RU2749644C1 - Method for measuring low absolute gas pressure and device for its implementation - Google Patents

Abstract

FIELD: measuring equipment.

SUBSTANCE: invention relates to measuring equipment and can be used to measure low absolute pressure of gas or gas mixtures. In the proposed method for measuring low absolute gas pressure, mechanical self-oscillations of given amplitude of a thin oscillator plate mounted on an elastic mechanical suspension are created in a plane-parallel plane with a given gap between two other fixed plates, the natural frequency of self-oscillations of the oscillator plate is measured once in the maximum achievable vacuum. Then the space in the gaps between the plates is filled with the measured gas and the self-oscillation frequency of the oscillator plate is measured, the pressure of the gas under study is calculated from the measured values of the self-oscillation natural frequency of the oscillator plate. Moreover, the measurement of the natural frequency of self-oscillations is performed by measuring the instantaneous values of the electrical capacitance formed between the oscillator plate and one of the fixed plates. In this case, the frequency of change in electrical capacitance is taken to be equal to the natural frequency of self-oscillations of the oscillator plate. The device that implements the method contains an oscillator plate, two flat electrodes, voltage source, unit for measuring the position of the oscillator plate, a control unit and a frequency meter. In this case, the plate-oscillator and two flat electrodes are simultaneously connected to the unit for measuring the position of the plate-oscillator and to a voltage source, which is controlled by the control unit in proportion to the signals coming from the unit for measuring the position of the plate-oscillator, and the frequency meter is connected to the control unit.

EFFECT: invention increases accuracy of measurements, expanding functionality and reducing the duration of measurements.

2 cl, 3 dwg

Description

The invention relates to measuring equipment and can be used to measure low absolute pressure of gas or gas mixtures.

At the present level of development of science and technology, the following technical solutions are known, which are close in essence to the proposed one.

There is a known method for measuring vacuum, which consists in measuring the sliding friction force between two objects moving relative to each other, placed in the investigated volume, at a given sliding speed and contact load, and based on the measured friction force, the sliding friction coefficient between these objects is determined, in this case, the desired coverage coefficient is determined according to a previously constructed calibration schedule for changing the dependence of the coating of the friction surfaces of objects exposed to vacuum on the sliding friction coefficient between these objects, and the residual gas pressure in the vacuum volume is determined by calculation based on the coverage coefficient determined from the calibration schedule (patent for the invention of the Russian Federation No. 2316744, IPC G01L 21/24, publ. 10.02.2008, BI No. 4). The disadvantage of this method is a relatively high measurement error due to the error in determining the calibration dependence of the surface coverage coefficient on the sliding friction coefficient of the objects used.

Known compression vacuum gauges, the principle of which is based on the Boyle-Mariotte law, in particular - the McLeod vacuum gauge, in which the residual pressure is measured indirectly along the height of the working fluid column in the measuring tank, consisting of measuring capillaries, a cylinder and a reservoir with mercury ( Bolton W. Pocket guide of the engineer-metrologist. - M .: Dodeka-XX1, 2002, pp. 332-334). These vacuum gauges are characterized by the long duration and laboriousness of the measurement operation, the bulkiness and fragility of the structure, and the toxicity of the working fluid-mercury.

Known manometric thermocouple converters designed to measure gas pressure by measuring the parameters of thermal transfer (thermal conductivity of gas), consisting of a measuring chamber, a heater and a thermocouple, which are located in the measuring chamber (Eshbakh G.L. Practical information on vacuum technology. - M.- L .: Energy, 1966, pp. 105-110). In view of the imperfect adequacy of the physical and mathematical model linking the thermal conductivity of a gas with its pressure, measurements of this kind are inaccurate and are characterized by a high error, which reaches a value of 30% or more.

Also known are the designs of pressure transducers containing a measuring and sample chambers, separated by an elastic sensitive element-membrane, while the pressure in the sample chamber is maintained by a separate pumping system (Rozanov L.N. Vacuum technological equipment. St. Petersburg: Publishing house of the Polytechnic University, 2012, p. 176).

The closest to the proposed method and device is a viscous method for measuring vacuum, which is based on measuring the resistance force from the gas side to a moving body, and how the device is implemented in the form of a viscous vacuum gauge containing an oscillating sensing element (Tenholte D., Kurth S., Gebner T. , Dotzel W. A MEMS friction gauge suitable for high temperature measure. Sensor and actuators 2008 P. 166-172).

The general disadvantages of the known methods and devices, including the prototype, are: the dependence of the measurement result on the type of gas, its temperature, the need to use a separate pumping system to create an exemplary pressure.

The purpose of the invention is to improve the accuracy of measurements, expand functionality and reduce the duration of the measurement process.

This goal is achieved due to the fact that in the proposed method for measuring low absolute gas pressure, mechanical self-oscillations of a given amplitude of a thin plate-oscillator, mounted on an elastic mechanical suspension, plane-parallel with a given gap between two other fixed plates are created, once the natural frequency of self-oscillations of the plate-oscillator is measured in the maximum achievable vacuum, then fill the space in the gaps between the plates with the measured gas and measure the natural frequency of self-oscillation of the oscillator plate, from the measured values of the self-oscillation natural frequency of the oscillator plate, calculate the pressure of the gas under study, and the measurement of the self-oscillation natural frequency is performed by measuring the instantaneous values of the electric capacity formed between the plate-oscillator and one of the fixed plates, while the frequency of change in electrical capacitance is taken to be equal to the natural frequency of self-oscillations of the plate-oscillator Torah.

This goal is realized with the help of a device for measuring low absolute gas pressure, containing an oscillator plate, two flat electrodes, a voltage source, a unit for measuring the position of an oscillator plate, a control unit and a frequency meter, while the oscillator plate and two flat electrodes are simultaneously connected to the unit measuring the position of the oscillator plate and to a voltage source, which is controlled by the control unit in proportion to the signals coming from the unit for measuring the position of the oscillator plate, and the frequency meter is connected to the control unit.

The essence of the claimed method and device is illustrated in FIG. 1, 2, 3. FIG. 1 is a generalized diagram for disclosing the scientific basis of the method; FIG. 2 shows a cross-section of a sensing element with a plate-oscillator, for which the equation for measuring the method is obtained, FIG. 3 shows a block diagram of an installation including a device that implements the claimed method.

The theoretical basis of the proposed method is as follows.

It is well known that the value of the natural frequency of self-oscillations of a mechanical oscillator, made in the form of a thin plate located plane-parallel between two other plates with given gaps, depends on the elasticity of the gas contained in the gaps, which, in turn, is directly proportional to the absolute pressure of this gas. Let's prove it.

Real gases at low absolute pressure can be considered ideal gases with a high degree of accuracy. For such gases, the Boyle-Mariotte law is applicable, according to which, at a constant temperature and mass of an ideal gas, the product of its pressure and volume is a constant value, i.e.:

PV = const, or P ₀ V ₀ = (P ₀ ± ΔP) (V ₀ ± ΔV) = const, or

Where

V ₀ - initial gas volume,

P ₀ - initial gas pressure,

ΔV, ΔР - small increments of gas volume and pressure, respectively.

If we take into consideration two identical plane-parallel flat plates located from each other with a small gap of thickness Z ₀ (Fig. 1), which is filled with a gas with low absolute pressure, then, as established experimentally, gas leakage from the gas gap during plate vibrations can be neglected when the thickness of the gas gap is much less than the linear size of the plate, i.e. Z ₀ << L. In this case, it is legitimate to assume that, according to relation (1), the change in the thickness of the gap ΔZ is associated with a change in the gas pressure ΔР by the following relation:

Where

S is the surface area of each plane-parallel plate.

We transform relation (2) to the form:

We transform the obtained relation (3), for this we consider two cases:

A) 1st case - when the thickness Z of the gap increases (ΔZ> 0), therefore, the gas pressure in the gap decreases by ΔР, and the gas volume increases by ΔV. In this case, relation (3) corresponds to the ratio:

We multiply the right side of relation (4) by a factor (1-ΔZ / Z ₀ ) and find the ratio for the change in pressure ΔР, after all mathematical operations in the final form we get:

B) 2nd case - when the thickness Z of the gap decreases (ΔZ <0), therefore, the gas pressure in the gap increases by ΔР, and the gas volume decreases by ΔV. In this case, relation (3) corresponds to the ratio:

We multiply the right-hand side of relation (4) by the factor (1 + ΔZ / Z ₀ ) and find the ratio for the change in pressure ΔР, after all mathematical operations in the final form we obtain a ratio identical to (5):

With small changes in the thickness ΔZ of the gap, the denominator 1- (ΔZ / Z ₀ ) ² in relations (5), (7) differs little from unity, for example, at ΔZ = 0.05Z it is equal to: 1- (ΔZ / Z ₀ ) ² = 0.9975. Therefore, with a high degree of reliability, this denominator can be taken equal to one, then relations (5), (7) are transformed to the form:

The increment in the force ΔF acting from the gas side in the gap on the surface of each parallel plate will be equal to:

And the coefficient of elasticity G of the gas in the gap between the plates will be equal to:

As follows from the obtained relation (10), the coefficient of elasticity G of the gas in the gas gap depends on the pressure P ₀ and is directly proportional to it.

When creating self-oscillations of the oscillator plate with a certain given mass m and a displacement from the mean position described by the equation ΔZ (τ) = Asin (ωτ), the oscillatory motion of the oscillator plate at a small oscillation amplitude A will be described by the equation of a harmonic oscillator with one degree of freedom (Andronov A A., Witt A.A. Theory of oscillations. - M .: Publishing house of physics and mathematics literature, 1959, p. 35), i.e .:

Where

- собственная циклическая частота колебаний пластины-осциллятора.

is the natural cyclic frequency of oscillations of the oscillator plate.

Thus, according to relations (10) and (11), the cyclic frequency of self-oscillations will be proportional to the gas pressure in the gas gap:

and the required gas pressure in the gap between the plates is, respectively, equal to:

In the claimed method, it is proposed to use three plane-parallel plates spaced apart from each other with gaps Z ₁ and Z ₂ from the inner plate (Fig. 2), and the inner plate has the ability to perform mechanical self-oscillations, i.e. oscillate, and the two outer plates are rigidly fixed and motionless. For each pair: inner - outer plate, the above relations and equation (13) are valid. In this case, the total coefficient of elasticity of this vibrational system, consisting of three plates, will be equal to the sum of the elastic coefficients of the gas in two gaps G ₁ , G ₂ and the coefficient of elasticity of the mechanical suspension of the movable plate-oscillator G _m :

Where

G ₁ = P ₀ S / Z ₁ - gas elasticity in the gap between one outer plate, for example, plate 1, and the oscillator plate 6 (Fig. 2) (according to the ratio 10),

G ₂ = P ₀ S / Z ₂ - gas elasticity in the gap between another outer plate, for example, plate 2, and the oscillator plate (according to the ratio 10),

G _m = ω _m ² m = (2πƒm) ² m is the elasticity of the mechanical suspension 5 of the oscillator plate 6 (according to relationship 11).

Based on relationship (11), the natural frequency of oscillations of the oscillator plate 6 will be described by the following relationship:

Transforming relation (15) taking into account (14), (11), (10), we obtain the measurement equation of the claimed method:

Where

- коэффициент преобразования,

- conversion factor,

ρ is the density of the material of the oscillator plate,

ƒ _m is the natural frequency of oscillations of the inner oscillator plate in the absence of gas in the gap between the plates,

ƒ is the natural frequency of oscillations of the inner oscillator plate in the presence of the test gas in the gap between the plates

h is the thickness of the oscillator plate.

In the particular case, when the gaps between the plates are equal, i.e. Z ₁ = Z ₂ = Z ₀ , the conversion factor is calculated as follows:

Thus, to implement the method, it is necessary to measure the value of the natural frequency of self-oscillations ƒ _{m of the} plate-oscillator 6 in the absence of gas in the gas gap and the value of the natural frequency of self-oscillations ƒ of the same plate-oscillator 6 in the presence of the test gas in the gap between the plates 1, 2, 6, then, using the measurement equation (16), calculate the value of the absolute pressure of the test gas P ₀ .

The method is implemented using a device, a block diagram of which is shown in FIG. 3. The device contains the first 1 and second 2 fixed plane-parallel plates, which are made of a dielectric material, and on the surface of each plate facing the inside of the gas gap between them, planar metal electrodes 3, 4 are installed. given gaps Z ₁ , Z ₂ from them on an elastic mechanical suspension 5 there is an electrically conductive thin movable plate-oscillator 6, while the thickness of the gaps Z ₁ and Z ₂ between plates 1, 2 and the plate-oscillator 6 can be the same and equal to Z ₀ , so it is different. To simplify the demonstration of the calculation of the design parameters of the sensitive element of the device, we will assume that Z ₁ = Z ₂ = Z ₀ . The value of Z _{0 is} determined by calculation, based on the upper limit of the measured absolute gas pressure P ₀ , _max . In addition, the thickness h of the oscillator plate 6 is also determined by calculation, based on the expected value of the lower limit of the measured absolute pressure P _{0, min} . Plates 1,2 together with electrodes 3, 4 and plate-oscillator 6 are enclosed in a sealed housing 7, which is connected by means of a valve 8 to a container 9 containing a measured gas and through a valve 14 is connected to a pumping device 15. Electrodes 3 and 4, plate- The oscillator 6 is connected to a voltage source 10 and to a position measuring unit 11 of the oscillator plate, which, in turn, is connected to a control unit 12. The control unit supplies signals to a voltage source 10 and a frequency meter 13.

In the claimed device, mechanical self-oscillations of the oscillator plate 6 are created and maintained by an electrostatic drive by applying an electric voltage of a given value to electrodes 3 and 4. To create these self-oscillations, the force of the electrostatic drive F _e must exceed the elastic force of the gas F located in the gap between the plates 1 , 2, i.e. F _e > F.

The modulus of electrostatic force is:

Where

U is the voltage applied to one of the electrodes 3, 4,

ε ₀ - dielectric constant,

ε is the dielectric constant of the gas in the gap between plates 1, 2.

The elastic force of the gas is determined by the ratio:

Since the displacement ΔZ of the oscillator plate 6 from the middle position Z _{0 is} insignificant in practice and usually amounts to ΔZ≈0.01Z ₀ , then according to (19), taking into account relation (10), it is legitimate to write:

The condition F _e > F, taking into account relations (20) and (18), takes the form:

From (21), the condition for setting the thickness of the gap Z _{0 is} obtained:

Where

Р _{0, max} - upper limit of the measured absolute pressure.

To maintain self-oscillations of the oscillator plate 6, a voltage proportional to the friction force acting on the oscillator plate 6 from the gas side and depending on its velocity and gas pressure should be applied to electrodes 3 and 4 relative to the oscillator plate 6. The speed of motion of the oscillator plate 6 is proportional to the first derivative of its displacement from the mean position ΔZ (τ) = Asin (ωτ), that is, to the amplitude and frequency of its oscillations and has a phase shift of 90 ° relative to the signal coming from the position measuring unit 11. Thus , the signal from the position measuring unit 11 of the oscillator plate 6 is transmitted to the control unit 12, where it is phase shifted by 90 °, the amplitude is regulated and the signal is applied to the voltage source 10. Since the electrostatic force is proportional to the square of the voltage difference and acts only as an attractive force, then a half-wave rectified voltage is applied to electrodes 3 and 4, when the oscillator plate 6 moves from electrode 3, voltage is applied to electrode 4, when moving from electrode 4, voltage is applied to electrode 3.

To calculate the required thickness h of the oscillator plate 6, in the first approximation, it is assumed that at the pressure of the measured gas equal to its lower limit P _{0, min} , the value of the natural cyclic oscillation frequency from the oscillator plate 6 is equal to:

Where

ρ is the density of the material of the oscillator plate.

This approximation is quite justified, in view of the fact that the elasticity of the mechanical suspension of the oscillator plate 6, equal to G _m = ω _m ² m = (2πƒ _m ) ² m, is less than the elasticity of the measured gas G. Taking into account that ω = 2πƒ = 2π / T, where T is the period of vibration of the oscillator plate 6, relation (23) is written in the form:

Whence follows the relation for the oscillation period of the oscillator plate:

To fulfill the previously formulated condition on the smallness of gas leaks from the gaps between plates 1, 2 through their lateral faces during oscillations of the oscillator plate 6, as established experimentally, the oscillation period should not exceed 0.002 s, i.e. T <0.002 s, therefore, taking into account (24), the condition for setting the thickness of the oscillator plate 6 has the form:

The device for measuring the absolute low gas pressure operates as follows. The valve 8 is closed once, the valve 14 is opened, and the pumping device 15 is used to pump out the gas contained in the gaps between the oscillator plate and the fixed plates to a pressure 2-3 orders of magnitude lower than P _{0, min} , i.e. to the maximum achievable vacuum. To electrode 3 or to electrode 4 (optionally), which is considered a potential electrode, a constant electric voltage of a given value is supplied from a constant voltage source 10. When a constant electric voltage is applied, an electrostatic force arises, which acts on the oscillator plate 6. The oscillator plate 6 is displaced towards the potential electrode. The magnitude of the displacement of the oscillator plate 6 is determined by the equality of the electrostatic force and the elastic force of the mechanical suspension 5 of the oscillator plate 6. When the constant electric voltage is removed, the oscillator plate 6 begins to oscillate. The signal from the unit for measuring the position 11 of the oscillator plate, proportional to the electrical capacitance between the oscillator plate and one of the electrodes 3, 4 of the plates 1, 2, is supplied to the control unit 12. The control unit generates commands to the voltage source 10 to supply electrical voltages to the electrodes 3 and 4, supporting the self-oscillations of the oscillator plate 6, compensating for the work of the forces acting on the oscillator plate 6 from the gas side, and the dissipation of energy in the material of the mechanical suspension 5. From the control unit 12, the signals enter the frequency meter 13, with the help of which the value of the natural frequency of self-oscillations is measured ƒ _{m of} the oscillator plate in the absence of gas in the gaps between plates 1, 2, i.e. in the maximum achievable vacuum.

After performing the above operations, the valve 14 is closed and the valve 8 is opened, as a result of which the measured gas or mixture of gases in the container 9 completely fills the inner space of the sealed housing 7 and the space in the gaps between the plates 1, 2, 6. After establishing gasostatic equilibrium Between the spaces of the sealed housing 7 and the container 9, using a frequency meter 13, operations are performed similar to those when measuring the natural frequency of self-oscillations of the oscillator plate 6 in the maximum achievable vacuum. As a result, the value of the natural frequency of self-oscillations ƒ of the oscillator plate 6 is measured in the presence of the measured gas, and the value of the absolute gas pressure is calculated from the measurement equation (16), (17).

A specific device has the following characteristics:

- lower limit of gas pressure measurement P _{0, min} = 10 Pa,

- upper limit of gas pressure measurement P _{0, max} = 1000 Pa,

- the thickness of the gap, calculated according to the relation (22) at an electric voltage U <10 V, ε = 1 (nitrogen), Z ₀ = 3 μm,

- material of the oscillator plate - silicon with density ρ = 2300 kg / m ³ ,

- the thickness of the oscillator plate is calculated according to the relation (25) h = 75 μm,

- the linear size of the oscillator plate, selected from the condition Z ₀ << L for the square shape of the oscillator plate (length and width), and for the round shape (diameter) is equal to L = 1 mm.

The use of the proposed method and device provides a number of advantages - independence from the type of gas, the possibility of obtaining a linear dependence of the square of the value of the natural oscillation frequency of the oscillator plate on the measured pressure. In addition, the device does not require a separate gas evacuation system each time to create an exemplary pressure. These technical solutions can significantly improve the accuracy of measurements and reduce the duration of the measurement process, expand the functionality. The estimated relative measurement uncertainty does not exceed 2%.

Claims (2)

1. A method for measuring low absolute gas pressure, which consists in creating mechanical self-oscillations of a given amplitude of a thin oscillator plate mounted on an elastic mechanical suspension in a plane-parallel plane with a given gap between two other fixed plates, filling the space in the gaps between the plates with the test gas, measuring its own the frequency of self-oscillations of the oscillator plate and the pressure of the test gas is calculated from it, while the self-oscillation frequency is measured by measuring the instantaneous values of the electrical capacitance formed between the oscillator plate and one of the fixed plates, the frequency of the electrical capacitance change is taken to be equal to the self-oscillation frequency of the oscillator plate. 2. A device for measuring low absolute gas pressure, containing a plate-oscillator, two flat electrodes, a voltage source, a unit for measuring the position of the plate-oscillator, a control unit and a frequency meter, while the plate-oscillator and two flat electrodes are placed in the investigated gas medium and simultaneously connected to the unit for measuring the position of the oscillator plate and to the voltage source, the voltage source is controlled by the control unit in proportion to the signals coming from the unit for measuring the position of the oscillator plate, the frequency meter is connected to the control unit.

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