RU2172967C1 - Gravitational variometer - Google Patents

Abstract

FIELD: measurement technology, measurement of gradients of gravitational field. SUBSTANCE: structure of gravitational variometer includes rocking shaft with weights suspended in air-tight body, transducer of angular movement of shaft with reference to body connected to input of electron unit of servo system, electrostatic torque generators whose rotor electrodes are positioned in symmetry on rocking shaft, pair of identical stator electrodes interacting with each of them anchored on body and connected to output of electron unit. Electrodes on rocking shaft and body come in the form of segments of cylinders. Each rotor electrode has pair of identical segments of cylinders so located on rocking shaft that central angle of half-planes passing through axes of cylinders differs from central angle of half-planes passing through axes of cylinders of stator by computed value determined by distance between axis of suspension of rocking shaft and axis of stator, radii of cylinders of rotor and stator and gap between cylindrical surfaces of segments of rotor and stator oriented in opposition. In this case output of electron unit has two channels, each being connected to segments of cylinders of stator whose axes lie in same plane with symmetry axis of rocking shaft. Gravitational variometer incorporates two pairs of torque generators whose symmetry planes are mutually perpendicular and are connected in parallel to output of electron unit. EFFECT: increased precision and widened measurement range. 2 cl, 2 dwg

Description

 The invention relates to the field of precision instrumentation and can be used to create such means of measuring the gradients of the gravitational field as gravitational variometers and gradiometers. These instruments are used in geological exploration and geodesy to generate information about gravitational anomalies by measuring the components of the acceleration gradient of gravity (second derivatives of the gravitational potential).

 The principle of operation of the gravitational variometer is based on the interaction of a pair of test masses (cargoes), spaced symmetrically relative to the measuring axis using the connecting structure (rocker), with the Earth's gravitational field.

 Known gravitational variometer [1], the sensitive element of which contains a beam made in the form of a rod, with loads fixed at the ends. In the center, the beam is suspended on a thin thread (torsion) with torsional rigidity. The components of the gravitational gradient in these instruments are measured by the torsion angle of rotation, when due to the torsional stiffness of the torsion, a torque is created that compensates for the moment, which twists the beam due to the unevenness of the gravitational field.

 The disadvantages of this design are low accuracy and low performance due to the fact that it does not provide any means of measuring the gravitational moment, except for indicators of the angle of rotation of the rocker arm (most often visual).

 As a prototype for the largest number of common essential features, the design of a gravity variometer [2] was adopted, containing a rocker with loads at the ends, hung in an airtight housing using a torsion bar, and a rocker arm control system including a capacitive displacement transducer, electrostatic moment transducer and electronic control units . In this design, flat rotor electrodes are placed on the side surfaces of the weights; opposite them, flat stator electrodes are installed on the housing so that each pair of electrodes on the rotor corresponds to a pair of electrodes on the stator. Identical pairs of electrodes of the rotor and stator form a capacitive displacement sensor, and other identical pairs form a torque sensor. The electrodes of the displacement sensors are connected to the bridge circuit; an alternator is included in one diagonal of the bridge, and an output signal amplifier in the other. The output signal is rectified by a phase detector, amplified and fed to the input of an electrostatic torque sensor.

 The rotation of the rocker arm under the influence of the gravitational moment leads to a change in the gap between the rotor and stator electrodes of the angle sensor and the appearance of a mismatch signal in the diagonal of the bridge. The signal is rectified, amplified and supplied as a control potential to the corresponding stator plates of the torque sensor.

 The electrostatic forces created in this way return the beam to its initial position. The signal of the position sensor, proportional to the change in the gap between the electrodes when the rocker is rotated by a certain angle, is used as a useful information signal for measuring the value of the gravitational moment.

 The disadvantages of the prototype design are the low accuracy of the measurement and the limited scope of use due to the following circumstances.

 1) The dependence of electrostatic interaction on the gap between the electrodes, since the torque sensor develops a moment proportional to the square of the voltage and inversely proportional to the square of the gap. Such a complex dependence of the moment on the gap makes it difficult both to control the rocker of the gravitational variometer and, what is especially important, to measure the gravitational gradient by the magnitude of the control moments in a wide range of its variation.

 2) Small limits of the angle of rotation of the rocker arm due to the fact that the counter-facing working surfaces of the rotor and stator electrodes of the torque sensor are made in the form of parallel planes.

 The task of the invention is to improve the accuracy and expansion of the measuring range of the gravitational variometer.

достигает максимума,
где

α - центральный угол между полуплоскостями, проходящими через оси цилиндров на роторе и статоре;
L - расстояние между осью подвеса коромысла и осью цилиндра статора;
R - радиус цилиндров ротора и статора;
d - зазор между встречно ориентированными цилиндрическими поверхностями сегментов ротора и статора.The problem is achieved in that the electrodes on the beam and the housing are made in the form of segments of cylinders, and each rotor electrode contains a pair of identical segments of the cylinders located on the beam so that the central angle between the half planes passing through the axis of the cylinders differs from the central angle between the half planes, passing through the axis of the cylinders of the stator associated with the housing, the cylindrical surfaces of the respective segments of the rotor and stator are oriented in the opposite direction, the intersection line is indicated half-planes coincides with the vertical axis of symmetry of the beam, and the output of the electronic unit has two channels, each of which is connected to the corresponding segments of the cylinders of the stators, the axes of which lie in the same plane as the axis of symmetry of the beam, while the gravitational variometer contains two pairs of torque sensors with mutually perpendicular the location of the planes of symmetry and parallel connection to the output of the electronic unit, and in each pair the difference of the above central angles is equal to twice the value of the angle α, pr which function

reaches a maximum
Where

α is the central angle between the half-planes passing through the axis of the cylinders on the rotor and stator;
L is the distance between the suspension axis of the rocker arm and the axis of the stator cylinder;
R is the radius of the cylinders of the rotor and stator;
d is the gap between the counter-oriented cylindrical surfaces of the rotor and stator segments.

 The invention is illustrated in the drawing, where in FIG. 1 is a functional diagram of a gravitational variometer, and FIG. Figure 2 shows a graph of the calculated dependence of the function K (α) proportional to f (α) for various values of the radius R of the cylinders.

- оси цилиндров ротора 3 в виде проекции на плоскость чертежа;

- оси цилиндров статора 4 в виде проекции на плоскость чертежа;

- полуплоскости, проходящие через оси цилиндров ротора 3 в виде проекции на плоскость чертежа;

- полуплоскости, проходящие через оси цилиндров статора 4 в виде проекции на плоскость чертежа;
α - центральный угол между полуплоскостями O₄O'₃ и O₂O'₁ (или O'₄O₃ и O₁O'₂).In FIG. 1 marked:
1 - a rocker arm posted in a sealed enclosure (not shown in FIG. 1);
2 - goods rigidly fixed at the ends of the rocker arm 1;
3 - rotary electrodes of an electrostatic torque sensor mounted on the beam 1;
4 - stator electrodes of an electrostatic moment sensor fixed on the body of a gravitational variometer;
5 - an electronic unit, to each of the two output channels of which cylinder segments are located located on one side of the stator electrodes 4;
6 - photoelectric sensor of angular displacements of the rocker 1 relative to the housing, connected to the input of the electronic unit 5;
U ₁ and U ₂ - control electric potentials coming from each channel of the output of the electronic unit to the segments of the cylinders of the electrodes of the stator 4;
M ₁ and M ₂ are the moments of forces created in each pair of opposite electrodes 3 and 4 of the torque sensors;
R is the radius of the cylinders of the rotor 3 and 4 of the torque sensors;
O is the vertical axis of symmetry of the rocker arm 1 in the form of a projection onto the plane of the drawing;

- the axis of the cylinders of the rotor 3 in the form of a projection onto the plane of the drawing;

- the axis of the cylinders of the stator 4 in the form of a projection onto the plane of the drawing;

- half-planes passing through the axis of the cylinders of the rotor 3 in the form of a projection onto the plane of the drawing;

- half-planes passing through the axis of the cylinders of the stator 4 in the form of a projection onto the plane of the drawing;
α is the central angle between the half-planes O ₄ O ' ₃ and O ₂ O' ₁ (or O ' ₄ O ₃ and O ₁ O' ₂ ).

 The gravitational variometer of the presented design functions as follows.

In the absence of a gravitational moment, the beam 1 is in equilibrium and the signal from the photoelectric angle sensor 6 is zero. The control potentials U ₁ and U ₂ supplied to the stator electrodes 4 from the electronic unit 5 are equal to each other. The pairs of electrodes of the torque sensor create moments 2M ₁ and 2M ₂ , equal in magnitude and opposite in direction. In this case, the total moment M _Σ acting on the rocker 1 is equal to zero.

Under the action of the gravitational moment, the rocker 1 deviates from the equilibrium position. The photoelectric angle sensor 6 generates a signal proportional to the angle of deviation of the rocker arm 1. This signal is converted by the electronic unit 5 into control potentials U ₁ and U ₂ , which are supplied to the stator 4 of the torque sensor. Since in each moment sensor one pair of stator segments is connected to one output channel of the electronic unit 5 (potential U ₁ ), and the other pair of segments is connected to another channel (potential U ₂ ) with a symmetrical connection structure, the potential difference (U ₁ - U ₂ ) causes the sensors to produce the moment of the total moment M _Σ = (2M ₁ -2M ₂ ), which compensates for the gravitational moment and returns the rocker 1 to the equilibrium position. Thus, the potential difference U ₁ - U ₂ is a measure of the gravitational moment.

ε₀ - диэлектрическая проницаемость сферы (ε₀ = 8,85 • 10^-12 Ф/м);
l - длина цилиндров ротора 3 и статора 4.The rocker control 1 of the gravitational variometer is based on the Coulomb attraction of parallel electrostatically charged cylinders. The tangential component of the attractive force F _{t of} two charged cylinders, one of which is placed on the beam 1 and the other on the device body, as a function of the angle α of rotation of the beam 1 is determined by the calculation formula
F _t = K (α) U ²
Where

ε ₀ is the dielectric constant of the sphere (ε ₀ = 8.85 • 10 ^-12 F / m);
l is the length of the cylinders of the rotor 3 and the stator 4.

где

Экспериментальная проверка показала, что силы притяжения двух сегментов цилиндров высотой ~ 2 мм отличаются от сил притяжения двух цилиндров того же радиуса не более чем в 1,5 раза. Это позволило спроектировать и испытать макет малогабаритного датчика момента с сегментами цилиндров в качестве электродов.In FIG. Figure 2 shows a graph of the calculated dependence of K (α) for various radii R of cylinders for a real version of the gradiometer with d = 1 mm, l = 30 mm, and L = 200 mm. As can be seen from FIG. 2, the tangential component of the attractive force F _{t of} two cylinders of radius R, the centers of which are shifted by an angle α ₀ , which corresponds to the maximum of the characteristic K (α), in a certain range of angles, does not depend much on angle α - a flat plot of dependence. In this range of angles α, the forces of electrostatic interaction are determined only by the squares of the potential difference between the cylinders. Having selected a coefficient independent of the angle α in the function K (α), we can write:

Where

Experimental verification showed that the attractive forces of two cylinder segments ~ 2 mm high differ from the attractive forces of two cylinders of the same radius by no more than 1.5 times. This made it possible to design and test a model of a small-sized torque sensor with cylinder segments as electrodes.

The moment acting on the beam of the gravitational variometer is determined by the expression:
M = 2M ₁ -2M ₂ = 2R′K (U $\genfrac{}{}{0ex}{}{\text{2}}{\text{1}}$ -U $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ ) = 2R′K (U ₁ + U ₂ ) ΔU,
where R 'is the arm of the beam.

Ensuring the constancy of U ₁ + U ₂ , for example, by turning on the stator electrodes according to the scheme of a double linear potentiometer, powered from 2 DC sources, we obtain a moment with a linear dependence on the difference of the control potentials.

As a result of experimental verification, it was found that the maximum moment developed by the moment sensor is ± 10 ^-8 N • m with an error of moment measurement of 10 ^-11 N • m. The range of working angles was ± 30 angular minutes at R = 30 mm and d = 1 mm. Such characteristics of the torque sensor provide compensation for the gravitational moment acting on the beam with a moment of inertia of about 10 ^-1 kg • m ² with a gravitational gradient of 1 atv.

 The location of the rotor electrodes on the end elements of the beam made it possible to expand the working range for controlling the movement of the beam of the gravitational variometer, and the use of cylinder segments located on the rotors and stators as electrodes in this way provided the possibility of generating a control moment, the value of which in the working range does not depend on the angle of rotation of the beam .

 Connecting the stator electrodes according to a scheme that determines the constancy of the sum of the control potentials made it possible to obtain a linear dependence of the magnitude of the torque on the difference of the control potentials and, as a result, provided a linear dependence of the measured gravitational moment on the control potential.

 The implementation of two pairs of torque sensors as part of the gravitational variometer with a mutually perpendicular arrangement of the axis of symmetry and parallel connection to the output of the electronic unit made it possible to realize the condition of independence of the control moment from the uneven gaps between the rotor and stator electrodes of the torque sensors caused by technological errors in the manufacture of the device, due to the fact that differential properties of the control system are provided as an increase in the number of interacting elec rows, and their distribution in space.

 In general, the proposed design of the gravitational variometer made it possible to increase the accuracy of measurements in a wide range of changes in the gravitational gradient.

 A prototype of a gravitational variometer was manufactured at the enterprise, the tests of which showed positive results. Currently, technical documentation is being developed for serial production of gravitational variometers.

 Technical and economic efficiency of the invention is associated with the possibility of obtaining more complete and reliable information about gravitational anomalies and a qualitatively new level of solving problems of geodesy and exploration.

Literature
1. Mironov BC "Course of gravimetry", L., Science, 1980, p. 265-312.

 2. Artamonov V.E., Pchelintsev V.A. "On a scheme of highly sensitive torsion scales" in Sat. "Long-term stability of gravity inertial devices", M., Nauka, 1979, pp. 47-52.

Claims (3)

 1. Gravity variometer containing a rocker with loads posted in a sealed housing, electrostatic torque sensors, rotor electrodes of which are symmetrically mounted on the beam, and a pair of identical stator electrodes interacting with each of the rotor electrodes connected to the output of the electronic unit of the tracking system, mounted on the housing, the sensor of angular displacements of the rocker arm relative to the housing, connected to the input of the electronic unit, characterized in that the electrodes on the beam and the housing are made e cylinder segments, each rotor electrode containing a pair of identical cylinder segments located on the beam so that the central angle between the half-planes passing through the cylinder axis differs from the central angle between the half-planes passing through the axis of the stator cylinders associated with the housing, while the surfaces of the respective segments of the rotor and stator are oriented opposite, the intersection line of these half-planes coincides with the vertical axis of symmetry of the rocker arm, and the exit ics block has two channels, each of which is connected to the stator segment cylinders, the axes of which lie in one plane with the axis of symmetry of the rocker.  2. The gravity variometer according to claim 1, characterized in that it contains two pairs of torque sensors with a mutually perpendicular arrangement of symmetry planes and parallel connection to the output of the electronic unit. 3. The gravitational variometer according to claims 1 and 2, characterized in that in each pair of orthogonal moment sensors, the difference in central angles is equal to twice the value of angle α at which the function

reaches a maximum
Where

α is the central angle between the half-planes passing through the axis of the cylinders on the rotor and stator;
L is the distance between the suspension axis of the rocker arm and the axis of the stator cylinder;
R is the radius of the cylinders of the rotor and stator;
d is the gap between the counter-oriented cylindrical surfaces of the rotor and stator segments.

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