Study on the biparametrical transudations circuits with distributed parameters

This paper highlights the methods of resenting mode in the transudation with distributed parameters. The transient parameters of the power supply were analyzed. It was discovered that resonance is provided in a small range of movement of the moving component of the sensor in known turbofan engines, indicating that the known techniques of sustaining the resonance mode are flawed. Further study should focus on developing novel methods for preserving resonance mode over the entire range of change of the converted value, general principles of turbojet engine construction, and a complete examination of their resonant circuits, according to the findings.


Introduction
Biparametric circuits here are called circuits in which two circuit parameters are variables simultaneously. Most often, the variables are the parameters of the reactive elements of the inductive coil and capacitor. Some electromagnetic sensors (for example, motion parameter sensors) -primary converters contain biparametric circuits. The advantage of these so-called biparametric sensors is that they combine the advantages of electromagnetic (high output power, stability of characteristics) and capacitive (linearity of the static characteristic, high sensitivity) sensors [1][2][3]. If in this case the reactive elements form a resonant circuit, the sensitivity of such sensors increases sharply. The circuits of biparametric resonant sensors are circuits with electrical and magnetic parameters distributed along the coordinate of the moving part. The distribution of parameters leads to the fact that in the operating range of the input value x, the circuit leaves the resonance mode, while sharply reducing the sensitivity of the sensors.

Methods
An important requirement for biparametric resonant sensors (circuits) with distributed parameters is the fulfillment of the resonance conditions in the entire range of changes in the parameter values of their reactive elements. The resonance mode can be saved in the following three ways. 1. By satisfying the condition which is achieved if the parameters of the reactive elements change according to , , where , -aspect ratios. The advantage of this method of maintaining the resonance mode is that with a known law of change or you can always find the function or , satisfying the condition (1). 2. By fulfilling the condition or [1], where и -respectively, the inductance and capacitance of the differential circuits of biparametric resonant motion sensors. 3. By satisfying the condition or [4], where -angular frequency of power supply voltage. According to this method, the change in the resonant frequency of the circuit when changing or automatically "tracked" by a variable frequency generator [3][4][5][6]. On the basis of biparametric resonant circuits with distributed parameters, it is possible to create sensors of displacement, speed and other motion parameters.

Results and Discussion
As an example, consider a biparametric resonant linear displacement transducer ( Figure 1) [6][7][8]. It consists of a U-shaped fixed magnetic circuit 1, on the base of which the excitation winding 2 and the measuring winding 3 are located. In the space between the parallel cores 4 and 5 of the magnetic circuit, there is a variable capacitor with a liquid crystal dielectric (LCD), made in the form of extended electrodes 6 and 7, the gap 9 between which is made unevenly in the section (it is smaller up to the movable electromagnetic screen 8, behind it -more) and the LCD is full. The measuring winding and capacitor are tuned to resonance voltages.

Figure 1. Construction of a biparametric resonant sensor linear displacement
When the excitation winding is powered from an alternating current source I, an EMF is induced in the measuring winding. Moving the screen 8 simultaneously changes the inductance L and winding 3 and the capacitance C of the variable capacitor so that the circuit is in resonance at any position of the screen along the length of the cores. With an increase in the x coordinate of the screen, the inductance Li increases, and the capacitance of the capacitor decreases due to the reorientation of the LCD molecules. The inductance of the measuring winding without taking into account the magnetic resistance of steel and the electrical resistance of the screen is determined as , where w -is the number of turns of the measuring winding; -the width of the cores of the magnetic circuit and the gap between them; -magnetic constant, -the width of the capacitor electrodes and the gap between them; -coordinate of the moving part of the sensor; х -initial and maximum values of respectively х 0 and X M ; -dielectric constant of LCD, the molecules of which are not oriented along the magnetic field х; is thedielectric constant of the LCD, the molecules of which are oriented along the magnetic field. The size of the gap The size of the gap: . (3)

Substituting expression (3) into equation (1), we get:
; The output signal or static characteristic of the sensor will be written as: .
The last expression shows that the static characteristic of the investigated sensor is linear under the above assumptions. However, the distributed nature of the magnetic resistance of steel and the magnetic conductivity of the gap has a significant effect on the resonance mode. Therefore, below we consider the influence of the distributed parameters of the magnetic circuit and the frequency of the power source on the resonant mode within the range of variation of the parameters L (x) and C (x) in the considered biparametric resonant linear displacement transducer. In biparametric circuits with distributed parameters operating in a resonant mode, inductance and capacitance are defined as Where -coefficient of propagation of a magnetic field along a magnetic circuit,the quantity is complex, but in the formulas at sufficiently low frequencies and the absence of a surface effect, the coefficient spread by a real number, linear values of the magnetic conductivity of the gap and the magnetic resistance of parallel cores per unit length х, µ is the relative magnetic permeability of the material (steel) of the magnetic circuit, is the thickness of parallel cores, S -is the active area of the capacitor electrodes.
The natural angular frequency of the circuit is (4) The relative detuning of the circuit frequency with respect to the resonant frequency is The ratio of the current in the circuit to the resonant current can be found as , Where Ractive resistance of the measuring circuit of the sensor. Figure 2 shows the curves of the dependences и at different values , where -the relative value of the input quantity. The curves show that with increasing (due to an increase in the magnetic resistance of steel ) the relative detuning increases, and the current in the circuit decreases sharply. The degree of unevenness of the magnetic field in the working gap of the magnetic circuit is determined by the formula [9][10][11][12][13][14][15]: Substituting (6) into (5), we obtain the expression for the dependence of the detuning on the degree of unevenness of the magnetic field in the working gap: Changing the mains frequency also affects the resonance mode, the current in this case is calculated as Dependency Curve Analysis at different values and indicates that with an increase in the frequency of the source voltage by the resonance effect is reduced to a greater extent than by decreasing the frequency by the same amount. This is due to a decrease in the increase in the inductance of the circuit with an increase in the magnetic resistance of the steel [16][17][18][19][20]. Thus, the article describes the methods of maintaining the resonant mode in biparametric circuits with distributed parameters and studies the influence of changing the parameter circuit and the power supply on the resonant mode.

Conclusions
It is shown that at present only separate designs of the transformer-type linear displacement turbojet engine have been developed, and inductive turbojet turbojet engines and sensors of this type for converting speed, acceleration and vibration are under development. It was found that in the known turbofan engines, resonance is provided in a narrow range of movement of the moving part of the sensor, which indicates the imperfection of the known methods of maintaining the resonance mode. It has been established that further research should be aimed at developing new methods of maintaining the resonance mode over the entire range of change of the converted value, general principles of constructing a turbojet engine, a detailed analysis of their resonant circuits, the study of their dynamic properties, a comparative assessment of the technical characteristics of inductive and transformer, conventional and differential turbofan engines, taking into account the type of their moving part.