RU2121134C1 - Process of calibration of gyroscopes - Google Patents

Abstract

FIELD: certification and tests of gyroscopes under laboratory and factory conditions, approval tests . SUBSTANCE: calibrated gyroscope is put on rotary table with input axis orthogonal to celestial axis. Several measurement positions are set by rotation of rotary table about celestial axis and input axis of gyroscope through fixed angles. Number of various values of angle of turn about input axis of gyroscope exceeds two. Summary drift in measurement positions of rotary table is measured. Components of drift of gyroscope are determined. EFFECT: complete calibration of gyroscope, decreased labor input in calibration, enhanced calibration precision. 4 cl, 1 dwg

Description

 The invention relates to gyroscopic instrumentation and can be used for calibrations (certification, verification) of gyroscopes in the process of laboratory, factory and acceptance tests.

 Known methods for calibrating gyroscopes on turntables (see U. Wrigley, U. Hollister, U. Denhard. Theory, design and testing of gyroscopes. M. Mir. 1972. S. 353-386), allowing calibration of gyroscopes in the Earth's gravitational field . These calibration methods impose restrictions on the gyroscope drift model, which reduces the accuracy and reliability of the calibration, and require twice to accurately exhibit the gyroscope under study on the turntable with respect to the angular velocity vector of the Earth's daily rotation. This operation is complex and time-consuming, in addition, in the process of its implementation, the conditions of the experiment can be substantially violated.

 The proposed method for calibrating gyroscopes does not have restrictions on the gyroscope error model and ensures that the entire program is executed by a single exhibition on the rotary table of the instrument under study with respect to the angular velocity vector of the Earth's daily rotation, followed by a change in its position only through the rotary table. Obviously, these conditions make it possible to carry out a more reliable and accurate calibration of the gyroscope, lead to a decrease in labor costs and time for calibration, and provide a higher technological effectiveness of the experiment.

где
ω - суммарный уход гироскопа;
ω_o - независящая от перегрузки составляющая ухода гироскопа;
ω_x , ω_y, ω_z - зависящие в первой степени от перегрузки составляющие ухода гироскопа;
ω_xy, ω_xz, ω_yz, ω_yy, ω_zz - зависящие во второй степени от перегрузки составляющие ухода гироскопа;
n_x, n_y, n_z - проекции единичной перегрузки на оси, связанные с гироскопом;
OX - выходная ось, OY - входная ось, OZ - ось собственного вращения гироскопа.The essence of the method is illustrated by the following. Consider a gyroscope drift model whose coefficients are observed in the Earth's gravitational field:

Where
ω is the total departure of the gyroscope;
ω _o - independent of the overload component of the departure of the gyroscope;
ω _x , ω _y , ω _z are the components of the gyroscope departure that depend, in the first degree, on overload;
ω _xy , ω _xz , ω _yz , ω _yy , ω _zz - components of the gyroscope departure depending on the second degree of overload;
n _x , n _y , n _z - projection of a single overload on the axis associated with the gyroscope;
OX is the output axis, OY is the input axis, OZ is the axis of rotation of the gyroscope.

This model shows the relationship of the total departure of the gyroscope ω with the nine components ω _o , ω _x , ω _y , ω _z , ω _xy , ω _xz , ω _yz , ω _yy , ω _zz , which must be determined by the calibration results.

 Obviously, in order to separate the desired coefficients of the error model from the measurements of the total drift ω, it is necessary to measure in several (at least nine) gyro orientations relative to the gravity acceleration vector. In order to exclude the influence on the calibration of the angular velocity of the Earth's daily rotation, the device under study is installed with the input axis orthogonal to the axis of the World.

Known calibration methods are performed on a rotary table, the axis of rotation of which is oriented along the axis of the World, the gyroscope is set by the input axis orthogonally to the axis of the World, and the output axis or axis of proper rotation is oriented along the axis of rotation of the table. Then the table is rotated around the axis of the World in order to measure the total drift ω at its various positions. Then, the gyroscope is reinstalled so that its output axis or axis of proper rotation takes the opposite direction and the measurement program for the total drift ω is repeated. Based on the totality of the information obtained, the sought coefficients of the withdrawal model are determined under the assumption that ω _yy = -ω _zz . This assumption is significant and leads to a decrease in the accuracy and reliability of the calibration. In addition, two operations of installing a gyroscope on a rotary table give rise to disadvantages that have been discussed in detail previously.

 In order to eliminate the disadvantages inherent in the known methods of calibrating gyroscopes, a method for calibrating a gyroscope on a rotary table is proposed, in which during the measurement the input axis occupies different positions relative to the plane of the meridian in the plane of the orthogonal axis of the World (the condition for eliminating the influence of the angular velocity of the daily rotation of the Earth on calibration) and the output axis or the axis of proper rotation is oriented relative to the axis of the World in several angular positions (there are more than two such angular positions). This calibration method can be implemented on a turntable having two rotation axes: one provides rotation around the axis of the World, the other around an axis orthogonal to the axis of the World. It is not difficult to construct this construction using, for example, a gimbal suspension used in triaxial gyrostabilizers.

(φ - ширина места), ось OZ_по - дополняет систему до правой. В процессе калибровки поворотный стол вращается вокруг оси Мира на угол α₁ (при этом ТГ X_поY_поZ_по переходит в ТГ X_пY_пZ_п) и вокруг оси поворотного стола OX_п, совпадающей с входной осью гироскопа, на угол α₂. Угол α₂ - это угол между осью Мира и осью собственного вращения или выходной осью исследуемого гироскопа, на чертеже и при последующем рассмотрении без потери общности выбрана ось собственного вращения гироскопа. Таким образом, множество всех возможных положений гироскопа в процессе калибровки по предлагаемому способу задается углами α₁ и α₂.
Установим набор углов α₁ и α₂, на которых можно произвести полную калибровку гироскопа по предлагаемому способу в соответствии с моделью (1). Нетрудно видеть, что проекции единичной перегрузки на оси, связанные с гироскопом, определяются так:
η_x = sinα₁•cosα₂•cosφ + sinα₂•sinφ,

Тогда выражение (1) (после подстановки формул (2) и преобразований) может быть записано в следующей векторно-матричной форме:

(3)
где

- вектор коэффициентов ряда Фурье;

- вектор калибруемых составляющих ухода гироскопа;
H₁(α₁) - матрица размерности 1х5, составленная из тригонометрических функций угла α₁, а H₂(α₂, φ) - матрица размерности 5х9, составленная из тригонометрических функций углов α_2/и φ, вида

Из системы (3) следует, что для определения искомого вектора

по измерениям значений суммарного ухода ω, необходимо выбрать такой набор углов α₁ и α₂, чтобы из первого уравнения данной системы определялся вектор коэффициентов Фурье

а из второго по значениям вектора

был бы найден вектор калибруемых составляющих ухода гироскопа

Первое уравнение системы (3) показывает, что для определения вектора

соответствующего фиксированному значению угла α₂, в общем случае достаточно произвести измерения в пяти различных ориентациях поворотного стола по углу α₁, обозначим их -

Определим оптимальные значения α $\genfrac{}{}{0ex}{}{\text{i}}{\text{1}}$ . Примем за критерий оптимальности максимум абсолютной величины определителя системы уравнений, построенной на матрице H₁ для пяти различных значений углов

вида

Выполнение данного критерия оптимальности, используемого и далее, соответствует минимальному влиянию измерительного шума на вычисление значений искомого вектора.The installation of the gyroscope on the rotary table and its angular position during the implementation of the proposed calibration method is illustrated in the drawing, which shows: a trihedron X _by Y _by Z _by characterizing the initial position of the rotary table; a trihedron X _p Y _p Z _p characterizing the position of the turntable during calibration; XYZ trihedron associated with the studied gyroscope. Trihedron X _on Y _by Z is focused _on in the following way: _{on the} OY axis - the axis of the world, the axis - OX _on a meridian plane and forms an angle φ with the acceleration vector due to gravity

(φ is the width of the space), the OZ axis _along - complements the system to the right. During calibration, the turntable rotates about the World axis by an angle α ₁ (wherein TG X _on Y _by Z _of passes in TG X _n Y _n Z _n) and about the axis of the turntable OX _n coincident with the input axis of the gyroscope, an angle α ₂ . The angle α ₂ is the angle between the axis of the World and the axis of proper rotation or the output axis of the studied gyroscope, in the drawing and upon subsequent consideration without loss of generality, the axis of proper rotation of the gyro is selected. Thus, the set of all possible positions of the gyroscope in the calibration process by the proposed method is set by the angles α ₁ and α ₂ .
We establish a set of angles α ₁ and α ₂ at which it is possible to perform a complete calibration of the gyroscope according to the proposed method in accordance with model (1). It is easy to see that the projections of the unit overload on the axis associated with the gyroscope are defined as follows:
η _x = sinα ₁ • cosα ₂ • cosφ + sinα ₂ • sinφ,

Then expression (1) (after substituting formulas (2) and transformations) can be written in the following vector-matrix form:

(3)
Where

is the vector of coefficients of the Fourier series;

- the vector of calibrated components of the care of the gyroscope;
H ₁ (α ₁ ) is a ₁ × 5 matrix composed of trigonometric functions of the angle α ₁ , and H ₂ (α ₂ , φ) is a 5 × 9 matrix composed of trigonometric functions of angles α _{2 /} and φ, of the form

From system (3) it follows that to determine the desired vector

from measurements of the values of the total drift ω, it is necessary to choose a set of angles α ₁ and α ₂ such that the vector of Fourier coefficients

and from the second vector

a vector of calibrated gyroscope care components would be found

The first equation of system (3) shows that to determine the vector

corresponding to a fixed value of the angle α ₂ , in the general case it is enough to take measurements in five different orientations of the rotary table along the angle α ₁ , we denote them -

We determine the optimal values of α $\genfrac{}{}{0ex}{}{\text{i}}{\text{1}}$ . We take as the optimality criterion the maximum of the absolute value of the determinant of the system of equations built on the matrix H ₁ for five different angles

kind of

The fulfillment of this optimality criterion, which is used further, corresponds to the minimal influence of the measuring noise on the calculation of the desired vector values.

Структура матрицы H₂(α₂,φ) во втором уравнении системы (3) такова, что оно распадается на два независимых уравнения. По значениям a₃, a₄ можно определить составляющие ухода ω_y , ω_xy, ω_yz. Для чего требуется произвести измерения не менее чем при двух значениях угла α₂ - α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ , α $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ , и пяти значениях угла α₁, задаваемых выражениями (5).It is easy to show that the determinant (4) does not depend on the choice of the first (initial) measuring position of the table α $\genfrac{}{}{0ex}{}{\text{1}}{\text{1}}$ , but it is determined only by the reorientation angles to the subsequent measuring positions and reaches a maximum on the next set of values of the angles α $\genfrac{}{}{0ex}{}{\text{i}}{\text{1}}$ :

The structure of the matrix H ₂ (α ₂ , φ) in the second equation of system (3) is such that it decomposes into two independent equations. The values of a ₃ , a ₄ can determine the components of the departure ω _y , ω _xy , ω _yz . Why do you need to measure at least two values of the angle α ₂ - α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ , α $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ , and five values of the angle α ₁ given by expressions (5).

 Obviously, the optimal orientation of the turntable in this case can be determined from the condition of the maximum absolute value of the next determinant.

Максимум в выражении (6) не зависит от выбора первого измерительного положения α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ , а определяется углом переориентации поворотного столам Δ₁ = α $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ -α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ и достигается при следующих значениях:

Главное значение угла в выражении (7) дает оптимальный набор для разделения ω_y, ω_xy, ω_yz при двух положениях поворотного стола по углу α₂:
α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ - любое, α $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ = α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2/}}$ + 90^o. (8).
Для разделения составляющих ухода ω_o, ω_x, ω_z, ω_xz, ω_yy, ω_zz по значениям a₁, a₂, a₅ двух измерительных положений по углу α₂ недостаточно, так как соответствующий определитель равен нулю при любых значениях углов α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ , α $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ :

Данное свойство матрицы H₂(α₂,φ) делает необходимым для разделения составляющих ухода ω_o, ω_x, ω_z, ω_xz, ω_yy, ω_zz проводить измерения в трех положениях поворотного стола по углу α₂ - α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ , α $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ , α $\genfrac{}{}{0ex}{}{\text{3}}{\text{2}}$ , при пяти положениях по углу α₁, задаваемых выражениями (5). Тогда оптимальная ориентация поворотного стола по углу α₂ может определяться из условия максимума абсолютного значения определителя:

Максимум в выражении (10) также не зависит от выбора первого измерительного положения

определяется только углами переориентации поворотного стола и достигается при следующих значениях углов переориентации:

Главные значения в выражениях (11) дают две группы оптимальных углов ориентации поворотного стола по углу α₂:

Первая группа углов не удовлетворяет условию максимума абсолютной величины определителя

выполнение которого необходимо для оптимального разделения всей группы составляющих ухода ω_o, ω_x, ω_z, ω_xz, ω_yy, ω_zz, а вторая группа удовлетворяет условию (13) и является искомым оптимальным набором углов. Данный набор углов α₂(α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ , α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ + 120^o, α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ + 240^o) не совпадает с полученным ранее набором α₂(α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ , α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ + 90^o) для калибровки составляющих ухода ω_y, ω_xy, ω_yz. Так как значение α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ - любое, то полная группа оптимальных ориентаций по углу α₂, обеспечивающих разделение составляющих ухода гироскопа с максимальным подавлением измерительного шума, будет задаваться четырьмя значениями, полученными объединением обоих результатов:

а набор оптимальных углов по α₁ естественно остается без изменений

(14)
Выражения (14) задают 20 измерительных положений поворотного стола, обеспечивающих с максимальной точностью калибровку всех 9 составляющих ухода гироскопа по предлагаемому способу. Эта программа измерений имеет значительную избыточность, которая может быть также использована для повышения точности калибровки.

The maximum in expression (6) does not depend on the choice of the first measuring position α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ , and is determined by the angle of reorientation of the rotary tables Δ ₁ = α $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ -α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ and is achieved with the following values:

The main value of the angle in expression (7) gives the optimal set for the separation of ω _y , ω _xy , ω _yz for two positions of the turntable in the angle α ₂ :
α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ - any, α $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ = α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2 /}}$ + 90 ^o . (eight).
To separate the care components ω _o , ω _x , ω _z , ω _xz , ω _yy , ω _zz according to the values a ₁ , a ₂ , a _5, two measuring positions in the angle α _{2 are} not enough, since the corresponding determinant is zero for any values of the angles α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ , α $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ :

This property of the matrix H ₂ (α ₂ , φ) makes it necessary to measure in three positions of the turntable along the angle α ₂ - α to separate the care components ω _o , ω _x , ω _z , ω _xz , ω _yy , ω _zz $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ , α $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ , α $\genfrac{}{}{0ex}{}{\text{3}}{\text{2}}$ , at five positions along the angle α ₁ defined by expressions (5). Then the optimal orientation of the rotary table in the angle α ₂ can be determined from the condition of the maximum absolute value of the determinant:

The maximum in expression (10) also does not depend on the choice of the first measuring position

it is determined only by the angles of reorientation of the turntable and is achieved with the following values of the angles of reorientation:

The main values in expressions (11) give two groups of optimal angles of orientation of the turntable in angle α ₂ :

The first group of angles does not satisfy the condition of the maximum absolute value of the determinant

the fulfillment of which is necessary for the optimal separation of the entire group of departure components ω _o , ω _x , ω _z , ω _xz , ω _yy , ω _zz , and the second group satisfies condition (13) and is the desired optimal set of angles. This set of angles α ₂ (α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ , α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ + 120 ^o , α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ + 240 ^o ) does not coincide with the previously obtained set of α ₂ (α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ , α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ + 90 ^o ) for the calibration of the components of the care ω _y , ω _xy , ω _yz . Since the value of α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ - any, then a full group of optimal orientations in the angle α ₂ , providing separation of the components of the gyroscope departure with the maximum suppression of the measuring noise, will be set by four values obtained by combining both results:

and the set of optimal angles with respect to α ₁ naturally remains unchanged

(fourteen)
Expressions (14) specify 20 measuring positions of the rotary table, which ensure with maximum accuracy the calibration of all 9 components of the gyroscope departure using the proposed method. This measurement program has significant redundancy, which can also be used to improve calibration accuracy.

доставляющих максимум компромиссному критерию:

являющемуся композицией критериев (6) и (10).Calibration using the maximum number of measurements, albeit optimal, is not always rational (for example, from the point of view of minimizing labor costs and calibration time). Obviously, the number of measuring positions can be reduced by reducing one value of the angle α ₂ in expression (14). Then for the optimal set of angles α ₂ it is advisable to take the second group of expression (12) or define a new group of angles

delivering a maximum of a compromise criterion:

which is a composition of criteria (6) and (10).

Зависимости (16) совместно с выражениями (5) определяют 15 субоптимальных измерительных положений поворотного стола:

Следует отметить, что реализация программы, задаваемой выражениями (17), обеспечивает отличие определителей det{ h₄₈, h₄₉} и det{h₅₄, h₅₅, h₅₆} от максимальных значений не более 7 и 4% соответственно, что практически незначительно. Тем самым обеспечивается мягкий компромисс между точностью калибровки и числом измерительных положений, то есть удалось сократить количество измерительных положений с 20 до 15 без какой-либо существенной потери в точности калибровки. Кроме того, использование симметричных наборов измерительных положений (17) и наборов, задаваемых выражением (5) и второй группой выражений (12), имеет практическую ценность и в том, что позволяет в значительной степени компенсировать или выявить влияние на уход гироскопа факторов, не учтенных в модели (1). Вместе с тем и данные наборы, задающие программы из 15 измерительных положений, избыточны.It is easy to show that the maximum in expression (15) does not depend on the choice of the first value of α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ and is achieved on the next main set of angles α $\genfrac{}{}{0ex}{}{\text{i}}{\text{2}}$ :

Dependencies (16) together with expressions (5) determine 15 suboptimal measuring positions of the turntable:

It should be noted that the implementation of the program defined by expressions (17) ensures that the determinants det {h ₄₈ , h ₄₉ } and det {h ₅₄ , h ₅₅ , h ₅₆ } differ from the maximum values of not more than 7 and 4%, respectively, which is practically insignificant . This ensures a soft compromise between calibration accuracy and the number of measuring positions, that is, it was possible to reduce the number of measuring positions from 20 to 15 without any significant loss in calibration accuracy. In addition, the use of symmetric sets of measuring positions (17) and sets specified by expression (5) and the second group of expressions (12) is of practical value in that it allows you to significantly compensate or reveal the effect on factors not taken into account in the gyroscope care in the model (1). At the same time, these sets defining programs of 15 measuring positions are redundant.

We define the minimum set of measuring positions that provides calibration of the gyroscope according to the proposed method. It is easy to see that if you rotate the turntable around the axis of the World by 90 ^o (α ₁ = 90 ^o ), then the projection of the acceleration vector of gravity on the input axis of the gyroscope will be zero (h _y = 0). Further controlling only the angle α ₂ , it is possible to realize the positions of the turntable in which the input axis and the axis of proper rotation of the gyroscope alternately coincide with the direction of gravity or have the opposite direction. In these positions, always two projections of a single overload will be equal to zero, which makes it possible to determine the four components of the gyroscope exit model (1).

α₂ = φ - π, входная ось и ось собственного вращения гироскопа ортогональны вектору ускорения силы тяжести

(h_y = 0, h_z = 0), а выходная ось занимает положения: по направлению вектора

α₂ = φ); противоположное направление к вектору

α₂ = φ - π). . Тогда выражение (1) принимает следующий вид:

(18)
Из уравнений (18) ясно определяются составляющие ухода ω_o и ω_x. При значениях углов

входная и выходная оси гироскопа ортогональны вектору

а ось собственного вращения занимает положения: по направлению вектора

противоположное направление к вектору

Из выражения (1) имеем:

Используя полученное из уравнений (18) значение ω_o, по уравнениям (19) легко определить ω_z и ω_zz.
Таким образом, в четырех положениях поворотного стола

при α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ = φ, α $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ = φ - π,

определяют четыре составляющих модели ухода гироскопа ω_o, ω_x, ω_z, ω_zz. . Тогда задача отыскания оставшихся составляющих ухода (ω_y, ω_z, ω_xy, ω_xz, ω_zz) может быть описана упрощенной системой векторно-матричных уравнений (3) вида:

где

- вектор калибруемых составляющих ухода гироскопа;

- вектор коррекции вектора коэффициентов Фурье

по откалиброванным значениям составляющих ухода гироскопа ω_o, ω_x, ω_z, ω_zz;

H $\genfrac{}{}{0ex}{}{\text{*}}{\text{2}}$ (α₂) - матрица размерности 5х5;

Матрица H $\genfrac{}{}{0ex}{}{\text{*}}{\text{2}}$ (α₂) при α_2/= 0 имеет следующий вид:

и обеспечивает на наборе углов вида (5) раздельное определение составляющих ухода ω_xz, ω_yy, ω_xy, а составляющие ухода ω_y и ω_yz находятся в линейной комбинации

Легко видеть, что для разделения полученной комбинации нужно использовать измерение в таком положении поворотного стола, когда h_z = 0, а n_y ≠ 0. Это положение может быть задано следующими углами α₁ = 0,

при которых h_x = sinφ, h_y = cosφ, n_z = 0 и выражение (1) имеет одно неизвестное ω_y и записывается так:

Вычисленное из уравнения (22) значение ω_y разрешает полученную ранее комбинацию

относительно последней неизвестной составляющей ухода ω_yz; в результате оказываются определенными все девять составляющих ухода гироскопа с использованием десяти измерительных положений.Indeed, from the drawing it follows that for

α ₂ = φ - π, the input axis and the axis of proper rotation of the gyroscope are orthogonal to the acceleration vector of gravity

(h _y = 0, h _z = 0), and the output axis occupies the positions: in the direction of the vector

α ₂ = φ); opposite direction to the vector

α ₂ = φ - π). . Then the expression (1) takes the following form:

(18)
From the equations (18), the departure components ω _o and ω _{x are} clearly determined. At angles

input and output axis of the gyroscope are orthogonal to the vector

and the axis of proper rotation occupies the position: in the direction of the vector

opposite direction to the vector

From the expression (1) we have:

Using the value of ω _o obtained from equations (18), it is easy to determine ω _z and ω _zz from equations (19).
Thus, in the four positions of the turntable

for α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ = φ, α $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ = φ - π,

determine the four components of the gyro care model ω _o , ω _x , ω _z , ω _zz . . Then the task of finding the remaining components of care (ω _y , ω _z , ω _xy , ω _xz , ω _zz ) can be described by a simplified system of vector-matrix equations (3) of the form:

Where

- the vector of calibrated components of the care of the gyroscope;

is the vector of correction of the vector of Fourier coefficients

according to the calibrated values of the components of the departure of the gyroscope ω _o , ω _x , ω _z , ω _zz ;

H $\genfrac{}{}{0ex}{}{\text{*}}{\text{2}}$ (α ₂ ) is a 5 × 5 matrix;

Matrix H $\genfrac{}{}{0ex}{}{\text{*}}{\text{2}}$ (α ₂ ) for α _{2 /} = 0 has the following form:

and provides a separate definition of the departure components ω _xz , ω _yy , ω _xy on the set of angles of the form (5), and the departure components ω _y and ω _yz are in a linear combination

It is easy to see that to separate the resulting combination, you need to use the measurement in the position of the turntable, when h _z = 0, and n _y ≠ 0. This position can be specified by the following angles α ₁ = 0,

for which h _x = sinφ, h _y = cosφ, n _z = 0 and expression (1) has one unknown ω _y and is written as follows:

The value of ω _y calculated from equation (22) allows the previously obtained combination

relative to the last unknown departure component ω _yz ; as a result, all nine components of the gyroscope exit are determined using ten measuring positions.

It should be noted that the accuracy of the gyroscope calibration by 10 of these measurement positions will be higher than that of the known calibration methods (see W. Wrigley, W. Hollister, W. Dernhard. Theory, design and testing of gyroscopes) not only because of the absence of restrictions on a model of the gyroscope error, but also due to the fact that the components of care are determined for α ₂ = 0 under similar conditions with known methods, and the components are determined from equations (18), (19), (22) at the maximum values of the corresponding determinants.

The analysis of the matrices H ₁ (α ₁ ), H ₂ (α ₂ , φ) shows that there are no nine measuring positions that allow one to separately determine all the components of the gyroscope departure by methods requiring orthogonality of the input axis of the gyroscope to the axis of the World during the entire program measurements, i.e. ten measurement positions are the smallest possible number.

 In the proposed method at 10 measuring positions, a complete calibration of all components of the gyroscope care is performed without imposing any restrictions on the gyroscope care model with an accuracy exceeding the calibration accuracy in the known methods.

 Thus, the proposed method for calibrating gyroscopes includes a single exposure of the studied gyroscope on the turntable with the input axis orthogonal to the axis of the world, setting several measurement positions by rotating the turntable around the axis of the world and around the input axis of the gyroscope at fixed angles, while the input axis of the gyroscope always remains orthogonal to the axis World and the number of different values of the angle of rotation around the input axis of the gyroscope - more than two, the measurement of the total departure in these measuring positions, determine the components of the gyroscope care from the totality of the data obtained from the measurements of the total care in the measuring positions of the turntable. The method provides a complete calibration of the gyroscope, reduces the complexity of the calibration by reducing the operations of exhibiting the gyroscope relative to the axis of the world, has no restrictions on the model of care of the gyroscope, increases the accuracy of calibration by making measurements in the optimal positions of the turntable and due to rational redundancy, can be implemented on a minimum set of measuring positions without loss of distinctive effective properties. Practical implementation of the proposed method can be carried out on a rotary table, providing the task of the measurement program for the proposed method, which can be built, for example, by using a cardan suspension of a triaxial gyrostabilizer.

Claims (3)

1. A method for calibrating gyroscopes, including setting the gyroscope on the turntable with the input axis orthogonal to the World axis, and the output axis or the axis of proper rotation along the World axis, setting measurement positions by rotating the turntable around the World axis, so that the input axis of the gyroscope is always orthogonal to the World axis, measuring the total departure of the gyroscope in each measuring position, determining the components of the departure of the gyroscope from the totality of information obtained during the measurement of the total departure of the gyroscope, characterized in the task of measuring positions by turning the turntable at fixed angles: around World axis by an angle α _1, measured from the meridian plane and around an input axis of the gyroscope by an angle α _2, measured from the plane orthogonal World axis so that coal α ₂ takes more two different meanings. 2. The method according to p. 1, characterized in that when setting the measuring positions, the angles α ₁ and α ₂ take the following values:

where α $\genfrac{}{}{0ex}{}{\text{1}}{\text{1}}$ , α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ - the initial values of the angles α ₁ and α _2, respectively;
α $\genfrac{}{}{0ex}{}{\text{i}}{\text{1}}$ , α $\genfrac{}{}{0ex}{}{\text{i}}{\text{2}}$ - the values of the angles α ₁ and α ₂ in other measuring positions. 3. The method according to p. 1, characterized in that when setting the measuring positions, the angles α ₁ and α ₂ take the following values:

α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ - any, α $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ = α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ +120 ^o , α $\genfrac{}{}{0ex}{}{\text{3}}{\text{2}}$ = α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ +240 ^o .
4. The method according to p. 1, characterized in that when setting the measuring positions, the angles α ₁ and α ₂ take the following values:

α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ - any, α $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ = α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ +125 ^o , 26 ′ α $\genfrac{}{}{0ex}{}{\text{3}}{\text{2}}$ = α $\genfrac{}{}{0ex}{}{\text{1}}{\text{2}}$ +250 ^o , 52 ′
5. The method according to p. 1, characterized in that 10 measuring positions are set by the following values of the angles α ₁ and α ₂ :

where φ is the latitude of the turntable installation site.