General remarks. Parametric converters, as noted in section 1, control the parameters of the energy flow coming from an external source and can operate in one of two modes. In the first of them, the converter is a constant current or voltage regulator.
The measuring information is carried by the law of changes in the level of an electrical quantity. Although such a converter should in principle be a nonlinear system, under certain conditions its output signal can be considered linearly related to the input signal, and even an analogy with generator MECs can be traced. For example, in the simplest case, a converter having electrical impedance is connected in series with the load and is powered by a source with and internal resistance. The external influence changes the impedance of the converter by, as a result of which the current in the circuit changes by the value. Hence we have
The nonlinearity of the transformation introduces the product But at
If the impedance is linearly related to the input value of the MET (usually this is displacement, i.e., then you can write
If an electric force acts in the converter and where does not depend on, then the force balance equation takes the form
The last two equations are similar to the system of equations (1) and (2), and If then such a converter is equivalent to a generator MET, and it can be called quasi-convertible. For it, the general remarks of section 2 remain valid. Converter powered DC, can be quasi-reversible only under the condition that the energy of the power source is spent mainly on creating electrical or magnetic field in the converter. If the voltage is small, then there are no ponderomotive signals. Almost the same result is obtained when powered by alternating current due to the difference in the spectral composition of the input and output quantities (the converter, being a modulator, carries out spectrum transfer, see Chapter 10).
The output signal of the converter can be current (at or voltage at the load (in the opposite case).
In addition to the current regulator mode, a parametric MEC can operate in exciter mode, being part of the frequency-setting circuit of a self-excited generator. The measured quantity modulates the frequency of the generated voltage. The frequency change can be used directly as an output signal or converted to another form (discrete or analog). In this mode the converter is always irreversible.
Rice. 10. Capacitive converter: o - with variable gap (area); 6 - with variable permeability; in - differential
The output signal of a parametric MET powered by alternating current must be subject to detection (demodulation), usually performed in amplification-converting equipment. Since this signal acts against the background of another, not carrying useful information, but stronger due to the fact that its isolation is carried out by differential or bridge circuits.
Capacitive converter. The principle of operation of this converter is based on the dependence of the capacitance between the conductors on their relative position, size and properties of the medium between them. In the simplest case of a flat capacitor, its capacitance
where is the area of the electrodes; 6 - gap between them; effective (i.e., taking into account the heterogeneity of properties) dielectric constant of the interelectrode space. Possible circuit diagrams capacitive converter are shown in Fig. 10. There are two types of dependences of capacitance on the displacement x of one of the electrodes:
The first of them corresponds to a change in area or effective permeability, the second to a change in gap.
For the first type
and for the second
Thus, equation (30) can be written as follows:
where or for types 1 and 2, respectively.
The expression for depends significantly on the electrical mode of the converter. Due to the complexity of analysis in general view Let's limit ourselves to two extreme cases when powered by a constant voltage source.
1 Changes in capacitance occur so slowly that the power source manages to charge the capacitance almost without delay, maintaining the same voltage on it, equal to if no other capacitances are connected in series with the converter. Then (32) takes the following form:
On the other hand, and since it is equal to or -
Since the charge on the capacitance
where is the variable part of the charge, then for type 2 we can write:
2. Changes in capacitance occur so quickly that the charge on it does not have time to change significantly and remains equal to the initial value. Therefore, the voltage on the capacitance changes according to the law. If the charge does not change, then the current passing through the capacitance is zero, and a power source is essentially needed only for the initial charge of the capacitance (ignoring the leakage current). However, there is a small current through the load supported by the work of an external force. For the dependence of the first type of capacitance on displacement (see page 197)
that is, in addition to constant force, there is additional electrical elasticity. For the second type of dependency
Equation (32) is written as follows
the second term is explained by the fact that at the beginning (at ) the impedance is capacitive? and not the load, determines the nature of the initial current.
The converter equations in all modes and their solutions are summarized in table. 2.
2. Equations of a capacitive converter
(see scan)
From those given in table. 2 expressions it is clear that in all cases the output current directly or indirectly depends on When operating in constant voltage mode and with an elastic nature, the converter is a differentiator. In constant charge mode, the output signal depends on the type of load, in particular, if the load is active, then the current is proportional to the force. However, in any case it is impossible to measure constant forces or displacements From the table. 2 it can be seen that in one of the modes the converter is quasi-reversible.
When the converter is powered from an alternating voltage source, current flows through it, even if the capacitance does not change, and the current can serve as a measure of capacitance under any law of its change. For the calculation, you should use equation (32) taking into account what is the function For example, when powered by a sinusoidal frequency voltage, the formulas in table. 2, you can determine the amplitude of the output current if, instead of the expression before taking its module at the frequency called the carrier, you choose significantly more highest frequency in the spectrum Depending on the ratio, the converter can operate in two extreme modes of short circuit and no-load. In the first of them, the equation holds
and in the second
The expressions for are divided into two parts, and the first does not depend on time, and the second pulsates with a frequency; they can almost always be neglected (see below), the converter is considered irreversible
The calculation shows that when making the right choice in any mode, the amplitude of the converter's output signal can be proportional to the acting force. For example, for idle mode and variable clearance
Therefore, it is necessary to choose so that the denominator is constant. With the elastic nature of the impedance, this corresponds to an active load: Bridge circuits are usually used for measurement.
The greatest specific force of attraction of the electrodes of the converter is determined by the breakdown field strength and for air is . If the acting force in all modes is significantly greater than the force of electrical interaction, then using the converter only at narrows the possible range of changes in the input value. An increase leads to a rapid increase in the nonlinearity of the transformation, which can be reduced by using various methods linearization. One of them is the use of differential converters (Fig. 10, c), in which the capacitances change simultaneously in different directions. In this case, along with linearization and increased sensitivity, good compensation for the influence of external conditions is achieved. Linearity increases significantly if the output is a parameter inverse to AC, such as a change in capacitance. Its linear connection with x is maintained until the electrodes of the converter are closed. Direct linearization can be achieved by converting the output signal in an additional microprocessor-based unit, which is now quite possible even in self-powered devices.
If the capacitance is included in the driving circuit of the alternating voltage generator, then it is possible to measure not currents or voltages, but time parameters - frequency or duration. In a classical generator with inductance, the oscillation period is proportional, and in a resistive-capacitive generator it linearly depends on C. This method has great flexibility, since you can always choose the optimal type of output signal. For example, when a converter is connected with a variable gap into the circuit of a resistive-capacitive generator, the oscillation frequency
The change in frequency is proportional to x and it is advisable to use it as an output signal. If the converter has a variable area, then the oscillation period is linearly related to the movement
Therefore, in both cases it is possible to operate without the above limitation with high overload resistance. When the converter is turned on oscillatory circuit these properties are largely lost, but much greater stability of the generator parameters is achieved. Therefore, the latter method is widely used in highly sensitive and stable measuring systems. The frequency output converter is irreversible in all cases.
The sensitivity of a capacitive transducer is determined by its geometric relationships, supply voltage and the stability of structural elements. The highest sensitivity is achieved with a variable gap, but at the same time the upper limit of measurement decreases. Therefore, the applications of variable area and variable gap converters are different. Transducers with variable permeability are rarely used in mechanical measurement technology, although there are crystalline substances with a large dependence of permeability on mechanical stress. Such dielectrics can be effective in force and pressure transducers.
Capacitive transducers are used when measuring forces and quantities reduced to them, as well as displacements, especially small and ultra-small ones.
Inductive converter. The action of inductive MECs is based on the use of the dependence of the inductance of a current-carrying circuit or the mutual inductance of two connected circuits on their size, shape, relative position and magnetic permeability of the environment in which they are located. In particular, the inductance of a coil with a magnetic core having a gap depends on the length of the latter (Fig. I).
Let us assume that the annular gap through which the power lines running outside the coil are closed is so small that it can be neglected. If denoted by the absolute magnetic permeability of the core; I is the average length of the power line in the core; the inductance of a coil without a core, then the inductance shown in Fig. 11 coils where is the effective magnetic permeability taking into account the gap;
This formula is true when If in addition to this then
Thus,
where is the inductance at
Rice. 11. Inductive converter: 1 - fixed core; 2 - coil; 3 - movable core
Magnetic field energy in a coil
where is the current at If we restrict ourselves to terms of the 2nd order of smallness and take into account that then
Substituting these quantities into (30), (31) and taking into account that we obtain the converter equations
From these equations it is clear that the converter is quasi-reversible with a coefficient (but not ) equal to
Output current
As usual, in the pre-resonance region the converter is differentiating, and behind the resonance it is scaling. Powering an inductive converter with a constant voltage is not practiced, since, unlike a capacitive converter, it consumes energy that is wasted on its active resistance. When powered by alternating voltage, energy consumption decreases and becomes
Possible measurement of constant quantities. The output parameters are calculated in the same way as for a capacitive converter. The conclusions about the possibility of using time or frequency measurement and linearization methods remain valid.
Converters have many design varieties. In addition to converters with variable gap length, which are characterized by the greatest sensitivity to core movement, converters with variable gap area are known; with an open magnetic circuit (without a fixed core); with variable mutual inductance, etc. Their sensitivity is sufficient to measure displacements up to
Inductive transducers are used to measure displacements and the forces and pressures converted into them.
Magnetoelastic transducer differs from inductive in the mechanism of changing inductance. It is carried out by direct force on the ferromagnetic core (Fig. 12). It is known that the permeability of a ferromagnet depends on the mechanical stresses in the material. If, in the absence of voltage, the permeability is equal, then the creation of a voltage a changes it to The sensitivity of a ferromagnet to stress is characterized by a coefficient that depends on a and the field in the ferromagnet In a certain range of changes can be accepted Then the inductance of the coil is where Since for the depicted converter where is the modulus of elasticity of the core material, its movement top end, height, then
Rice. 12. Magnetoelastic converter: 1 - core; 2 - coil
Substituting this value into (30), we obtain the equation for the output current of the converter. The magnetoelastic transducer is always supplied with alternating voltage, which is why it is practically irreversible. The output signal is found using a formula similar to (35). Since the coefficient values can reach several hundred, the converter is sensitive to low voltages. However, noise in the ferromagnet and hysteresis phenomena limit the Minimum measurable voltages to a value of the order of
A natural area of application for a magnetoelastic transducer is the measurement of forces and pressures. However, it is used less frequently than inductive, mainly for measuring slowly changing quantities of the same sign.
Resistive converters. The action of resistive MECs is based on the use of the dependence of the quantities included in the formula for electrical resistance - the length of the conductor of its cross-section and the specific electrical conductivity of the material y - on mechanical influences. In the simplest case, a resistive MET is a straight or spiral-wound wire with a variable active length determined by the position of the sliding contact (Fig. 13). Such a converter is called rheostat. The depicted converter with spiral winding is not analog, but discrete with a step equal to the interturn distance. When the contact moves by x, the relative change in resistance is equal to where I is the winding length. Thus, can vary from to unity, but usually starting position the contact is selected in the middle of the winding. Another example is a strain gauge - a current-conducting element subject to deformation, often uniaxial (Fig. 14). In this case, all the quantities on which the resistance depends change.
To assess the properties of the strain gauge material, a strain sensitivity coefficient is introduced equal to Calculation of changes in wire dimensions during deformation
gives the value for where the Poisson's ratio is equal to But since in addition to this the density of the material changes, and therefore the concentration of charge carriers, and the crystal lattice is deformed, it turns out to be significantly larger for metals). In semiconductors, where there are charge carriers of two types and mechanical stresses change the structure of energy bands and mobility of carriers, the strain sensitivity coefficient is an order of magnitude higher, but depends on the type of conductivity, its value and the orientation of the resistor axis relative to the crystallographic axes of the material.
Rice. 13. Rheostat converter
Rice. 14. Resistive strain transducer
In resistive converters, the influence of the electrical side on the mechanical side can be completely neglected and both can be considered as independent. The mechanical impedance of the strain gauge is relatively small and elastic in nature; in a rheostatic converter, the sliding contact is a nonlinear element (such as friction without lubrication). The sensitivity of resistive converters of both types, for example for current, is determined by the formulas
where is the coefficient of conversion of the object deformation into the deformation of the strain gauge. The transfer of strain is carried out either along the entire length of the strain gauge, or at individual points. The designs of strain gauge MEPs are varied. They are made in various shapes from wire, foil, sprayed film or a piece of single crystal.
The sensitivity of strain gauge MEPs makes it possible to measure dynamic deformations up to
Rheostatic transducers are used to measure relatively large relative displacements, and tensor-resistive transducers are used to measure deformations and the quantities converted into them: forces, pressures, moments.
Converters with variable characteristics. A special type of parametric MECs are converters with a nonlinear current-voltage characteristic that changes under mechanical influence on the converter. A typical example is a mechatronic converter - an electric vacuum device with a movable electrode. In Fig. Figure 15 schematically shows a diode mechatron with a movable anode. When the anode moves relative to the cathode, which occurs under the influence of force on the elastic membrane of the diode, the dependence of the anode current on the voltage between the electrodes changes. This can be seen from the formula for the anode current
where B is a coefficient depending on the material and temperature of the cathode and the area of the electrodes; anode voltage. The change is shown in Fig. 16, in the right quadrant of which a family of characteristics is depicted at different interelectrode distances. Representation of dependencies in the form of graphs is often the only possible option if there are no analytical expressions with sufficient accuracy. Since a load resistor is included in the diode circuit, an equality is satisfied, as a result of which the current changes in accordance with the dynamic characteristic, the construction of which is shown in the left quadrant of Fig. 16. Despite the pronounced nonlinearity of the initial current-voltage characteristics, the dynamic characteristic is close to straight.
Rice. 15. Diode mechatronic converter: 1 - membrane, 2 - movable iodine
Rice. 16. Scheme for constructing the dynamic characteristics of the converter
Counting the displacement of the anode x from the initial distance 60 and denoting it, we can therefore write down the equations of the converter:
Thus, both equations are independent. Converter output current
The mechanical impedance of the mechatron is significant. In the pre-resonance region, which is usually working for this type of MET, the converter will be large-scale.
The diode mechatron is the simplest among converters with movable electrodes. Designs have been developed with two anodes and a differential switching circuit, made in both diode and triode circuits, with sensitivity up to several hundred microamps per micrometer. Due to their high rigidity, mechanotrons are more suitable for measuring forces and pressures.
Along with vacuum converters, solid-state type converters are known - semiconductor diodes and triodes (transistors), in which it is a function of the mechanical stress applied to the active region of the crystal: - junction, channel. Almost all known types of semiconductor devices can be used for these purposes. The effect here is achieved due to the fact that when the size of the active region changes, the concentration and mobility of charge carriers change, and in field effect transistor With an insulated gate, piezoelectric polarization also occurs in the insulating layer. Semiconductor METs of this type have a significantly lower mechanical impedance than a mechatron and can measure small forces because their sensitivity is high; however
stability is not good enough. They have not yet become widespread.
Resonator converters. Converters of this type are generators with electromechanical feedback through a frequency-selective element, the parameters of which depend on the impact produced on it (Fig. 17). Generator with a piezoelectric resonator in a circuit feedback is excited at a frequency equal to where is the speed of propagation of the sound waves used; integer; I is the wave path length in the resonator. If a force acts on the resonator, its dimensions and mechanical properties, and with them the generation frequency, change to a first approximation in proportion to the force. Thus, the converter is a force-controlled generator with frequency modulation and is close to capacitive or inductive METs with frequency output, however, the latter use electrical rather than mechanical resonance. But
where is the mass of the resonator; thickness; shear modulus in direction
Stability is determined by the stability of the combination of geometric and elastic parameters in parentheses. Importance at the same time, there is the elimination of energy leaks generated in the resonator, which is achieved by a rational choice of the type of excited waves, the design of the resonator and connecting elements.
It is inappropriate to describe resonator MEPs by a system of equations (1) and (2), since they have a frequency output, and the reverse influence of the electrical side on the mechanical side is determined by weak effects of the second order of smallness, and can be neglected.
The most common are resonator MEPs of another type - the so-called vibration-frequency (string) ones. Their action is based on the use of the fact that the natural frequency of a string stretched with force is proportional to Therefore, if the frequency deviation from
the initial value is proportional to However, solid-state resonators have good prospects, since they have a number of advantages, in particular in terms of speed. Their sensitivity makes it possible to measure forces that cause voltages of the order of magnitude. Converters with purely electrical resonators of the klystron type are also known, which, however, did not go beyond laboratory research due to significant operational inconveniences. Resonator METs are used to measure forces and quantities that can be reduced to them.
Rice. 18. Eddy current transducer
Eddy current transducer. The action of eddy current (or eddy current) transducers is based on the use of the phenomenon of electromagnetic induction. If there is a conducting body in the magnetic field of the current, then when the field changes, short-circuited (eddy) currents are excited in it, sucking out the field energy)
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