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RESEARCH OF ELECTROMECHANICAL DEVICES WITH LEVITATION ELEMENTS IN CONTROL
SYSTEMS
G.S.Kerimzade1, G.V.Mamedova2
Azerbaijan State Oil and Industry University, Baku, Azerbaijan 1 gulschen98@mail.ru ; 2 gulaya68@mail.ru
Abstract
The work examines the main technical indicators of electromechanical converters callers with levitation elements, a generalized design method has been developed tions, as well as design diagrams and functional dependencies of the main varieties of electromechanical devices with elements of levitation. Analytical expressions for the levitation coefficient as a function of the dimensions of the magnetic core and coefficient factor of force multiplicity, technical characteristics of levitation material element, set superheat temperature. A mathematical model has been compiled for based on the parameters of the current mode and forces from the equations of electrical, magnetic, mechanical and thermal circuits of the magnetic system. As a result, the main dimensions of the magnetic system and dimensionless quantities. Analytic expressions for the main dimensions, the specified values of the winding overheating temperature are taken into account, input and output parameters, the condition of uniformity of the magnetic field in the working air nom gap. The optimal values of the dimensions of the magnetic circuit, active resistors have been determined winding voltages are minimal, resulting in minimization of losses active capacities.
Key words: levitation element, electromechanical apparatus, research, method, magnetic system, mathematical model, current mode, force mode, stability, mechanism.
I. Introduction
The widespread use of electromechanical devices with levitation elements in automatic control systems ensures high reliability, accuracy, and stability during control and regulation of parameters and the technological process as a whole.
The designs of electromechanical devices with a levitation screen are more effectively involved in solving these problems, since in these devices there are no friction forces, the working stroke of the moving part is automatically controlled and additional elements are not required (for example, mechanical springs, guides, gearboxes, supports, etc.) [5-18].
Automation of technological processes requires automatic control of the vertical positions of the moving parts of working mechanisms using external force and alternating current voltage. In this case, there is a need to measure external force, stabilize the current on a variable load and obtain several nominal values of the current on the load. The design of a simple electromechanical device with a levitation element consists of a vertically located magnetic circuit 1, a stationary alternating current winding 2 and a levitation element 3 (fiqure 1). In the force mode, the levitation element is made in the form of a solid aluminum frame, and in the current mode - in the form of a short-circuited winding. When the device is turned on to the power source, the levitation element may
strike the upper yoke of the magnetic circuit.
Figure 1. Design of a simple electromechanical device with LE
A magnetic system with a levitation element (straight and stepped forms) is shown in figure 2. To eliminate this undesirable phenomenon, a compensation winding 4 is placed near the yoke, which is connected in series with the power winding 1; a signal winding 5 is also provided. During operation of the device with the levitation element, the compensation winding is turned off. The AC winding (or excitation winding) is powered by an AC voltage source Ui and is made of several sections, by switching which a family of control characteristics is achieved [1-4, 9].
Figure 2. Magnetic system with levitation element (straight (a) and step b))
II. Formulation of the problem
When the excitation winding (EW) is connected to the power source, currents flow through the EW and the levitation element (LE), which significantly exceed the rated currents. As a result, losses in the LE sharply increase and all the energy released in it goes to heating it. Depending on its size, the temperature can reach a high value and, before reaching the steady-state value, the LE can melt. Therefore, the minimum dimensions of the LE must be limited.
In accordance with the insulation class, the permissible values of the LE overheating temperature are set. To reduce it, it is necessary to reduce the lateral heat transfer surface of the LE, which in turn is associated with an increase in the aspect ratio ne2=h2/c2 under the condition So2=c2.h2=const and this can lead to an increase in the height of the magnetic system and a deterioration in the lateral stability of the LE. To determine the optimal relationship between the main dimensions of the LE c2 and h2, the dependence of the dimensionless quantity ne2 on the geometric dimensions of the magnetic circuit (a, b, c), the force multiplicity factor np, the physical and technical characteristics of the LE material and the given overheating temperature X2 is determined.
III. Problem solution
Based on the established dependencies of dimensions and parameters, a mathematical model is compiled for certain parameters of current and force modes:
,2 i . \
P
T2 =
2
= F
2 b2 P2
ky Sy ^
i
i
2
VS2ST2 J
F12 = 2 (Px + PT )=
%
^ x T> ~'-32'> 2 Here generally accepted designations. Force multiplicity factor:
P
n„ = 1 + -
P
(1) (2)
(3)
As is known, for LE made of copper and aluminum:
(S ) = 2c n k 2 2 2 e2 u
Accordingly we have:
(4)
VS2ST2 J
2n<?2c2 (1 - ne2>
By jointly solving equations (1)-(2) for LE made of copper and aluminum, we have:
where are the coefficients:
n ~ = E M n e2 m m p
n ~ = E M n -1 e2 aap
E = 2.2585 • 10
m
10
' P,
VT2 J
VT2 J
1.72 • 10
- 8
-(1.063 + 0.0042r ) 2
(5)
(6)
(7)
(8) (9)
/
1
2
m
m
T
2
m
M =-m
m + m + 0.5m m a c a c
(0.909m + m + m + mm ) m m + 2.92m \ a a c a c A a c a
1 +
n
m
a J
(10)
E = 0.3432 • 10
a
10
A,
VT2 J
A
VT2 J
2.8 • 10
- 8
T„
-(1.063 + 0.0042t ) 2
(11)
(12)
Expressions (6)-(12) when implemented using the appropriate calculation program make it possible to compile tables 1-3, which show the parameter values for LE made of copper and aluminum. Figure 3 respectively show the graphical dependences of the coefficient ne2 =f(x2) on the current at the stroke values [7-16].
Table 1. Values of coefficients Mm, Ma
a
a
mc ma
2 3 4 5 6 Mm, Ma
2 0.573464 0.53438 0.518343 0.510589 0.506504 Mm
0.938378 0.916929 0.914149 0.91672 0.920897 Ma
3 0.594826 0.530443 0.49976 0.482146 0.470856 Mm
0.953061 0.89554 0.870198 0.85682 0.848954 Ma
4 0.608226 0.528249 0.489108 0.466072 0.450967 Mm
0.962093 0.882866 0.844812 0.822862 0.808747 Ma
5 0.617415 0.526858 0.482207 0.455742 0.43828 Mm
0.96821 0.874482 0.828279 0.800992 0.783072 Ma
6 0.624107 0.525901 0.477373 0.448546 0.429485 Mm
0.972627 0.868526 0.816656 0.785732 0.765256 Ma
Table 2. Values of levitation element parameters depending on overheating temperature
Parameter p 20,Om • m T 2,0C
80 90 100 110
p 20 • 10-8Om-m 1.72-10-8 2.420 2.494 2.567 2.642
p 20/r 2 • 10-12 302.50 277.10 256.70 240.18
Em 6.8323 6.2584 5.7977 5.4246
p 20 • 10-8Om-m 2.87-10-8 4.015 4.135 4.256 4.376
p 20/r 2 • 10-12 501.890 459.510 425.620 397.880
Em 1.7226 1.5771 1.4608 1.3652
Table 3. ne2 values for a levitation element made of copper and aluminum at T2 = 800C and np=1
mc Material ma
2 3 4 5 6
2 Al 3.918 3.651 3.541 3.488 3.460
Cu 0.615 0.578 0.574 0.570 0.585
3 Al 4.064 3.624 3.414 3.294 3.217
Cu 0.641 0.542 0.498 0.475 0.462
4 Al 4.155 3.609 3.341 3.184 3.081
Cu 0.656 0.520 0.454 0.417 0.393
5 Al 4.218 3.599 3.294 3.114 2.994
Cu 0.667 0.505 0.426 0.379 0.348
6 Al 4.264 3.593 3.261 3.065 2.934
Cu 0.675 0.495 0.406 0.353 0.318
18 16
Figure 3. Coefficient dependency na =f(n)
The patterns of changes in the values of the coefficients Mm, Ma from the dimensionless quantities ma, mc show that the smallest values of the coefficients Mm, Ma occur at ma = 6, mc =6, and the largest values correspond to the values ma=2, mc=6. At ma=6, mc=6, the values of specific magnetic conductivity X and cross-sectional area of the magnetic core rod Sc are minimal. At ma=2, mc=6, the values of these parameters, on the contrary, are maximum. Therefore, the overall dimensions in the first option are smaller than in the second. With increasing coefficients Mm, Ma and load capacity, the value of the coefficient ne2 increases, which leads to an increase in the overall size of the magnetic system. An increase in the overheating temperature leads to a decrease in the coefficients Em, Ea, as a result, the overall size and dimensionless value ne2 decrease [6-14,18]. The given values of the coefficient ne2 in Table 3 allow you to pre-select the minimum values of the coefficient and the corresponding values of ma, mc. Next, the main dimensions of the magnetic system, other dimensions and parameters are determined, the minimum values of the coefficients, temperature, etc. are taken into account. in order to ensure the reliability of control of electromechanical devices in general.
IV. Conclusions
The obtained values take into account the minimum values of the coefficients nei and ne2, the specified values of the overheating temperature t and t2, the working stroke xp, the condition of uniformity of the magnetic field, the load current Ii, ma =2 4- 6 ; mc =2 4 6. Electromechanical devices with levitation elements are low-current electrical devices, have simple designs, high accuracy, and stable performance characteristics. The active resistance of the excitation windings and the levitation element is minimal; as a result, losses of active power will also be reduced to a minimum.
Analytical expressions for the main parameters necessary for the design of electromechanical devices with levitation elements for various purposes are obtained. The calculation of electromechanical devices with levitation elements is significantly simplified by determining the optimal values for the height and thickness of the excitation winding and the levitation element.
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