RU2530451C1 - Method of determining perturbation and wobbling of vertical axis of rotary support - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: method includes using two autocollimating theodolites and a polygonal mirror prism which is placed in a horizontal plane, aligning its centre with the vertical axis of rotation. The theodolites are directed on the faces of the polygonal prism such that their axes of sight are on the same level with the polygonal prism and form an angle of 90° with each other. For each j-th installation, where j=1,2,…, n is the number of prism faces, of the vertical axis, the inclination angles of corresponding prism faces are measured for forward and reverse rotation of the axis. The values of the angles are read from the vertical circle of the theodolite when the grid of the theodolite is superimposed with its autocollimation image. The values of coordinates V_1j, V_2j of the perturbation vector of the vertical axis are calculated using the formula: $$V_{\mathrm{1,}j}=\frac{x_{for}-x_{rev}}{2},$$

$$V_{\mathrm{2,}j}=\frac{y_{for}-y_{rev}}{2}$$

and values of coordinates B_1j, B_2j of the wobbling vector are calculated using the formula: B_1,j=x_jfor-x_jrev, B_2,j=y_jfor-y_jrev, where: x_j is the value of the inclination angle of the j-th face, which corresponds to the first theodolite and is measured during forward and reverse rotation of the axis; y_j is the value of the inclination angle of the j-th face which corresponds to the second theodolite and is measured during forward and reverse rotation of the axis.

EFFECT: simplification and shorter time required to calculate perturbation and wobbling of vertical axes.

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Description

The invention relates to measuring equipment. The proposed method is used to measure and evaluate perturbations and beats of the vertical axis of the slewing ring (OPU).

A known method of measuring disturbances and beats of the vertical axes of slewing rings (SI Gryzulin Alignment of optical paths: Monograph. - M .: Max Press, 2011. - 100-102 p.), Which is the closest in the set of essential features to the invention.

The method consists in the fact that a pair of mutually perpendicular cylindrical levels or a two-axis tilt sensor that measures the angular coordinates of the free vector in a plumb line system is fixed on the rotating part of the slewing ring. Figure 1 shows a diagram of the implementation of the method, where: 1 - axis of rotation; 2 - instrumental vector; 3, 4 - cylindrical levels; 5 - plumb line. In this case, the vector is formed by the line of intersection of the planes passing through zero - points of the levels or reference planes of the tilt sensor. In the process of measuring, the operating range of the axial system is passed at least two times, in the forward and backward directions, with stops at equal intervals of the angles of rotation and they are taken by levels. To go to the coordinates of the instrumental vector in a fixed system, you need to know the orientation of the levels relative to the meridian of the place in the initial position. Recalculation of level readings into angular values is performed in accordance with the instructions for the use of devices. Then, the coordinates of the hodograph points are calculated by multiplying the matrices of the measured coordinates of the instrumental vector by the rotation matrices of the coordinate system. After approximation of the hodograph, the coordinates of the axial vector are calculated. By studying the trajectory of the axial vector, the necessary rotation characteristics are obtained, namely perturbations (axis oscillations are repeated with sufficient accuracy with new rotation cycles) and beats (axis oscillations are random in nature).

The disadvantage of the prototype is the complexity of the mathematical calculation, the need to create a platform for setting levels or a sensor at the stage of design of the slewing ring.

The objective of the invention is to provide a method for measuring perturbations and beats of the vertical axes of slewing rings, which reduces the time to calculate perturbations and beats of vertical axes.

The technical result of the method is its simplification and reduction of labor costs due to the reduction of the time required to calculate disturbances and beats of the vertical axes.

The technical result is achieved due to the fact that in the method for determining perturbations and beats of the vertical axis of the slewing ring device, which consists in the use of two devices that measure angular coordinates, while in the process of measuring the working range of rotation of the vertical axis in the forward and backward directions with stops at equal intervals of rotation angles and take readings of the tilt angles, the new is that a multifaceted mirror prism is introduced into the measuring system, which is installed horizontally of the nthal plane, combining its center with the vertical axis of rotation, and two autocollimation (AK) theodolites are used as instruments for measuring angular coordinates, while theodolites point to the faces of a multifaceted prism, and they are positioned so that the target axes of the theodolites are on one level with a multifaceted prism and formed an angle of 90 ° between each other, and with each j-th installation (where j = l, 2, ..., n is the number of prism faces) of the vertical axis, theodolites measure the slope angles of the corresponding prism faces with a straight and in the opposite direction of rotation of the axis, the value of the angles is read along the vertical circle of the theodolite when combining the grid of the theodolite with its autocollimation image, then the coordinate values (V _1j , V _2j ) of the perturbation vector of the vertical axis are calculated by the formula:

, $$V_{\mathrm{one,}j}=\frac{x_{jPR-}{x}_{j\mathrm{about}b\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="00000012.png"\; state="\{\{state\}\}">R</figure-callout>}}}{2}$$

,

$$V_{2j}=\frac{y_{jPR-}{y}_{j\mathrm{about}b\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="00000012.png"\; state="\{\{state\}\}">R</figure-callout>}}}{2},$$

and the coordinate values (B _1j , B _2j ) of the beating vector of the vertical axis are calculated by the formula:

, $$B_{\mathrm{one,}j}=\frac{x_{jPR-}{x}_{j\mathrm{about}b\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="00000012.png"\; state="\{\{state\}\}">R</figure-callout>}}}{2}$$

,

$$B_{2j}=\frac{y_{jPR-}{y}_{j\mathrm{about}b\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="00000012.png"\; state="\{\{state\}\}">R</figure-callout>}}}{2},$$

Where:

x _j is the value of the angle of inclination of the j-th face corresponding to the first theodolite, and measured by it with the forward and reverse direction of rotation of the axis,

y _j is the value of the angle of inclination of the jth face corresponding to the second theodolite, and measured by it with the forward and reverse directions of rotation of the axis.

Using a mirrored polyhedral prism arranged in such a way that its center is aligned with the vertical axis of rotation, and AK theodolites for measuring the angles of inclination of the faces of the prism relative to the vertical, can directly measure the coordinates of the axial rotation vector of the vertical axis without measuring the coordinates of the instrumental vector. In this method, there is no need to know the orientation of the multifaceted prism and theodolites relative to the meridian of the place in the initial position. Therefore, the calculation of perturbations and beats of the vertical axis is carried out in one step, by substituting the values of the measured angles in the formula. Therefore, the advantage of this method in the simple calculation of disturbances and beats.

Figure 2 shows a diagram of the implementation of the method on the example of an alt-azimuth mount with a mirror, where: 1 - the first theodolite; 2 - the second theodolite; 3 - multifaceted mirror prism; 4 - mirror OPU; El, E2 - axis OPU.

Figure 3 shows the hodograph of the beating vector of the vertical axis of the alt-azimuthal mount of the MEADE LX200GPS telescope.

Figure 4 shows the hodograph of the perturbation vector of the vertical axis of the alt-azimuthal mount of the MEADE LX200GPS telescope.

Previously, the mount axis E1 is brought into a vertical position, then the mirror (4) is rotated around the E2 axis by an angle Δе2 = 90 °, so that the plane of the mirror is located in a horizontal plane, after which a polyhedral prism (3) is mounted on its center, combining it center with a vertical axis of rotation.

The first theodolite (1) is pointing at one of the faces of a multifaceted prism, the second theodolite (2) is pointing at the corresponding face of the prism, while theodolites are positioned so that the target axes of the theodolites are at the same level with the multifaceted prism (3) and form an angle between them equal to 90 °. The determination of perturbations and beats of the vertical axis with an assessment of the accuracy of the determined parameters is performed from processing the measurements by theodolites in the full range of rotation of the E1 axis.

Measurement processing is performed in the following sequence. The axis under investigation is rotated with stops at equal intervals of rotation angles. For each j-th installation (where j = l, 2, ..., n is the number of faces of the prism) of the vertical axis of the slewing ring, theodolites measure the slopes of the corresponding faces of the prism in the forward (in the clockwise direction) and in the opposite direction of rotation of the control gear, the value of the angles are read in the vertical circle of the theodolite when combining the grid of the theodolite with its autocollimation image.

The root-mean-square error m and the root-mean-square error determining the quality of axis rotation are calculated:

, $$m=\sqrt{\frac{{\Sigma }_j\left(x_{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="00000012.png"\; state="\{\{state\}\}">j</figure-callout>}}^2+y_j^2\right)}{2\cdot N-\mathrm{four}}}$$

,

$$m_{\Sigma }{}_{\mathrm{one}}=\sqrt{m^2-m_u^2},$$

where m _u is the mean square error characterizing the instrumental accuracy of theodolite measurements.

In an example of a specific implementation, the inventive method was implemented using the following technical means: two 3T2KA theodolites with a self-stabilizing zero vertical circle and a multifaceted reference prism PM-12. The alt-azimuthal mount of the MEADE LX200GPS telescope was chosen as the object of study. OPU was rotated at the command of the control computer 360 ° with stops at 30 °. The rotation was carried out in the forward (clockwise) direction and in the opposite direction. At each stop, theodolites took readings and recorded in the observation log. Processing of the measurement results was carried out according to the above method.

Based on the calculation formula and the accuracy of theodolites used, the standard deviation, which determines the quality of rotation of the axis, was m _E1 = 15.41 ".

Claims (1)

The method for determining perturbations and beats of the vertical axis of the slewing ring device, which consists in the fact that two instruments are used that measure the angular coordinates, while during the measurement process they pass the working range of rotation of the vertical axis in the forward and backward directions with stops at equal intervals of rotation angles and remove indications of tilt angles, characterized in that a multifaceted mirror prism is introduced into the measuring system, which is installed in the horizontal plane, combining its center with the vertical axis rotation, and as instruments measuring angular coordinates, two autocollimation theodolites are used, while theodolites are brought to the verge of a multifaceted prism, and they are positioned so that the target axes of the theodolites are at the same level with the multifaceted prism and form an angle equal to each other 90 °, and with each j-th installation (where j = 1,2, ..., n is the number of prism faces) of the vertical axis, theodolites measure the tilt angles of the corresponding prism faces for the forward and reverse directions of axis rotation, read the angle values t along the vertical circle of the theodolite when combining the grid of the theodolite with its autocollimation image, then the coordinates (V _1j , V _2j ) of the perturbation vector of the vertical axis are calculated by the formula:
$$V_{\mathrm{one,}j}=\frac{x_{jPR}-x_{j\mathrm{about}bR}}{2}$$

$$V_{2j}=\frac{y_{jPR}-y_{j\mathrm{about}bR}}{2},$$

and the coordinate values (B _1j , B _2j ) of the beating vector of the vertical axis are calculated by the formula:
B _{1, j} = x _jpr - x _jbr
B _{2, j} = y _jpr - y _j
Where:
x _j is the value of the angle of inclination of the jth face corresponding to the first theodolite, and measured by it with the forward and reverse directions of rotation of the axis;
y _j is the value of the angle of inclination of the jth face corresponding to the second theodolite, and measured by it with the forward and reverse directions of rotation of the axis.

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