +
vdv
dz
dt
(14)
+ 0,125^^ ^2mVz2(t ),
# = i 2(tk (*) - KpAz(tk) - KTvz (tk) -dz
- 0,125^^ v2(tk ).
Thermal processes. In the absence of displacement of the armature, which occurs either before the start of the forward stroke, or after the return stroke, there is a thermal contact between the inductor and armature coils through the insulation gasket. The temperatures of the n-th active elements of the LPEc of electrodynamic type can be described by the recurrent relation [12]:
T„ (tk+1) = Tn (tk K + (1 - t[nr\(tk )Rn (Tn )j - Di2« ) +
+ 0,25 KT^DenH n«Tn + Tm (tk )^a(T )rfa-1K25^«TnDenHn + (17)
+ 4,(T )da
1Г1.
where ^ = exp<! -
Ж
Cn (Tn )Yn
Q,25DenaTn +
4(T )
da Hn у
Xa(T) is the thermal conductivity of the insulation gasket; da is the gasket thickness; Den, Din are the outer and inner diameters of the active elements, respectively; aTn is the heat transfer coefficient of the n-th active element; Cn is the heat capacity of the n-th active element.
Temperatures of the n-th active elements when the armature is moved and there is no thermal contact between the armature and the inductor can be described by the recurrence relation:
Tn (tk+l) = Tn (tk )X + (l - zfc + 4^n (tk )Rn (Tn Wn "
x DenH
1 (d2 - D2 )
X^en ^in /
where % = expj- Q,25AtD,
(18)
where m2, ma are the mass of the armature and A, respectively; KP is the value of elasticity of the return spring; Az(t) is the value of the displacement of the armature with A; KT is the coefficient of dynamic friction; 7a is the density of the medium of displacement; is the aerodynamic resistance coefficient; D2m is the outer diameter of the A.
The effectiveness of the axial force action on the armature will be estimated by the value of the impulse of EF [ll]:
PI =J F ( z, t )dt, (15)
where F(z, t) is the instantaneous value of axial EF acting on the armature.
Based on equation (14), the value of the displacement of the armature with A can be represented as a recurrent relation:
s(tk+n) = s(tk ) + vz(tk )At + SAt2/(ma + m2 ), (16) where vz(tk+1) = vz(tk) + 5At/(ma + m2) is the speed of the armature with A along the z axis;
■^enaTnCn (Tnj.
The initial conditions of the mathematical model of LPEC are as follows:
Tn(0) = T0 - the temperature of the n-th active element;
Ц0) = 0 - the current of the n-th active element;
s(0) = s0 -the initial axial distance between the coils of
the armature and the inductor;
Uc(0)=U0 - the CES voltage;
vz(0) = 0 - the armature speed along the z axis.
The efficiency of the LPEC of electrodynamic type will be estimated by the relation:
(m2 + ma )v2 + KPs2 „, 7 = 1QQ^-—P— %.
CU Q2
(19)
Main parameters of LPEC of electrodynamic
type. Consider LPEC, whose movable armature and fixed inductor are made in the form of flat coaxially mounted disk coils. At the armature, one end side faces the inductor, and the second one interacts with A. The inductor (n=1) and the armature (n=2) are tightly wound with Kpn layers of a square-section copper tire with thickness a. The outer diameter of the n-th element is Den=100 mm, the inner diameter is Din=10 mm. The CES has the following parameters: capacitance C = 3 mF, voltage U0 = 0,4 kV. The initial distance between the inductor and the armature is s0=1 mm. The coefficient of elasticity of the return spring KP=25 kN/m. Mass of A is ma=0,25 kg.
We investigate the influence of the thickness a of a copper square tire and the number Kpn of its layers in the
inductor and armature coils on the characteristics and indicators of the LPEC of electrodynamic type. These parameters determine the number of turns
D - D-Nn = Ent\05 Den D"
a + 25
K
pn
and the axial height
Hn = (a + 28) vn
of the n-th coils with limited radial dimensions, where Ent(f) is the largest integer not exceeding f 5 is the insulation thickness of the copper tire.
Investigation of operation processes in LPEC. Consider the electrical and mechanical characteristics of the LPEC of electrodynamic type, in which both the inductor and armature coils are tightly wound in four layers Kpn=4 with a square tire of different thickness (Fig. 2). As the thickness of the copper tire a increases from 1 to 2,5 mm, the number of turns of each coil Nn decreases from 160 to 68, and the axial height Hn increases from 4,4 to 10,4 mm. In this case, the amplitude of the current im increases significantly - from 0,30 to 1,56 kA, and the amplitude of the current density jm decreases slightly from 304,3 to 250,4 A/mm2.
1,0 b
Fig. 2. Electrical (a) and mechanical (b) characteristics of LPEC, the coils of which are wound with a copper tire of different thickness a
An increase in the thickness of the copper tire a changes the regularities of the flow of electrical processes: the CES voltage uC decreases to zero value
faster, and the current takes the form of a clear pulse with a significant increase in the leading front and falling of the falling front. With an increase in the thickness of the copper tire a from 1 to 2,5 mm, the power indicators of LPEC increase. The amplitude of the EF Fm increases from 3,78 to 12,65 kN, and the impulse of the EF PI increases from 4,52 to 9,16 N-s. However, speed indicators depending on the thickness of the tire do not have an unequivocal pattern.
The maximum speed of the armature Vm is the greatest at LPEC, whose coils are wound with a tire of thickness a = 1,5 mm, and is 11,24 m/s. If the tire has a smaller or greater thickness, then the speed decreases: at a = 1 mm -Vm = 8,16 m/s, and at a = 2,5 mm - Vm = 9,44 m/s.
An ambiguous dependence on tire thickness is also demonstrated by the efficiency of the LPEC of electrodynamic type. The highest efficiency value n = 21,8 % has LPEC, in which the inductor and armature coils are wound with a tire of thickness of a = 2 mm. If the coils are wound with thinner or thicker tires, the efficiency decreases: at a = 1,5 mm n = 20 %, at a = 2.5 mm n = 18,8 %. Note that if the coils are wound with an even thinner tire a = 1 mm, then the efficiency takes an even lower value n = 8,5 %.
With increasing thickness of copper tire a from 1 to 2,5 mm, the temperature rise of the inductor and armature coils 6n decreases from 0,6 to 0,23 °C..
On the basis of the analysis performed, it can be concluded that the most effective is the LPEC of electrodynamic type, in which the inductor and armature coils are wound with a copper tire with a thickness of a = 2 mm. The number of turns of each coil is Nn = 84, and their axial height is Hn = 8,4 mm.
Investigate the effect of the number of layers of the tire of the inductor coil Kpi on the indicators of the LPEC of electrodynamic type. Obviously, as Kp1 increases, the number of turns N1 and the axial height H1 of the inductor coil increase. We will consider LPEC, in which the inductor and armature coils are wound with a copper tire with thickness of a = 2 mm. The armature coil is wound in two layers, contains the number of turns N2 = 22 and has the axial height H2 = 4,2 mm. Consider the electrical and mechanical characteristics of LPEC, in which the inductor coil is wound with several layers Kpi (Fig. 3).
With an increase in the number of tire layers of the inductor coil Kpi three times (from 2 to 6), the amplitude of the current im decreases almost in the same proportion (from 2,57 to 0,86 kA), and the current pulse itself becomes more stretched due to an increase in the front and rear fronts. When the parameter Kpi is increased, the voltage of the CES uC decreases to zero value more slowly.
With an increase in the number of tire layers of the inductor coil Kp 3 times the amplitude of the EF Fm decreases 4.1 times (from 18,72 to 4,57 kN), while the impulse of the EF PI decreases slightly (from 6,79 to 5,69 N-s). As a result, the maximum speed of the armature with A Vm (from 12,54 to 10,53 m/s), efficiency n (from 18,08 to 13,57%) and temperature rise of the coils 6n (from 0,73 to 0,3 °C) are reduced. These patterns of change in the maximum speeds Vm depending on the number of layers
of the tire of the inductor coil Kp1 manifest themselves in a change in the nature of the displacement of the armature with A 5 (see Fig. 3,6).
600
500
400
300
200
100
UC,V, J, A
^Pl — - 2 --4 -6 -
1 r \ / ^-îic
\ ^
0,5
1,0
1,5 f.
2,0
p2,
Kp2 = 6 the current amplitude decreases to
Kp2 =1 the current
Similar dependencies on the number of tire layers of the inductor Kp1 and armature Kp2 coils are observed at the coil temperature rises. The maximum temperature rise (612 = 1,5 °C) occurs at the minimum number of layers of the coil tire Kp1 = Kp2 = 1 and minimum (612=0,21 °C) at the maximum number of layers of the tire Kp1 = Kp2 = 6. At Kp1 = 1 and Kp2 = 6 the temperature rises 612 = 0,33 °C, and at Kp1 = 6 u Kp2 = 1 the temperature rises 612 = 0,31 °C.
The ratio of the number of layers of tire of coils significantly affects the power indicators of the LPEC of electrodynamic type (Fig. 4).
Fit), kN
/10
/ --"
/ / J
-^20) / 7 y
-7/, // / 10,
12 3 4
a
Pl} N-s
5 KP1 6
b
Fig. 3. Electrical (a) and mechanical (b) characteristics of LPEC, the coils of which are wound with tire thickness a = 2 mm with a different number of layers of the inductor coil tire Kp1
Influence of the number of layers of the tire of inductor and armature coils on the indicators of
LPEC. Consider the effect of the mutual ratio of the number of layers of the tire of inductor Kp1 and armature Kp2 coils of thickness a = 2 mm on operation indicators of LPEC of electrodynamic type. We assume that the maximum number of layers of the tire coils Kp1 = Kp2 = 6.
With an increase in the number of tire layers of the inductor coil Kp1 and/or of the armature coil Kp2, the
1 10
V9
8 V
16 x7__
I 5 ^
5 K-
PI
b
amplitude of the current im decreases, but in different degrees. So, if the number of tire layers of both coils is minimal Kp1 = Kp2 = 1, then im = 5,8 kA. If the number of tire layers of one of the coils is minimal and of the second one is maximum, then the following pattern is observed: at Kpi = 1,
im = 0,865 kA, and at Kp1 = 6 amplitude decreases to im = 0,846 kA. If the number of tire layers of both coils is maximum Kp1 = Kp2 = 6, then the current amplitude decreases to the greatest extent (to the value im = 0.7 kA).
Fig. 4. Distributions of the maximum value (a) and impulse (b) of the EF depending on the ratio of the number of tire layers of the inductor and armature coils of the LIEP
The amplitude of the EF Fm is the greatest at the minimum number of layers of tires of inductor and armature coils. At Kp1=Kp2=1, the value of Kp1=Kp2=1 kN. With an increase in the number of layers of the tire of one of the coils, this value is significantly reduced. So, at Kp1=1 and Kp2=6 the amplitude of the EF is Fm=2,75, and at Kp1=6 and Kp2=1 the amplitude of the EF is Fm =2,34 kN. If the number of tire turns of the inductor and armature coils is maximum Kp1=Kp2=6, then the amplitude of the EF increases to Fm=7,6 kN. We can note the following pattern: the largest values of the amplitude of the EF Fm are observed under the condition that the numbers of tire layers of the inductor and armature coils are the same.
a
Impulse of EF PI has a different pattern on the ratio of the number of tire layers of the inductor and armature coils. The largest value of the impulse of EF occurs at the maximum number of layers of the tire of coils. At Kpi=Kp2=6 the value of PI= 10,06 N-s. If the number of layers of the inductor and the armature tire is minimal, then the value of the impulse of EF is reduced by more than two times. At Kp1=Kp2=1 the value of PI=4,49 N-s. The highest impulse values of the EF PI are realized when the number of tire layers of the inductor and armature
T] , %
T] , %
coils is equal. If the number of tire layers of one of the coils is maximal, and in the second one is minimal, then the EF impulse decreases. At Kp1=1 and Kp2=6 the impulse of EF PI=4,06 N-s, and at Kp1=6 and Kp2=1 PI=3,3 N-s.
Let us consider the regularity of the distribution of the efficiency of LPEC of electrodynamic type as a function of the ratio of the number of tire layers of the inductor and the armature coils for its various thickness a (Fig. 5).
11, %
/// //„ 16
«// up /// -ib
// 20 / /
L
("A
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11 |A
it / / 10 / / / /14 / / 16
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5 Kp
5 KP1 6
5 Kp, 6
b
Fig.
5. The LPEC efficiency distributions depending on the ratios of the number of tire layers of the inductor and armature coils at
the tire thickness a: 1,5 mm (a); 2 mm (b); 2,5 mm (c)
The highest values of efficiency are realized at a certain ratio of Kp1 and Kp2. If the tire thickness a is equal to 1,5 mm or 2 mm, then the highest efficiency value is realized at Kp1=Kp2=4 and takes the values n = 20,01 % and n = 21,82 %, respectively. If the tire thickness is a = 2,5 mm, then the greatest efficiency value (n = 18,91 %) is realized at Kp1=4 and Kp2=3.
On the basis of the research carried out, it can be concluded that there is an optimal thickness of the copper tire a = 2 mm and the corresponding number of turns in each layer of the inductor and armature coils. From the point of view of power indicators, the number of layers of the tire of coils should be the maximum of the considered range (Kp1=Kp2=6). From the point of view of the efficiency of acceleration of A, coils should have fewer layers (Kp1=Kp2=4).
Taking into account the relationships obtained, on the basis of an LPEC of electrodynamic type a model of a catapult for launching an unmanned aerial vehicle (UAV) was made (Fig. 6).
In this model, both inductor and armature coils are wound with a copper tire and are compounded with epoxy resin in a rectangular insulating frame. The inductor coil is attached to the starting stop wall, and the armature coil is made with the possibility of axial movement along the central guide.
The electrical leads of the inductor and armature coils are located between the two dielectric guide plates and are connected by flexible wires to each other and to the power source. The armature coil is braked by means of an elastic damper attached to the brake stop wall. To the coil of the armature accelerating protrusion is attached that pushes the UAV.
Fig. 6. Model of a catapult for launching an UAV: 1 - guide plates for moving an UAV; 2 - UAV;
3 - guide plates for moving the current leads of the armature coil; 4 - brake stop wall; 5 - brake elastic damper; 6 - accelerating protrusion; 7 - armature coil; 8 - inductor coil;
9 - starting stop wall; 10 - current lead coils
The carried out tests of the model with the parameters set above confirmed the validity of the theoretical studies carried out on the LPEC of electrodynamic type.
Conclusions.
1. On the basis of the developed chain mathematical model, recurrent relations are obtained for the calculation of interconnected electromagnetic, mechanical and thermal processes in LPEC of electrodynamic type.
2. It is established that with an increase in the thickness of the square copper tire of the inductor and armature coils from 1 to 2,5 mm, the amplitude and impulse of the EF increase. However, the maximum speed of the armature is the highest at LPEC, the coils of which are wound with a tire 1,5 mm thick. The highest efficiency value is demonstrated by LPEC, in which the coils are wound with a tire 2 mm thick.
a
c
3. With an increase in the number of layers of the inductor coil tire, the amplitude of the EF decreases significantly, while the value of the EF impulse decreases slightly. This reduces the maximum speed of the armature, efficiency and temperature rise of the inductor and armature coils.
4. The greatest amplitude of the EF is implemented in LPEC at the minimum number of tire layers of the inductor and armature coils. The largest value of the impulse of the EF occurs at the maximum number of layers of the tire of coils. In this case, the largest values of the amplitude and impulse of the EF occur under the condition that the number of tire layers of both coils is the same.
5. The highest efficiency (21,82%) is realized in LPEC, in which the inductor and armature coils have four layers of square tire 2 mm thick.
6. A catapult model for launching an unmanned aerial vehicle was made and tested on the basis of the LPEC of electrodynamic type.
REFERENCES
1. Balikci A., Zabar Z., Birenbaum L., Czarkowski D. Improved performance of linear induction launchers. IEEE Transactions on Magnetics, 2005, vol.41, no.1, pp. 171-175. doi: 10.1109/tmag.2004.839283.
2. Tomashevsky D.N., Koshkin A.N. Modeling of linear impulse electric motors. Russian Electrical Engineering, 2006, no.1, pp. 24-27. (Rus).
3. Bissal A., Magnusson J., Engdahl G. Electric to mechanical energy conversion of linear ultrafast electromechanical actuators based on stroke requirements. IEEE Transactions on Industry Applications, 2015, vol.51, no.4, pp. 3059-3067. doi: 10.1109/tia.2015.2411733.
4. Bolyukh V.F., Shchukin I.S. Lineinye induktsionno-dinamicheskie preobrazovateli [Linear induction-dynamic converters]. Saarbrucken, Germany, LAP Lambert Academic Publ., 2014. 496 p. (Rus).
5. Bissal A., Eriksson A., Magnusson A., Engdahl G. Hybrid multi-physics modeling of an ultra-fast electro-mechanical actuator. Actuators, 2015, vol.4, no.4, pp. 314-335. doi: 10.3390/act4040314.
6. Bolyukh V.F., Oleksenko S.V., Shchukin I.S. Comparative analysis of linear pulse electromechanical converters
electromagnetic and induction types. Technical
Electrodynamics, 2016, no.5, pp. 46-48. (Rus).
ZBissal A., Magnusson J., Engdahl G. Comparison of two
ultra-fast actuator concept. IEEE Transactions on Magnetics,
2012, vol.48, no.11, pp. 3315-3318. doi:
10.1109/tmag.2012.2198447.
8. D.-K. Lim, D.-K. Woo, I.-W. Kim, D.-K. Shin, J.-S. Ro, T.K. Chung, H.-K. Jung. Characteristic Analysis and Design of a Thomson Coil Actuator Using an Analytic Method and a Numerical Method. IEEE Transactions on Magnetics, 2013, vol.49, no.12, pp. 5749-5755. doi: 10.1109/tmag.2013.2272561.
9. Li W., Koh C.S. Parametric analysis of Thomson-coil actuator using adaptive equivalent circuit method. Digests of the 2010 14th Biennial IEEE Conference on Electromagnetic Field Computation, May 2010, pp. 1-9. doi: 10.1109/cefc.2010.5481673.
10. Bolyukh V.F., Kocherga A.I., Schukin I.S. Investigation of a linear pulse-induction electromechanical converter with different inductor power supply circuits. Electrical engineering & electromechanics, 2018, no.1, pp. 21-28. doi: 10.20998/2074-272X.2018.1.03.
11. Bolyukh V.F., Oleksenko S.V., Schukin I.S. Efficiency of linear pulse electromechanical converters designed to create impact loads and high speeds. Electrical engineering & electromechanics, 2015, no.3, pp. 31-40. doi: 10.20998/2074-272X.2015.3.05.
12. Bolyukh V.F., Schukin I.S. Investigation of thermal processes in a linear pulse-induction electromechanical converter of cyclic action. Electrical engineering & electromechanics, 2017, no.5, pp. 14-22. doi: 10.20998/2074-272X.2017.5.02.
Received 05.03.2019
V.F. Bolyukh1, Doctor of Technical Science, Professor, Yu.V. Kashanskij1, Postgraduate Student, I.S. Schukin2, Candidate of Technical Science, Associate Professor,
1 National Technical University «Kharkiv Polytechnic Institute», 2, Kyrpychova Str., Kharkiv, 61002, Ukraine,
phone +380 57 7076427, e-mail: vfbolyukh@gmail.com
2 Firm Tetra, LTD,
2, Kyrpychova Str., Kharkiv, 61002, Ukraine,
phone +380 57 7076427, e-mail: tech@tetra.kharkiv.com.ua
How to cite this article:
Bolyukh V.F., Kashanskij Yu.V., Schukin I.S. Influence of geometrical parameters of the inductor and armature on the indicators of a linear pulse electromechanical converter of an electrodynamic type. Electrical engineering & electromechanics, 2019, no.3, pp. 11-17. doi: 10.20998/2074-272X.2019.3.02.
