CALCULATION METHOD AND METHODS FOR INCREASING THE RANGE OF THE INDUCTION CONTROL SUPPORT

ABSTRACT

The purpose of the presented article is to increase the range of forces of the induction control support. The scientific novelty of the work lies in the development of calculation methods, as well as methods for expanding the range of forces of the induction support. The main tasks include ways to increase the range of forces, development of a structural diagram of the control support, determination of the optimal dimensions of the induction support, and the influence of overheating temperature on the main parameters of the support. The theoretical and practical significance of the work lies in the development of new induction control supports, the possibility of their use in the automation of technological processes for ways to increase the range of forces. The results obtained make it possible to ensure control of the vertical position working mechanism and the use of automatic control of the technological process as a whole.

АННОТАЦИЯ

Цель представленной статьи – увеличение диапазона сил индукционной опоры управления. Научная новизна работы заключается в разработке методов расчета, а также методов расширения диапазона сил индукционной опоры. К основным задачам относятся пути увеличения диапазона усилий, разработка структурной схемы опоры управления, определение оптимальных размеров индукционной опоры, влияние температуры перегрева на основные параметры опоры. Теоретическая и практическая значимость работы заключается в разработке новых индукционных опор управления, возможности их использования при автоматизации технологических процессов для путей увеличения диапазона усилий. Полученные результаты позволяют обеспечить управление рабочим механизмом вертикального положения и использовать автоматическое управление технологическим процессом в целом.

Keywords: methodology, calculation, induction support, range, force, control, method, dimensions, coefficient, working mechanism.

Ключевые слова: методология, расчет, индукционная опора, диапазон, сила, управление, метод, размеры, коэффициент, рабочий механизм.

INTRODUCTION

Increasing the range of electromagnetic force created by the induction control support is currently a scientific and technical problem. In the automation of various technologies. In such processes, induction control supports are widely used in measuring the created mechanical forces, movement, and also the mass of working mechanisms [8-13]. They are also used to automatically control movement and maintain a certain vertical position. The induction control support includes a force converter, an excitation winding, a levitation element, and a load winding. By the influence of the external force of the force converter on the levitation element, which then falls down, the levitation height h decreases. The levitation height h is the distance between the excitation winding and the levitation element. Therefore, with a decrease in the height of levitation, the force P_e acting on the levitation element reduces the inductive resistance of the field winding x₁=wL₁ and at the same time the current I₁ flowing through the field winding increases. The presence of mutual magnetic coupling between the field and load windings contributes to an increase in the control current  I_control  flowing  through Z_control. According to the levitation condition [1-6]:

 ,

here P_T and F_e are the gravity of the levitation element and the electromagnetic force acting on the levitation element.

ALGORITHM FOR SOLVING THE PROBLEM

The load winding is located in the lower part of the field winding, therefore the currents flowing through these windings are determined from the mutual magnetic coupling of these windings [7-13]:  

;

Electromagnetic force acting on levitation element:

Inductive reactance of the excitation winding:

Here x_p - working stroke, h₁₂ – equivalent height determined by the height of the excitation winding and levitation element:

In this case, the current values are determined as:

​  

Here k_u » 0.96 ¸ 0.98; b₂ »0.97¸0.98.

According to expressions for the electromagnetic force, we can write:

From the obtained mathematical expressions, you can determine ways to increase the effort values [7-13]:

1.increase the voltage at the terminals of the field winding U₁;

2.reduce frequency w;

3.reduce stroke x_p;

4.reduce equivalent height  h₁₂;

5.reduce the number of turns W₁;

6.reduce the specific magnetic conductivity l of the working air gap.

As a result of the analysis of the electromagnetic dependences of effort from various parameters can be noted regulation of voltage, frequency. When the source voltage U₁ changes in a given range DU₁=U_min¸U_max, the magnetic induction in the steel core changes in the interval  DB_M=B_min ¸B_max, that is:

The cross-sectional area of the steel core S_c=2ab, frequency w and number of turns W₁ are constant parameters. The range of changes in magnetic induction DB_M must correspond to a straight line in part of the machining curve B_M(H), otherwise the core is saturated and the principle of proportionality of the magnetic induction of the working air gap is violated. In this case, the specific magnetic conductivity l takes on different values along the core and levitation stability is disruptedth element. Typically, the saturation induction values are (1.8¸1.9)Tl., in this case DB_M=(1.2¸1.9)Tl. Therefore, to increase the range of forces, it is necessary to take into account this condition [1-5]. When the frequency w changes in a certain range Dw=w₁¸w₂ for given values of voltage U₁, the number of turns W₁, the cross-sectional area of the core S_c, the magnetic induction B_M changes:

  .

Changing the frequency is advisable in the range Dw=(90¸100)Hs. Thus, according to the restrictions on magnetic induction, the frequency is regulated within a very small range of changes [8-11].Based on the above, to increase the range, the electromagnet greater effort, it is necessary to increase the number of turns W₁ and the working stroke of the х_р. The calculation results are shown in Table 1. The optimal dimensions of the controlled induction support are determined by the overheating temperature of the windings (excitation and levitation), as well as magnetic losses in the steel core_. The dependence of the gain on the permissible overheating temperatures [10-12] is also observed. As a result of the analysis of methods for increasing the range of electromagnetic force, it was found that by regulating the network voltage, the range of force can be expanded within a wide range. 

Table 1.

Dependency values  F(X;Y)

Along with the above, we also determine the optimal size values and calculate the influence of the heating process on the main parameters. The values of dimensionless coefficients are given in the Table 2.

Table 2.

Values of dimensionless coefficients

The overall dimensions of the control support depend on these ratios. To take into account the restrictions imposed on overall dimensions, it is necessary to take into account the range of changes in the coefficients. Losses also depend on the coefficients. Therefore, to minimize losses, it is necessary to solve the problems of determining the ratio of overall dimensions, the range of changes in magnetic conductivity and dimensions, the dependence of losses on dimensions, the dependence of copper losses in windings on winding dimensions and temperature rises [8-13]. In these relationships, both active and reactive magnetic resistances of copper sections are taken into account. The formulation of the problem taking into account the minimization of losses is associated with difficulties in determining mathematical expressions for losses. In this case, it is necessary to take into account the relationships between the parameters of the windings, magnetic circuit and temperature. As can be seen from expressions, to reduce the overall dimensions A, B, H, it is necessary to reduce the working air gap c and the coefficient m_c. As the coefficient n_c increases, the overall dimensions A and B increase. With the coefficient m_a increasing, the overall dimensions A and H decrease. Therefore, to eliminate the excess height of the levitator, it is necessary to increase the coefficient n_c and reduce the levitation constant n_e2 [1,6-14]. The main functional dependencies of electromagnetic parameters (current, electromagnetic force, stroke, levitation coordinates on voltage, displacement ) are presented in figure 1.

Figure 1. Functional dependencies of electromagnetic parameters

CONCLUSION

A developed method for calculating a magnetic system in order to determine magnetic losses in a steel core at optimal values of the control support with the overheating temperature of the excitation windings and the levitation element. The developed block diagram of an induction support describes ways to increase the range of forces and establishes that by regulating the network voltage it is possible to increase the range of forces within a wide range. The dependences of the power factor K_p on the permissible overheating temperature have been established. When solving these problems, it is necessary to take into account the dimensional ratios, the thickness of the levitation element, the magnetization characteristics, temperature rises, thermal conductivity, impact force, etc. Determining the overall dimensions of the control support establishes that  [1-7, 10-16] to reduce them it is necessary to reduce the dimensionless coefficient m_c=b/c, working air gap.

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