CONTROLLED AC STABILIZERS ON THE PRINCIPLE OF INDUCTION LEVITATION

ABSTRACT

In the presented article, some characteristic features of the characteristics of precision controlled high-precision AC stabilizers based on the principle of induction levitation are considered. Determining the output characteristics, establishing analytical relationships between the initial data and the output parameters of the stabilizer is one of the stages of the algorithm for solving the problems of designing the parameters of an AC stabilizer with induction levitation of the moving part.

The stability and shape of the load current determines the reliability, accuracy, efficiency, service life of automation devices, test equipment and galvanic baths. This, in turn, contributes to the development of a mathematical model of the system of equations of electrical, magnetic, mechanical and thermal circuits of the stabilizer, the joint solution of which allows you to establish analytical relationships between the initial data and parameters such as working stroke, weight force, winding and core cross-sections, copper losses.

АННОТАЦИЯ

В представленной статье рассмотрены некоторые характерные особенности характеристик  прецизионных управляемых высокоточных стабилизаторов переменного тока на принципе индукционной левитации. Определение выходных характеристик, установление аналитических связей между исходными данными и выходными параметрами стабилизатора является одним из этапов алгоритма для решения задач проектирования параметров стабилизатора переменного тока с индукционной левитацией подвижной части.

Стабильность и форма тока нагрузки определяет надежность, точность, экономичность, срок службы устройств автоматики, испытательной аппаратуры и гальванических ванн. Это в свою очередь способствует разработке математической модели системы уравнений электрических, магнитных, механических и тепловых цепей стабилизатора, совместное решение которых позволяет установить аналитические связи между исходными данными и параметрами как рабочий ход, сила веса, сечения обмоток и сердечника, потери в меди.

Keywords: current stabilizer, induction levitation, moving part, high-precision, controlled, precision, source, dependence, levitation winding.

Ключевые слова: стабилизатор тока, индукционная левитация, подвижная часть, высокоточный, управляемый, прецизионный, источник, зависимость, левитационная обмотка.

Introduction

Reliability, accuracy, efficiency and service life of automation devices, information and measuring equipment, test equipment and galvanic baths are determined by the stability and shape of the load current. Basically, the sources of power for various devices and installations are power networks, and the constancy of the voltage in such networks is usually not observed, and there are always short-term and slow voltage fluctuations. Such voltage fluctuations in many cases are unacceptable, as they lead to disruption of the normal operation of the equipment. A necessary condition for ensuring the specified accuracy is the stability of the load current. The task of stabilizing the current and voltage at the load is characterized by parametric and controlled stabilizers, the principle of operation of which is based on the use of various physical phenomena. The operation of most of these stabilizers is based on the use of a non-linear current-voltage characteristic of various elements used in stabilizer circuits. The movable anchor, being subjected to the action of the weight force Р_в and the force of attraction F_e, automatically finds the equilibrium position F_e=Р_в(the point of intersection of the traction characteristic F_e(X) and the horizontal direct weight force Р_в).When the armature is moved, the inductance of the winding and its resistance change. In this case, the steady state value of the current is defined as:

                                                           (1)

The derivative inductance L with respect to the displacement of the core X is a constant value only for a narrow range of displacements x = X₂ - X₁. Therefore, the current stabilizes in a small range of supply voltage changes (6-8)%. The operation of these stabilizers is based on the principle of magnetic suspension of ferromagnetic cores. A controlled electrodynamic stabilizer allows you to smoothly adjust the value of the stabilized current. The stabilizer has an elongated magnetic circuit, on which a fixed and a moving AC coil are located. The moving coil is mounted on a mobile device (trolley) and can move freely along the magnetic circuit.

Another type of controlled stabilizers are stabilizers with induction levitation windings, which are much simpler than existing ones in design, provide high stabilization accuracy when the supply voltage changes over a wide range, allow you to simultaneously obtain several nominal values of the stabilized current, the shape of the stabilized current curves is close to a sinusoid if the supply voltage sinusoidally (fig. 1). The main disadvantages of these stabilizers are the possibility of their operation in the vertical position of the magnetic circuit and in the absence of vibration and shaking [1,3-8].

Figure 1. Volt-ampere characteristic of electrodynamic stabilizer

Algorithm for solving the problem

 One of the stages of the algorithm for solving the problems of designing the parameters of an AC stabilizer with inductive levitation of the moving part is the determination of output characteristics, the establishment of analytical relationships between the initial data and the output parameters of the stabilizer, design, which includes the fluctuation and magnitude of the mains voltage ΔU_с=U_cmax-U_cmin, U_nom and load current I_н. The stabilizer must be designed for the rated load current I_н and for the rated voltage U_н, at which the levitation coordinate corresponds to the initial position of the levitation winding. Design criteria: allowable overheating of the windings τ_д1 and τ_д2, allowable voltage increment at the terminals of the supply winding ΔU₁ and allowable increment of the stabilized current at the load ΔI_н [3-6]. The basis of design is the establishment of analytical relationships between the initial data and geometric dimensions. This requires the development of a mathematical model consisting of a system of equations of electric, magnetic, mechanical and thermal stabilizer circuits, the joint solution of which allows you to establish analytical relationships between the initial data and the working stroke x_M, the weight force P_в, the sections of the windings S_o and the core S_c, copper losses Р_М . The initial values for calculating an AC stabilizer with inductive levitation of the moving part are the range of mains voltage change ΔU_с, load currents I_н1, I_н2, …I_нн, mains frequency w, load resistance R_н or load power Р_н, as well as the stroke of the moving part x_М or minimum levitation coordinate value h_min. The levitation coordinate h is a linear function of the voltage U₁:                               

                                                             (2)

The maximum and minimum values of the levitation coordinate will be determined by the voltages U_1max and U_1min, respectively. Maximum stroke LW:

                            (3)

The specific magnetic conductivity of the working air gap can be determined by the formula:

                                                 (4)

To ensure the uniformity of the magnetic field of the working air gap, the following ratios are recommended:

                                                 (5)

Table 1 shows the calculated values of the specific magnetic conductivity λ and the buckling coefficient σ_в. Figure 2 shows the dependence  for different values of the weight force, which shows that with an increase in the nominal values of the current I₁, the ratio  decreases if the weight force of the levitation winding is constant. This is the case for multi-rated AC stabilizers, where with the switching of sections of the fixed winding, the current I₁ changes, and the weight force remains constant. The coefficient К_н takes into account the voltage drop U_R on the load R_н. Figure 3 shows the dependence. К_н=f(Р_н) for different values of load resistance R_н. [4]. Another important characteristic is the dependence of the weight force of the induction levitation winding (ILW) P_в on the current I₁, which is shown in fig. 4 for various values of the stroke x_M. It shows that with an increase in current, the force of the weight increases, and with an increase in the stroke x_M, it decreases. For supplying electroplating baths and test benches, for automated control of calibration parameters of measuring instruments, etc. precision current stabilizers are used as a power source.

 Table 1.

Estimated values of  l and  s_в

Figure 2. Dependence  for different values of the weight force Рв.

Figure 3. Dependence Кн=f(Рн) for different values of Rн

Analytical expressions for a number of basic dependencies have been obtained that characterize the ability of current stabilizers with a levitation winding to satisfy their functions as an element of the general circuit of the device: dependence of the voltage increment at the excitation winding terminals on mains voltage fluctuations; dependence of the maximum stroke of the LW on the voltage increments (supply winding) of the EW; dependence of the course of the LW, input, output and overall powers on the initial data for design; dependence of the load current on the ambient temperature and the temperature rise of the windings; dependence of the main dimensions on power, electromagnetic load and winding overheating temperature; dependence of the increment of induction in the core on fluctuations in the mains voltage, load power and rated power of the stabilizer [9].

Figure 4. Dependence of the weight force Рв on the current I1

The main criteria for designing a current stabilizer are: allowable overheating τ, allowable voltage drop U₁, allowable stroke X_M of the levitation winding, allowable ratio of the height of the windings (or magnetic circuit) to their thickness (or width of the magnetic circuit) and the accuracy of current stabilization for a given range of changes in mains voltage  ΔU = U_max-U_min. As a generalized model, the design of a stabilizer with maximum symmetry and homogeneity of the magnetic system is considered [7-8].

For this purpose, a mathematical model has been developed that allows, on the basis of solving the equations of the levitation coordinate, mechanical forces, winding MMF and winding excess temperature, to establish the most important analytical relationships between the initial design data and the main parameters of the stabilizer [8-10]. The developed technique was used for a three-limit stabilizer for stands and galvanic baths as an adjustable source of stabilized current at 7,8,9 A. The current stabilization error of the prototype current stabilizer was 0.1% when the mains voltage fluctuated in the range (160-250) V.

Conclusion

Analytical expressions for a number of basic dependencies are obtained that characterize the ability of AC stabilizers based on the principle of induction levitation. A calculation of a three-section AC stabilizer for powering galvanic baths was made, a method for calculating a current stabilizer for testing equipment and galvanic baths was given, a computer study of the current stabilizer coupling equation using the program (EXEL) was carried out.

The current states of power sources for galvanic baths are analyzed. The features of operation and varieties of electroplating baths, their fields of application are considered, the requirements for modeling the optimal temperature control of electroplating baths are established.     

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