CC BY
79
Electrical Machines and Apparatus
UDC 621.313:536.2.24:539.2 doi: 10.20998/2074-272X.2018.2.02
V.F. Bolyukh, A.I. Kocherga, I.S. Schukin
ELECTROMECHANICAL PROCESSES IN A LINEAR PULSE-INDUCTION ELECTROMECHANICAL CONVERTER WITH A MOVABLE INDUCTOR AND TWO ARMATURES
Purpose. The purpose of the paper is to determine the influence of the height of the mobile and stationary disk electrically conductive armatures covering the movable inductor on the electromechanical processes of linear pulsed-induction electromechanical converter (LPIEC). Methodology. With the help of the developed mathematical model that describes electromechanical and thermal processes of LPIEC, the influence of the heights of the armatures on electromechanical processes, the values of the electrodynamic forces acting on the inductor and armature, and the moving speed of the movable armature (MA) is established. Results. It is shown that if the height of the stationary armature (SA) is twice the height of the MA, then the inductor at the initial instant of time is acted upon by electrodynamics forces pressing it to the SA, and the displacement of the inductor begins with a delay of 0.35 ms. If the height of the MA is twice the height of the SA, then the electrodynamics forces act on the inductor at the initial instant of time, repelling it from the SA, and its movement begins with a delay of 0.1 ms. If the heights of the SA and the MA are equal, then until the time 0.15 ms on the inductor, the electrodynamics forces practically do not act and the inductor moving relative to the SA begins with a delay of 0.25 ms. Originality. The effect of the geometric parameters of the SA and MA on the velocity of the inductor moving relative to the SA, MA relative to the inductor and the MA relative to the SA is established. It has been established that the highest velocity of the MA relative to the SA develops the lowest MA, and the height of the SA does not affect it practically. However, with the increase in the height of the MA, the effect of SA begins to affect. In this case, it is expedient to select the height of the SA to be 0.4-0.42 of the height of the inductor. Practical value. It is shown that as the weight of the actuating element increases, the currents in the active elements of the LPIEC increase, the induction velocities of the inductor relative to the SA and the MA decrease relative to the inductor. At the same time, the maximum the electrodynamic forces values acting on the inductor decrease, and the armatures increase. Moreover, the maximum the electrodynamic forces acting on the MA are less than similar forces acting on the SA. References 12, figures 7.
Key words: linear pulse-induction electromechanical converter, mathematical model, mobile inductor, stationary armature, movable armature, electromechanical processes.
Разработана математическую модель, которая описывает электромеханические процессы в линейном импульсно-индукционном электромеханическом преобразователе с подвижным индуктором, взаимодействующим со стационарным якорем (СЯ) и подвижным якорем (ПЯ), ускоряющим исполнительный элемент. Установлено влияние высот якорей на электромеханические процессы в преобразователе. Если высота СЯ в два раза больше высоты ПЯ, то на индуктор в начальный момент времени действуют электродинамические усилия (ЭДУ), прижимающие его к СЯ и перемещение индуктора начинается с задержкой 0,35 мс. Если высота ПЯ в два раза больше высоты СЯ, то на индуктор в начальный момент времени действуют ЭДУ, отталкивающие его от СЯ, и его перемещение начинается с задержкой 0,1 мс. Если высоты СЯ и ПЯ равны, то до момента времени 0,15 мс на индуктор практически не действуют ЭДУ и перемещение индуктора начинается с задержкой 0,25 мс. Установлены комбинации геометрических параметров якорей, при которых действуют как наибольшие, так и наименьшие импульсы ЭДУ. Наибольшие скорости развивает наиболее низкий ПЯ, причем высота СЯ на них практически не влияет. С увеличением массы исполнительного элемента происходит увеличение токов в активных элементах преобразователя и уменьшение скоростей индуктора и ПЯ. При этом максимальные значения ЭДУ, действующих на индуктор, уменьшаются, а на якоря - увеличиваются. Библ. 12, рис. 7.
Ключевые слова: линейный импульсно-индукционный электромеханический преобразователь, математическая модель, подвижный индуктор, стационарный якорь, подвижный якоря, электромеханические процессы.
Introduction. Linear pulsed electromechanical converters are designed to provide high speed of the actuating element (AE) on a short active section, and/or to create shock force pulses [1-4]. Such converters are used in many branches of science and technology as electromechanical accelerators and shock-power devices [5-7]. The most widely used are linear pulse-induction electromechanical converters (LPIEC) of a coaxial configuration in which the accelerated electrically conductive armature interacts non-contact with a stationary inductor [1, 2, 8]. At excitation of a multi-turn inductor from capacitive energy storage (CES) in an electrically conductive armature made in the form of a copper disk, eddy currents are induced. As a result, the electrodynamic forces (EDF) of the repulsion act on the armature, causing its axial movement together with the AE relative to the inductor.
However, when operating in a dynamic mode with a rapid change in the electromagnetic, mechanical, and thermal parameters, the force and speed indicators of the LPIEC of traditional design are not high enough [9]. One of the ways to increase these indicators is the development of new design schemes of the LPIEC [10, 11]. Since in the traditional LPIEC design with an armature only one side of the inductor interacts inductively, a significant part of the magnetic field from the opposite side of the inductor is scattered into the surrounding space, negatively affecting closely located electronic and biological objects and is not used to create additional EDF.
Let us consider a constructive scheme of a LPIEC of a coaxial configuration, containing a movable inductor, enveloped on opposite sides by two electrically
© V.F. Bolyukh, A.I. Kocherga, I.S. Schukin
conductive armatures (Fig. 1). One of the armatures interacts with the fixed stop, and the second one interacts with an actuating element, for example, of a shock-power device.
When the inductor is excited through flexible or sliding contacts from the CES C, the EDF of repulsion occur between the inductor and the armature, which leads to the movement of the movable armature (MA) relative to the inductor, which in turn repels with respect to the stationary armature (SA). This raises the question of the effect of geometric parameters of armatures on electromechanical processes in LPIEC. Since the radial dimensions of the armatures, as a rule, correspond to the radial dimensions of the inductor, the question arises as to the effect of the axial dimensions of the electrically conductive armatures on the force and speed indicators of the LPIEC.
Fig. 1. Constructive scheme of the LPIEC: 1 - inductor; 2 - stationary armature; 3 - movable armature; 4 - actuating element; 5 - stop; 6 - case; 7 - damper spring
The goal of the paper is determination of the influence of the height of the mobile and stationary disk armatures covering the movable inductor on electromechanical processes in the LPIEC.
Mathematical model. Consider a mathematical model that describes electromechanical processes in LPIEC using lumped parameters of active elements -inductor, stationary and mobile armatures:
i1R1 (T1) + L1A +1 f udt + M12( z) ^ + M13 (z) ^ +
111 1 dt CJ 1 1 dt 13 dt
,. dM12 , N dM13 „ 1 \ + V12(tt)i2—ZL + V13(t)i3—11 = 0; - f id = Uo; (1)
dz
i2K2(T2) + L2 +M12 (z)-A + M23 (z)d3 + ii4i + ¿3^3 = 0 ;(2) dt dt dt
¿3^3(T3) + L3+Mi3(z^^L+M23(z)—2 + ii#2 + ¿243 = 0 ;(3)
di
di2
dt
dt
dt
¥3
dMi3 . . dM 12 / \dvi3 „ „ N
13 = 'l'l—T2 + ( + »2 + »ej— + KTVi3(t) ;(4) dz
dz
dt
dM
12 "
12
dz
dM23 / \dv17 ^ / , N\
¿2i3—T23 +(»2 + »e - T2 + KT '(v13(t ) + v12(t )— dz dt
+ 0.125*yaPcP2m [v12 (t) + V13(t)]2 + Kp [[t) + AzB(t)] ,(5) where & = V!2(0^ & = V13(t)^ P=1, 2, 3 are
dz dz
the indexes of the inductor, MA and SA;
43 =(v12(t ) + V13(t )-
dM
23 •
dz
Rp(Tp), Lp, ip are the resistance,
inductance and current of the p-th active element,
respectively; M12(z), M13(z), M23(z) are the mutual
inductances between corresponding p-th active elements;
v13(t), v12(t) are the speeds of the inductor relative SA and
MA along the z-axis, respectively; Az13(t), Az12(t) are the
displacements of the inductor relative SA and of the MA
relative inductor, respectively; m1, m2, me are the masses
of the inductor, MA and actuating element, respectively.
The coupled solution of equations (1) - (3) allows us
to reduce them to one differential equation:
4 3 2
d i d i d i dii a4 —j- + a3 —^- + a2 —± + ai —- + a0 = 0 , (6) 4 dt4 3 dt3 dt21 dt 0
where a4 = Lfa + M13d2 + M12d3;
a3 = R1b1 + Rqb2 + R3b3 + 2(d1 + e2d 2 + e3d3);
a2 = bylC + LxR2R3 -ej2)+ L2R1R3 -e22)+ L3RR -e32)+ + 2[m12(e1e2 -R3e3)+M13(e1e3 -R2e2) + M23(e2e3 -R1e1)];
a1 = R1R2R3 - e12 )+ e2 (e1e3 - R2e2 ) + e3 (e1e2 - R3e3 ) +
+ (R2L3 + R3L2 - 2M23ej)l C ;
ao = R2R3 - e2)lC ; b = L2L3 -m23 ; b2 = L1L3 -M123 ;
b3 = l1l2 - M12; d1 = M12M13 - LM23; d2 = M12M23 - L2M13; d3 = M13M23 - L3M12;
e1 =(v13 + v12 -dM 23 '
dM13 dM12
e2 = v13^—' e3 = v12-
dz dz dz
The characteristic equation of the differential equation (6)
4 3 2
a4 x + Ü3 x + Ü2 x + a^x + üq = 0 (7)
by means of a substitution m = x + 0.25ü3 / ü4 is transformed into the reduced form with a cubic resolvent:
3 2 2
w + q1 - m + q2 - w - ^3 = 0,
(8)
where q1 = 2 - 0.75
a4
( a Y
a3 V a4
q2 =3
q3 =
a3 2 - a4
a3
4 2 2 a3 - a2 a1 - a3 + a2
3 a4
- + -
2 a4
- 4
a4
2 - a4
0 5a2 -a3 + aL. a| a4
If the discriminant of the resolvent
D = (u/3)3 -(v/2)2, (9)
where u = q2 - qj2 /3 ; v = 2 • qj3 /27 - qj • q2 /3 - q2 , is less than zero, then, using the trigonometric solution of equation (8), we obtain:
Wp = 2 • 31
f 3 ^
I u
27
2x(p -1-
arccosl - 0
27/ af
.(10)
In this case, the roots of equation (7): xi = 0.5 -(+.^1 )-0 25 • a3 la4, (11)
where l = 1, 2, 3, 4.
If all the roots of (11) are real, then for the currents in the p-th active elements of the LPIEC we can write:
lP =
Uci
a4&
(12)
3
0.5
cos
3
3
where
i = Ap1 exp(X1t) + Ap2 exp(X2t) + Ap3 exp(x3t) + Ap4 exp(x^f)
$ = 721743 (21 + £43 ) + 724731 (24 + £31) + 732741 (32 + ^41), Ap1 = 732(«4 pS32)+^24(«3 pS24)+^43(«2 pS43); Ap2 = 713 («2 -® p£13 )+r41(«3 -® pS41 )+^34 («1 -® pS34 ); Ap3 =721(«4 -®pS21 )+742(«1 -®p£42)+714 («2 -®p£14); Ap4 = 712 («3 -®pS12)+731(«2 -®p£31 )+723 («1 -®p£23);
n = 2, 3; m = 5 - n ;
7ki = xk- xi; = (Apxk- Sp )xt; 8ki = x2x?; ®1 = -b1; ®n = -dm; A1 = Ci / «4; An =G /a4;
Sj =[a4 !C+ e2d2 + e3d3 )-C2 (R2d 3 +e3b1 + e1d2 )--C3 ((3d 2 + e2b1 + e1d3 )]/a4;
Sn = [a4 b1dmlC - C1 ((dm + embn + end1 )- Cn ((nbn + emdm + e1d1 )" ~Cm ((md1 + endm + e1bn
C1 = R\b\ + R2d2 + R-3d2 + 2[b1(e2d2 + e3d3 ) + e^2d3]; Cn = dm (( + Rnbn) + Rmd1dn + em (b1b
n + dm ) (en b1 + e1dm )x
1 nm - LnM1
m (ndm + e1bn ^ m M1n (e1d1 + endn )
If the discriminant of the resolvent (9) is greater than zero, then, using Cardano solution for equation (8), we obtain one real and two complex conjugate roots:
=^ + C- ft/3; ^2,3 =s± jX, (13) where <p = 3- 0.5 • v + 45 ; C=3- 0.5 • v -Jd ;
e = -0.5•( + C)-91/3; * = 0.5•V3(-C).
In this case, the roots of equation (7) have the form:
x12 = 0.5 - 0.25 • a3 /a4 0.5 ^s + ijs2 + %2 jj ;
(14)
where
x3,4 = c± c = 0.5 ■■Jmî - 0,25 • «3 / «4 ;
If x1 and x2 are real and different, the currents in the p-th active elements can be represented as:
a4K
where
(15)
K = ^1^2(3c2 - 2cXl - #2 + X1X2)+ /2(z2 + Z3 - 2cX\) ; X = -B^i exp(xii) + Bp2 exp(^2Î) + exp(c • t)[-Bp3 cos(#i) + Bp4 sin(#t)J;
Bpi = p [x22 (3c2-#2 - 2x2c)-^ J+A p [2^2-X2 (3c2-#2 - x| )J-
-s p (-X2 )2 +#2 (/(X2-#);
Bp2 = fcp[z22 +c2(#2 -3c2 + 2xic)J+Ap[xi(3c2 -#2)-2cZ2J+ + sp (2 -2x1c)}/(x2 -f);
Bp3 = © p [(#2 - 3c2 )Zi + 2cZ3 J+ A p [(3c2 - #2 )- Z3 J+ + s p (1 - 2c);
Bp4 = ©p 1^32 -c2)+ zc(c2 - 3#2)+ x2x2]+ Ap(Z3c --X1X2Z1 + 3c#2 -c3)+sp{c2 -#2 + X1X2 -c#1 )}/# ;
%1 = x1 + x2; /2 = c2 +#2; 23 = X12 + X1X2 + x|.
The displacements of the inductor relative to the SA, as well as the MA relative to the inductor on the basis of equations (4) and (5) can be represented in the form of recurrence relations:
Az13(tk+1) =
dM 13
i 1(tk )\i3(tk )—TL - h(tk )
dM
12
dz
dz
- KTv13(tk )
X 0.5-
At2
m1 + m2 + me
- + Az13(tk ) + V13(tk )At, (16)
Az12(tk+1) = Azu(tk ) + V12 (tk )At +
At2
2(m2 + P)
i1(tk )"
dM,
12
dM
-i3(tk)—TL \h(tk) - KT(tk)+V13(tk))-
(17)
dz dz
- 0,125 ■ ^ ■ PaTa^D^m [k) + V13 (tk)J 2 -
-KP(Az12(tk) + Az13(tk)) ■
The temperature of the p-th active element at moving the armature and inductor, when there is no thermal contact between them, can be described by the recurrence relation [10]:
Tp (tk+1) = Tp (tk )x + (1 - 4?0 + 4^"2'p (tk)Rp (Tn )«7p x
X D-pH~p[plp - Dip )-1 J ,
(18)
are
where ^ = exp{- 0.25AtDepa Tpcp (Tp)7pl); Dep, D
the outer and inner diameters of the p-th active element, respectively; aTp is the heat transfer coefficient of the p-th active element; cp is the heat capacity of the p-th active element.
The initial conditions of the system of equations (1) - (18): Tp(0)=T0 is the temperature of the p-th active element; ip(0)=0 is the current of the p-th active element; Az(0)= 1 mm is the initial axial distance between the armatures and the inductor; wc(0)=^0 is the voltage of the CES; vz(0)=0 is the armature speed along the z-axis.
In order to take into account the complex of interconnected electric, magnetic, thermal and mechanical processes and various nonlinear dependencies, the transient process is divided into a large number of time intervals At = tk+1 - tk within which all quantities are assumed to be unchanged. With such a numerical-analytical approach within a small interval At the previously defined analytical expressions are used to calculate the basic quantities, and the transient process is calculated using iterative relationships using computer.
LPIEC main parameters. Let us consider LPIEC of a coaxial configuration, in which both armatures are made in the form of a flat disc of technical copper, one of whose sides faces the inductor.
Inductor: outer diameter Dex1=100 mm, inner diameter Din1=10 mm, height H1 = 10 mm, copper bus section axb=1.8*4.8 mm2, bus number of turns N1= 46. The inductor is made in the form of a double-layer winding with external electrical terminals.
Armatures: outer diameter Dex2,3 = 100 mm, inner diameter Din2,3 = 10 mm, height H2 = H3 = 3 - 7 mm.
X
CES: capacitance C = 500 pF, voltage ^0=1.5 kV.
Actuating element has mass me = 1 kg.
LPIEC electromechanical characteristics. We consider the influence of the height of armatures on electromechanical processes of the LPIEC. The height of the MA will be estimated by a dimensionless geometric * —1
parameter h2 = H 2 H1 , and the height of the SA by a
* —1 parameter h3 = H3H1 .
Let us consider the electromechanical characteristics of the LPIEC having various combinations of the heights of the SA and the MA.
Fig. 2 shows the electromechanical characteristics of the LPIEC, in which the height of the SA is twice the height of the MA (armatures parameters h2*=0.3, h3*=0.6).
The current in the inductor with density j1 has a vibrationally damped character. The maximum inductor current density is A/mm2. At the initial moment of the operation process the current densities in the MA j2 and in the SA j3 have a polarity opposite to the inductor. The maximum current density in the MA is 554.6 A/mm2, and in the SA 303 A/mm2. Due to the interaction of currents, on the MA, electrodynamic forces of repulsion f2 act with maximum value of 13.6 kN.
j, A/mm2; fz, kN; v, m/s
SQQ
600
400
200
G
-200
-400
-600
sof„ 200 Vj2
f
S / 200 V13 s \
jy À V\
U J/
\ h h
V. fh
Fig. 3 shows the electromechanical characteristics of the LPIEC, in which the height of the MA is twice the height of the SA (armatures parameters h2*=0.6, h3*=0.3).
In this LPIEC, as in the considered above, the character of the current flow is preserved. The maximum current density in the inductor j1 slightly increases to 450.1 A/mm2. The maximum current density j2 in the MA decreases to 294.3 A/mm2, and in SA j3 the current density rises to 573 A/mm2. As a result, the maximum EDF of repulsion acting on f2 decreases to 12.7 kN. As a result, the maximum speed of moving the MA relative to the inductor v12 decreases to 2.95 m/s.
However, in this LPIEC, positive EDF f 1 act on the inductor at the initial instant of time, repelling it from the SA and its movement begins in about 0.1 ms. The maximum value of these forces is observed in the second peak of repulsion, reaching 2.18 kN. As a result, the inductor moves relative to the SA with a velocity v13, the maximum value of which reaches 0.63 m/s. The maximum speed of the MA relative to the SA v23 is 3.58 m/s. The decrease in the speed of the MA can be explained by its increased mass.
j, A/mm2; f, kN; v, m/s
800 600 400 200
o-
-200
-400
-600
50
200 *13
/ 200 vn \ \
\ V
JiS j h
fh
0 0.25 0.5 0.75 1.0 t, ms
Fig. 2. Electromechanical characteristics of the LPIEC with armatures geometrical parameters h2 =0.3, h3 =0.6
In the interval 0.5-0.65 ms EDF change direction, after which a repetition of repulsive forces, but much less than in the original one, takes place. As a result, the MA moves relative to the inductor at a speed v12 the maximum value of which is 3.65 m/s.
On the inductor at the initial instant of time, negative EDFs fz1 act, pressing it to the SA. However, after 0.25 ms, these EDFs, changing the direction, repel the inductor from the SA with a maximum value of 3.9 kN. As a result, the inductor moves relative to the SA with a speed v13 the maximum value of which is 0.4 m/s. And the displacement of the inductor begins with a delay of 0.35 ms. The value of the maximum speed of the MA relative to the SA is 4.05 m/s.
0 0.25 0.5 0.75 i 1.0 t, ms
Fig. 3. Electromechanical characteristics of the LPIEC with armatures geometrical parameters h2 =0.6, h3 =0.3
Let us consider the LPIEC variant, in which the heights of the SA and the MA are equal. Fig. 4 presents the electromechanical characteristics of the LPIEC with parameters h2*=0.4, h3*=0.4.
In this LPIEC the maximum current density in the inductor ji is 442.8 A/mm2. The currents in the armatures, especially in the initial part of the process, where there is no movement of the active elements, are practically the same. The maximum current density j2 in the MA is 420.3 A/mm2, and in the SA j3 it is 434.8 A/mm2. The maximum EDF of repulsion acting on f2 is 12.8 kN, which results in the displacement of the MA relative to the inductor at a speed of v12, the maximum value of which is 3.28 m/s.
j, A/mm2; fz, kN; v, m/s
800
■200
-400
■600
Fig. 4. Electromechanical characteristics of the LPIEC with armatures geometrical parameters h2 =0.4, h3 =0.4
In this LPIEC, the EDF fz1 is practically not effective on the inductor until the time 0.15 ms. As a result, the displacement of the inductor relative to the SA begins almost in 0.25 ms. The maximum value of these forces is observed in the second peak of repulsion and is only 1.85 kN. As a result, the inductor moves relative to the SA with a speed v13, the maximum value of which is 0.56 m/s. The maximum speed of the MA relative to the SA V23 is 3.84 m/s.
LPIEC force and speed indicators. Let us consider influence of the geometrical parameters of the SA
h2 e [0.3; 0.7] and the MA h3* e [0.3; 0.7] on the value of the EDF impulse Fzp = j fzpdt, where p = 1, 2, 3 are the
indexes of the inductor, MA and SA.
The values of the EDF impulses acting on the inductor Fz1 are much smaller than the values of the impulses acting on the MA Fz2 and SA Fz3. The maximum values of the EDF impulse Fz1, acting on the inductor,
arise at geometrical parameters of armatures h3 =0.4 and h2 =0.7 (Fig. 5). The minimum values of Fz1 arise when h3*=0.7 and h2*=0.4. The largest value of the EDF impulse Fz1 at any height of the MA is realized for a SA with a parameter h3*=0.4.
The smallest values of the EDF impulse Fz2 acting on the MA, on the contrary, arise for h3 =0.4 (the minimum value takes place for a high MA h2*=0.7.). The greatest values of the EDF impulse Fz2 occur at h2*=0.42-0.45 (the maximum value takes place at a high SA h3*=0.7).
The largest values of the EDF impulse Fz3, acting on the SA, arise for h3*=0.4 (the maximum value occurs for h2*=0.7). And the largest values of the EDF impulse Fz3 take place when h2*=0.4 (the minimum value occurs for h3*=0.7).
Let us consider the influence of the geometric parameters of the SA h* e [0.3; 0.7] and MA
h* e [0.3; 0.7] on the speed of the inductor and the MA, realized at the end of the operating process (Fig. 6).
The maximum value of the speed of the MA relative to the inductor V12 is realized with its minimum height h2 =0.3 and the maximum height of the SA h3 =0.7, and the minimum value of the speed of the MA relative to the inductor V12 is realized at its maximum height h2*=0.7 and the minimum height of the SA h3*=0.3.
In turn, the highest values of the speeds of the displacement of the inductor relative to the SA V13 occur at a relatively low SA h3*=0.4 (the maximum speed occurs at a high MA h2*=0.7). The lowest values of the speeds V13 are realized at h2*=0.45 (the minimum speed V13 occurs for high SA h3*=0.7).
Of greatest interest is the speed of the displacement of the MA relative to the SA V23. As the calculations show, the highest speeds V23 the lowest MA h2*=0.3 develops, and the height of the SA does not affect it practically. However, with the increase in the height of the MA, the influence of the SA begins to affect. In this case, it is expedient to select the height of the SA with geometric parameters h3*= 0.4-0.42.
Fzi, N-s
Fz2, N-s
Fz3, N-s
0.7 ■ \p.u
0.6
0.5
0.4
0.3
1,4 / / / /
1,2 / / //
1,0/ / f
1 I \ \
■ p.u
0.3 0.4 0.5 .-. ;,p.u 0.7
0.3 0.4 0.5 .-. \ p.u 0.7
0.3, 0.4 0.5 p.u 0.7
a b c
Fig. 5. Dependence of the EDF impulses acting on the inductor (a), MA (b) and SA (c) on the
geometrical parameters h2 and h3
p.u
0.7 Pu 0.6
0.5
0.4
0.3 0.4 0.5 ,',p.u 0.7
0.3 0.4 0.5 p.u 0.7 b
0.3
0.3 0.4 0.5 p.u 0.7
Fig. 6. Dependence of the speeds of the MA relative to the inductor (a), of the inductor relative to the SA (b) and the MA relative to the SA (c) on the geometrical parameters h2 and h3
Effect of the mass of the actuating element on the LPIEC indicators. In order to more fully understand the electromechanical processes in the LPIEC, let us consider the effect of the mass of the actuating element me on its electromechanical indicators. Fig. 7 shows the dependencies of the indicators of the LPIEC having geometrical parameters of armatures h2*=0.5, h3*=0.5, on the mass of the actuating element. With an increase in the mass me, there is a significant decrease in the speed of displacement of the inductor relative to the SA V13, which practically decreases to zero even at a mass me=3 kg. The speed of the MA relative to the inductor V12 with an increase in the mass of the actuating element from 0 to 5 kg decreases from 9.83 m/s to 0.9 m/s.
15
12
0
j, A/mm2; f, kN; V, m/s
fzlm/5 0 -ft—-f-
A m
\
\Hm h\mi.50 Jn
\- —-i-g-^
1 2 3 me, kg 5
Fig. 7. Dependencies of the indicators of the LPIEC with parameters h2 =0.5, h3 =0.5 on the mass of the actuating element
Dependencies of the maximum EDF values acting on the active elements of the LPIEC, on the mass of the actuating element, have the following features. With increasing mass me, the maximum EDF values acting on the inductor fz1m decrease and on the armatures increase. Moreover, the maximum EDFs acting on the MA fz2m are smaller than the analogous forces acting on the SA f3m. However, as the mass of the actuating element increases, these forces tend to equalize. Obviously, with a fully retarded MA, these EDFs will be equal.
With an increase in mass me, there is an increase in currents both in the inductor and in the armatures, especially strongly in the interval 0 ... 1 kg. This can be explained by a stronger induction interaction of the inductor with armatures, which are in a strong magnetic coupling.
Conclusions.
1. A mathematical model is developed that describes the electromechanical processes of LPIEC with a movable inductor interacting with stationary and mobile electrically conductive armatures.
2. The effect of armatures heights on electromechanical processes of LPIEC was established. It is shown that at the initial moment of the operating process, the currents in the armatures have a polarity opposite to the inductor current.
3. It is shown that if the height of the SA is two times more than the height of the MA, then the EDF acts on the inductor at the initial instant of time, pressing it to the SA, and the displacement of the inductor begins with a delay of 0.35 ms. If the height of the MA is twice the height of the SA, then the EDFs act on the inductor at the initial instant of time, repelling it from the SA, and its movement begins with a delay of 0.1 ms. If the heights of the SA and the MA are equal, then until the time 0.15 ms the EDFs practically does not act on the inductor and the inductor moving relative to the SA begins with a delay of 0.25 ms.
4. The influence of the heights of the disk armatures on the values of the EDF impulses acting on the inductor and the armatures is established. The values of the EDF impulses acting on the inductor are much smaller than the EDF impulses acting on the armatures. Combinations of armatures heights are established, in which both the largest and the smallest impulses of the EDF act on them and on the inductor.
5. The effect of the geometric parameters of the SA and the MA on the speeds of the inductor and the MA is established. The highest speeds are developed by the lowest MA, and the height of the SA practically has no effect on them. However, with the increase in the height of the MA, the influence of the SA begins to affect. In this case, it is expedient to choose the height of the SA with a geometric parameter h3 =0.4-0.42.
6. It is shown that with an increase in the mass of the actuating element, the currents in the active elements of
a
the LPIEC increase and the speeds of the inductor and the MA decrease. In this case, the maximum values of the EDFs acting on the inductor reduce, and on the armatures increase. The maximum EDFs acting on the MA are less than similar forces acting on the SA.
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. 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.
3. Tomashevsky D.N., Koshkin A.N. Modeling of linear impulse electric motors. Russian Electrical Engineering, 2006, no.1, pp. 24-27. (Rus).
4. 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).
5. Young-woo Jeong, Seok-won Lee, Young-geun Kim, Hyun-wook Lee. High-speed AC circuit breaker and high-speed OCD. 22nd International Conference and Exhibition on Electricity Distribution (CIRED 2013), 2013, 10-13 June, Stockholm, Paper 608. doi: 10.1049/cp.2013.0834.
6. Ivanov V.V., Paranin S.N., Nozdrin A.A. Semiautomatic installation of magnetic pulse compaction of powders. Materialovedenie, 2011, no.7, pp. 42-45. (Rus).
7. Ivashin V.V., Penchev V.P. Features of the dynamics of work and energy diagrams of pulsed electromagnetic drive with parallel and series connection of excitation windings. Electrical engineering, 2013, no.6, pp. 42-46. (Rus).
8. Bolyukh V.F., Luchuk V.F., Rassokha M.A., Shchukin I.S. High-efficiency impact electromechanical converter. Russian electrical engineering, 2011, vol.82, no.2, pp. 104-110. doi: 10.3103/s1068371211020027.
9. Bolyukh V.F., Shchukin I.S. Lineinye induktsionno-dinamicheskie preobrazovateli [Linear induction-dynamic converters]. Saarbrucken, Germany, LAP Lambert Academic Publ., 2014. 496 p. (Rus).
10. Bissal 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.
11. Schneider Electric Industries SAS. Electric switching device with ultra-fast actuating mechanism and hybrid switch comprising one such device. Patent USA, no.8686814, 2014.
12. Bolyukh V.F., Shchukin I.S. The thermal state of an electromechanical induction converter with impact action in the cyclic operation mode. Russian electrical engineering, 2012, vol.83, no.10, pp. 571-576. doi: 10.3103/s1068371212100045.
Received 05.01.2018
V.F. Bolyukh1, Doctor of Technical Science, Professor,
A.I. Kocherga1, 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: [email protected]
2 Firm Tetra, LTD,
2, Kyrpychova Str., Kharkiv, 61002, Ukraine,
phone +380 57 7076427,
e-mail: [email protected]
How to cite this article:
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.2, pp. 11-17. doi: 10.20998/2074-272X.2018.2.02.
