CN100367004C - A precise decoupling test method for gyroscope scale factor and input axis misalignment angle - Google Patents

Abstract

A precise decoupling test method for gyroscope scale factor and input axis misalignment angle. First, install the gyroscope in state one, that is, keep the gyroscope OY axis parallel to the turntable surface and adjust the OZ axis to form an angle _θi with the turntable axis , give the input angular velocity in turn, test and record the average value of the gyroscope output when the turntable is stationary before turning, when the turntable is rotating forward, when it is stationary, when the turntable is reversed, and when it is stationary, change the θ of step (1) _i , repeat step (2); change the installation state of the gyroscope to state two, three, and four in turn, repeat steps (1)-(3); process the measured data to realize the scale factor of the gyroscope and the input axis Decoupling of misalignment angles. The invention ensures the correctness and accuracy of test values, reduces parameter errors, can be used to calibrate various gyroscopes and their inertial measurement units, and is especially suitable for microminiature, low-cost, low-precision MEMS gyroscopes, fiber optic gyroscopes and the like.

Description

A precise decoupling test method for gyroscope scale factor and input axis misalignment angle

technical field

The invention relates to an accurate decoupling test method for a scale factor of a gyroscope and an input axis misalignment angle, and belongs to the field of navigation, guidance and control.

Background technique

In the process of inertial navigation, the error caused by inertial devices usually accounts for more than 70% of the entire guidance error, which leads to higher and higher requirements for inertial devices. By improving the processing technology, the precision of the inertial device can be improved, but the cost is huge, and it brings great difficulties to mass production. Therefore, people pay more attention to the testing, calibration and compensation technology of inertial devices. Among them, inertial navigation testing technology is a new discipline developed on the basis of inertial navigation technology. It includes inertial navigation testing equipment, testing methods, and data processing technology. aspect. Through the inertial navigation test technology, people strive to accurately evaluate the performance and accuracy of the gyroscope, accurately test the relevant parameters, and improve the accuracy of the inertial device through error compensation measures.

In the gyroscope, the gyroscope scale factor and the gyroscope input shaft misalignment angle are two very critical parameters that need to be tested to improve the accuracy. The scale factor K refers to the ratio of the output voltage V of the gyroscope to the input angular velocity ω. Usually, the axis perpendicular to the installation reference plane of the gyroscope is called the input reference axis IR. As shown in Figure 1, the sensitive axis of the gyroscope is usually called the input axis. Axis IA, when the gyroscope rotates around this axis, will cause the maximum output voltage; the input axis misalignment angle δ is the angle between the input axis IA and the input reference axis IR. Usually the axes of the gyroscope are defined as follows: the OZ axis coincides with the input reference axis IR, OX and OY are perpendicular to each other in the gyroscope installation plane, and the positive directions of the three axes meet the requirements of OX×OY=IA.

Although the current test methods for inertial devices (especially gyroscopes) vary due to different test conditions, but in order to standardize the test standards, people in the industry usually refer to the IEEE gyroscope test specifications. In these test specifications, the scale factor test value is obtained from the rate experiment. At this time, the gyro input reference axis IR (coinciding with the OZ axis) is placed upwards, parallel to the rate turntable rotation axis (TI axis), as shown in Figure 2; When calculating the misalignment angle test value of the gyro input axis, the gyro input pump (still coincident with the OZ axis) is placed horizontally, and vertical to the rate turntable rotation axis (TI axis), as shown in Figure 3 (TI axis). It can be seen from the mechanics and kinematics principles involved in the gyroscope that in the above-mentioned test method, the data processing models of the scale factor and the misalignment angle of the input axis are respectively (taking the single-degree-of-freedom gyroscope as an example):

V＝V ₀ +K·ω·cosδ (1)

V′＝K·ω′· _sinδT (2)

In the formula:

V is the output voltage value of the gyroscope output shaft when the scale factor is tested, the unit is V;

V'—the output voltage value of the gyro output shaft when testing the misalignment angle of the input shaft, the unit is V;

V _0— the constant value drift of the gyro output shaft, the unit is V;

K—the scale factor of the gyroscope output shaft, the unit is V/(°/S);

ω is the input angular velocity of the turntable when the scale factor is tested;

ω′—the input angular velocity of the turntable when testing the misalignment angle of the input shaft;

δ—misalignment angle of gyroscope input shaft;

δ _T —the projection of the misalignment angle of the gyro input axis in the current test plane, where T=x or y;

It can be seen that the two parameters of gyroscope scale factor and gyroscope input shaft misalignment angle are coupled with each other, called $\left[\begin{array}{c}K\&Center\; Dot;\cos \mathrm{\δ}\\ K\&Center\; Dot;\sin \mathrm{\δ}\end{array}\right]$ is the coupling coefficient, which is a two-dimensional column vector. Using the experimental data obtained in the above experimental method, the scaling factor and the misalignment angle of the input axis cannot be separated in data processing. Considering that the traditional gyroscope is precision-made, expensive, high-precision, and the misalignment angle δ is very small, the above-mentioned test standard is approximately taken as:

cosδ≈1, _{sinδT≈δT (} 3)

For traditional gyroscopes, the introduced approximation error is not large, and the sacrificed navigation accuracy is small. Equations (1) and (2) can be simplified as:

V＝V ₀ +K·ω (4)

V′＝K·ω′· _δT (5)

Practice has proved that although the above test method brings approximate errors, in the inertial navigation system with high precision, the error value is small, and under certain application environments and requirements, it can basically meet the requirements.

However, since the 1980s, many tiny, low-cost, and low-precision inertial measurement devices have become popular, especially with the successful application of optoelectronic technology and micro/nano technology, the combination of MEMS technology, optoelectronic technology and inertial technology has brought A great change in inertial technology was brought about. For a time, fiber optic gyroscopes and MEMS gyroscopes received great attention. They are small in size, light in weight, low in cost, simple in structure, and convenient in application, and have great application prospects. However, their input axis misalignment angles are relatively large. For example, MEMS gyroscopes are generally packaged in patches, which need to be soldered to the circuit board in application, and can be used with other electronic components such as resistors and capacitors. The installation of the circuit board The accuracy is far lower than the installation accuracy of traditional gyroscopes. In particular, during the manual welding process, it will cause a large error in the parallelism and perpendicularity of the sensitive axis of the device, and some even reach more than 5°. Therefore, MEMS gyroscopes The input shaft misalignment angle is very large. At present, there are relatively few reports on the testing of micro-miniature, low-cost, and low-precision gyroscopes, and there is no unified and standardized testing method. Basically, the test standards for traditional gyroscopes are used in reference. Neglecting the approximate error value will bring great errors to the improvement of the accuracy of the gyroscope, the subsequent strapdown calculation and integrated navigation. Therefore, according to the data processing model represented by formula (4) and formula (5) to test Gyroscope, it seems very unscientific, it has the following disadvantages:

1. The scale factor K of the gyroscope calibrated by the traditional gyroscope test standard is not accurate. The K of the gyroscope tested is actually K cosδ, especially for low-precision fiber optic gyroscopes, quartz gyroscopes, and microsilicon gyroscopes. MEMS gyroscopes, etc., δ is generally a few degrees, or even a dozen degrees, and the error caused by cosδ is very large;

2. The value δ of the misalignment angle of the input axis of the gyroscope calibrated by the traditional gyroscope test standard is inaccurate, and the calculation of the projection δ _T of δ in the current test plane involves the value of K, and the disadvantage 1 shows that the K value is inaccurate , therefore, the calculated value of δ _T is also inaccurate; at the same time, the calculation of δ _T value involves sin _{δ T} ≈ δ _T , which will bring approximate errors, especially for low-precision fiber optic gyroscopes, quartz gyroscopes, and microsilicon MEMS gyroscopes. Instruments, etc., generally the misalignment angle δ is very large, and the resulting error will also be large;

3. In the traditional gyroscope test standard, it is necessary to calibrate the K value and δ value in two steps. The gyroscope calibration process is generally relatively long, and the K value and δ value are tested at different times. The test environment is such as temperature and humidity. , air pressure, etc., will also affect the experimental results.

Contents of the invention

The technical problem of the present invention is to overcome the shortcomings of the traditional method of testing the gyroscope scale factor and the input axis misalignment angle, and provide an accurate decoupling test method for the gyroscope scale factor and the input axis misalignment angle, and realize the two parameters The separation, and to ensure the correctness and accuracy of the test value, reduce the impact of parameter errors on navigation accuracy.

The technical solution of the present invention is: an accurate decoupling test method for the scale factor of the gyroscope and the misalignment angle of the input shaft, which is characterized in that the test process includes the following steps:

(1) Install the gyroscope so that the reference plane of the gyroscope and the turntable have an initial inclination angle θ _i , and when the gyroscope can be fixed on the turntable at different angles θ _i relative to the rotation axis of the turntable, keep the OY axis parallel to the turntable surface , this state is installation state one;

(2) Under the initial _θi angle of the step (1), determine the input angular velocity, test and record the turntable in turn before it rotates, when it is stationary, when the turntable is rotating forward, when it is stationary, when the turntable is reversed, when it is stationary The average value of the gyroscope output at time;

(3) change the gyroscope inclination angle θ _i value of described step (1), repeat the experiment of above-mentioned step (2);

(4) Change the installation state of the gyroscope in sequence to state two, that is, rotate the gyroscope 180° clockwise in its installation plane, state three, that is, rotate 90° clockwise again, and state four, that is, rotate 180° clockwise again Afterwards, repeat the experiment of above-mentioned steps (1)-(3);

(5) Process the above-mentioned measured data to obtain the values of the scale factor of the gyroscope and the misalignment angle of the input axis.

Wherein, the parameter model utilized in the data processing in the above-mentioned step (5) does not contain a small angle approximation error, jointly processes the data of the four states, and eliminates the fixture error. The specific data processing includes the following methods and steps:

(1) Collect the output data corresponding to the tilt angle and input angular velocity of each gyroscope under the above four installation states;

(2) Under the excitation of each input angular velocity, use the average value of the output data of the gyroscope collected when the turntable is rotating, and subtract the average value of the output data when the turntable is stationary before and after the input of the angular velocity, and use it as the gyroscope when calculating the applied parameter model output value for calculation;

(3) According to establishing the gyroscope input-output relationship model, adopting the least squares method to fit out at each tilt angle, the slope representation between the output voltage and the input angular velocity;

(4) Establish a linear matrix model about each gyroscope inclination angle, coupling coefficient and slope to represent the three, and fit the coupling coefficient value in the whole experiment;

(5) Decoupling calculation, separating the scale factor and input axis misalignment angle;

(6) Combine the calculation results of the four states to eliminate the fixture error and calculate the actual parameter value.

The principle of the present invention is: the relational expression between the gyroscope scale factor K and the input shaft misalignment angle δ strictly satisfies the formula (1), thus it can be known that the scale factor K and the input shaft misalignment angle δ are coupled to each other, by the formula (1) Transformation can be introduced:

K·cosδ=(VV ₀ )/ω (6)

If we artificially apply a set of different inclination angles θ _i to the gyroscope on the basis of the misalignment angle δ of the input axis, and give the angular velocity ω _j excitation while keeping the inclination angle θ _i unchanged, we can get :

K·cos(δ+θ _i )=(V _ij -V _0i )/ω _j (7)

The value (V _ij -V _0i )ω _j on the right side of the equal sign in formula (7) can be obtained by processing experimental data, where V _ij is the output voltage value of the gyro output shaft when the gyro tilt angle is θ _i and the turntable angular velocity is ω _j , $V_{0i}=\frac{1}{J}\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{V}_{\mathrm{ij}}-\frac{K}{J}\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{\mathrm{\ω}}_{\mathrm{ij}},$ It is the fitting zero position corresponding to the tilt angle θ _i of the gyroscope. At this time, the slope between the corresponding output voltage V _ij and the input angular velocity ω _j is represented by the letter "K _i ", then K _i is:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}$

$<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}$

$<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& <span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\end{array}\right]<span\; class="notranslate">\; \&Center\; Dot;</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}\\ \mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}\end{array}\right]$

in, $\left[\begin{array}{c}K\&CenterDot;\cos \mathrm{\&delta;}\\ K\&Center\; Dot;\sin \mathrm{\&delta;}\end{array}\right]$ is the coupling coefficient between the scale factor K of the gyroscope and the misalignment angle δ of the input axis, considering all the cases of applying the tilt angle _θi , there are n, and we get:

$\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ \mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; m</span>}& \mathrm{<span\; class="notranslate">\; m</span>}\\ \mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\end{array}\right]<span\; class="notranslate">\; \&CenterDot;</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}\\ \mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; m</span>}\\ {\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

make:

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}\\ \mathrm{<span\; class="notranslate">\; m</span>}& \mathrm{<span\; class="notranslate">\; m</span>}\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ \mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; m</span>}& \mathrm{<span\; class="notranslate">\; m</span>}\\ \mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\end{array}\right]$

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}\\ \mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}\end{array}\right]$

$\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; m</span>}\\ {\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}\end{array}\right]$

but

HX=Z (10)

Fitting by least square method:

X＝(H ^T H) ^-1 H ^T Z (11)

So far, the scale factor K and the input shaft misalignment angle δ can be decoupled to determine the values of K and δ:

$\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arctan</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}}{\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arctan</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>\sqrt{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\sqrt{{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

The above is the mathematical principle of the decoupling of the two parameters, the scaling factor K and the input shaft misalignment angle δ, and is also the theoretical basis for designing experiments.

However, in practical applications, as shown in Figure 4, it is not known which direction the actual input axis misalignment angle δ deviates relative to the input reference axis before the experiment, and it is difficult to make the gyroscope tilt angle θ _i just misalign along the input axis The direction of the angle δ is superimposed. Therefore, in the actual experiment, arbitrarily select a coordinate system on the gyroscope, it is generally recommended to take the axes of the gyroscope to form a coordinate system: the OZ axis coincides with the input reference axis IR, OX and OY are perpendicular to each other in the gyroscope installation plane, And the positive directions of the three axes satisfy OX×OY=IA. Then, as shown in Figure 4, project the misalignment angle δ of the input axis of the gyroscope onto two vertical coordinate planes XOZ and YOZ to obtain the projection angles δ _x and δ _y respectively, and the two projection angles can be determined from the coordinate system The directions of δ _x and δ _y , according to the decoupling principle of the scale factor and the misalignment angle of the input axis, superimpose the gyroscope tilt angle θ _i on the directions of the two projection angles δ _x and δ _y respectively, and the scale can be respectively The factor K is decoupled from the projection angle δ _x , the scale factor K is decoupled from the projection angle δ _y , and finally the gyro input axis misalignment angle δ is calculated according to the two projection angles δ _x and δ _y ; meanwhile, in order to effectively eliminate the fixture error, After testing the projection angle, it is necessary to rotate the gyroscope 180° to repeat the test, and add the two results to eliminate the fixture error.

Therefore, in the present invention, it is generally necessary to test four states, define the gyroscope installation reference plane to form a certain inclination angle with the turntable surface, and keep the OY axis parallel to the turntable surface, which is state one, and rotate the gyroscope 180 degrees clockwise in its installation plane ° is state two, then rotate 90° clockwise to be state three, and then rotate 180° clockwise to be state four, and set the scaling factors corresponding to the first, second, third, and fourth states to be K _one , K _two , K _three , K _four input axis misalignment angles are δ _one , δ _two , δ _three , δ _fout , then finally calculate the value of the gyroscope scale factor K:

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; one</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; two</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; three</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; four</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 14</span>}<span\; class="notranslate">\; )</span>$

Calculate the value of the gyroscope input axis misalignment angle δ: as shown in Figure 4, the projection of the gyroscope input axis misalignment angle δ in the XOZ plane is δ _x , and the projection in the YOZ plane is δ _y , then:

${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; one</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; two</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; there</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; four</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

Then the final value of the misalignment angle δ of the gyroscope input axis can be obtained as:

$\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arctan</span>}<span\; class="notranslate">\; (</span>\sqrt{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; tan</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; tan</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

The advantages of the present invention compared with existing testing technology are:

(1) The data processing model used in the present invention has not undergone small-angle approximation, the relationship between parameters is strict, and does not contain approximation errors, which avoids the errors caused by cosδ≈1 and sinδ≈δ, and the parameters tested have high precision . It is especially suitable for gyroscopes with low precision, such as micro-miniature, low-cost silicon micro-gyroscopes, quartz gyroscopes, low-precision fiber optic gyroscopes, etc.

(2) The experiment uses the four installation states of the gyroscope, which can effectively eliminate the positioning error of the fixture.

(3) This method is highly operable, and can simultaneously decouple and calculate the two parameters of the scale factor K and the input shaft misalignment angle δ in one experiment, which saves the preparation work and time for the experiment, and ensures that the K value and δ The test environment of the value such as temperature, air pressure, humidity, etc. is the same.

Description of drawings

Fig. 1 is the stipulation schematic diagram of each axis of gyroscope and input axis misalignment angle in the test of the present invention;

Figure 2 is a schematic diagram of the installation of the gyroscope when the IEEE standard tests the scale factor;

Figure 3 is a schematic diagram of the installation of the gyroscope when the IEEE standard tests the input shaft misalignment angle;

Fig. 4 is the installation schematic diagram of gyroscope when testing scale factor and input shaft misalignment angle of the present invention;

Fig. 5 is a test flow chart of the present invention.

Detailed ways

Concrete implementation method of the present invention, in conjunction with Fig. 4, Fig. 5, describe in detail as follows:

This test method includes two parts: turntable experiment and data processing. The axes of the gyroscope are specified as follows: the OZ axis coincides with the input reference axis IR, and OX and OY are perpendicular to each other in the gyroscope installation plane. Generally, OX is parallel to the output axis, and the positive directions of the three axes satisfy the requirement of OX×OY=IA Regulation;

The turntable experiment of this test method can use a three-axis turntable or a single-axis rate turntable with equipment that can provide an inclination angle. The preparation work includes the following: The ambient temperature is required to be within 15-35°C and kept relatively stable. No more than ±2°C, relative humidity between 20% and 80%, and no abnormal atmospheric pressure; the test bench is required to be installed on an independent foundation, with precise geographic latitude angle and geographic north reference; the vibration frequency and The amplitude and the magnetic field of the environment should meet the requirements of the tested specifications. The gyroscope is installed in the jig on the test turntable, and the positioning accuracy in each test is guaranteed by the accuracy of the test workbench and the installation jig. The axis of the turntable is parallel to the vertical line of the ground, the alignment accuracy is within several angular minutes, and the gyroscope can be fixed on the turntable by a mounting fixture. If the turntable is a single-axis turntable, the installation fixture has the following functions: ① It can fix the gyroscope on the turntable; ② It can adjust the clamp relative to the turntable shaft within a considerable range, such as 90°. angle θ _i , ③ the fixture can rotate 90° in the gyroscope installation plane, repeating the functions of the ① and ② steps; if the turntable is a two-axis or three-axis turntable, only the fixture is needed to fix the gyroscope on the turntable Yes, the adjustment of the inclination angle θ _i is realized by the inner frame of the turntable. The specific steps of the turntable experiment are as follows:

(1) To install the gyroscope, use a single-axis turntable and a fixture or a three-axis turntable to make the gyroscope installation reference plane and the turntable surface form an inclination angle of _θi = 5°, and make the gyroscope rotate at different angles θ with respect to the turntable rotation axis. _i is fixed on the turntable, when θ _i changes, keep the OY axis parallel to the turntable surface, and define this state as state one;

(2) Set the sampling interval time and sampling times, turn on the power of the gyroscope, and warm up for 20 minutes. The test data can only be started after the working state of the gyroscope is stable. Keep the gyroscope in the working state throughout the experiment until the experiment Power off only after the end;

(3) Select the value of θ _i . Generally, θ _i should be greater than 5° and less than 75°. When θ _i is small, the value of θ _i should be denser, that is, the interval of _{θ i should} be smaller. θ _i should be sparser, that is, the interval of θ _i is larger, usually take 9 values of θ _i ;

(4) Calculate the maximum input angular velocity ω _max that the gyroscope can withstand = ω _m /cosθ _i , where ω _m is the measuring range of the gyroscope. Select the input angular velocity ω _j between the negative maximum input angular velocity (-ω _max ) and the positive maximum input angular velocity (+ω _max ). Generally, when the speed is low, the selection is denser, and when the speed is high, The selection should be sparse. Within the range of input angular velocity in forward rotation and reverse rotation direction, generally no less than 11 angular velocity gears are selected, including the maximum input angular velocity that the gyroscope can withstand;

(5) Before the turntable rotates, test the average value of the gyroscope output when the turntable is stationary; when the turntable rotates forward, test and record the output of the gyroscope, stop rotating, and test the average value of the output when the turntable is stationary; when the turntable is reversed, test and record the output of the gyroscope , stop, and test the average value of the output at rest. The input angular velocity of the turntable changes from small to large;

(6) Calculate the average value of the output of the gyroscope when the turntable is stationary before and after the test of each input angular velocity, and remove it from the average output value of the gyroscope corresponding to the input angular velocity, and use it as the gyroscope used in data processing output the value and save it;

(7) Change the value of θ _i , repeat step 4 to step 8;

(8) Rotate the gyroscope 180° clockwise in its installation plane, and fix the gyroscope on the turntable at different angles _θi relative to the rotation axis of the turntable, while keeping the OX axis parallel to the turntable surface, define this state as State 2, repeat steps 4 to 9;

(9) Rotate the gyroscope 90° clockwise in its installation plane, and make the gyroscope fixed on the turntable at different angles _θi relative to the turntable rotation axis, while keeping the OY axis parallel to the turntable surface, define this state as State three, repeat steps 4 to 9;

(10) Rotate the gyroscope 180° clockwise in its installation plane, and fix the gyroscope on the turntable at different angles _θi relative to the rotation axis of the turntable, while keeping the OX axis parallel to the turntable surface, define this state as State four, repeat steps 4 to 9;

(11) Carry out data processing, and accurately calculate the values of the gyroscope scale factor K and input axis misalignment angle δ according to the recorded gyroscope's different inclination angles θ _i , output voltage V _ij and input angular velocity ω _j .

After data collection, use computer to realize the specific implementation method of data processing algorithm. In combination with Fig. 4 and Fig. 5, the steps of data processing are described in detail as follows:

(1) collecting data corresponding to the first state;

(2) Collect data packets corresponding to the first inclination angle θ _i in the current state; (3) Calculate the average value of the gyroscope output _at the jth input angular velocity ω _ij under the current inclination angle θ i

$\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}}\underset{\mathrm{<span\; class="notranslate">\; P</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; jP</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; )</span>$

In the formula:

V _jp -- the Pth output value of the gyroscope;

n - the number of samples.

(4) Add the average value of the gyroscope output at the beginning of the test to the average value of the gyroscope output at the end of the test to determine the average value of the gyroscope output when the turntable is stationary:

$\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; +</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 19</span>}<span\; class="notranslate">\; )</span>$

In the formula:

--转台静止时，陀螺仪输出的平均值；

--When the turntable is stationary, the average value of the output of the gyroscope;

--转台转动之前静止时，陀螺仪输出的平均值；

--The average value of the output of the gyroscope when the turntable is at rest before turning;

--The average value of the output of the gyroscope when the turntable is stationary after rotation;

(5) Use the average value of the output to subtract the average value of the gyroscope output when the turntable is stationary, and calculate the output value V _ij of the gyroscope when it is sensitive to the jth input angular velocity ω _ij under the inclination angle θ _i ;

${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 20</span>}<span\; class="notranslate">\; )</span>$

In the formula:

--为第j个输入角速度ω_j时陀螺仪的输出值(6)建立的陀螺仪输入输出关系模型如下：

--The gyroscope input-output relationship model established for the output value (6) of the gyroscope when the jth input angular velocity ω _j is as follows:

V _ij =K _i ·ω _ij +V _0i (21)

In the formula:

K _i -- the slope of the output voltage corresponding to the inclination angle θ _i and the input angular velocity

V _0i -- the fitting zero position corresponding to the tilt angle θ _i of the gyroscope

The least square method is used to fit the _slope K _i between the corresponding output voltage V _ij and the input angular velocity ω _ij at the current inclination angle θ i, that is, the ratio. Calculate K _i and V _0i by least square method:

${\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; J</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; J</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; J</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; J</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}{\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; J</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; J</span>}}{<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; J</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; two</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; J</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; J</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; K</span>}}{\mathrm{<span\; class="notranslate">\; J</span>}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; J</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; three</span>}<span\; class="notranslate">\; )</span>$

In the formula:

J--Input the number of angular velocities

(7) Collect data packets corresponding to other inclination angles θ _i , repeat steps 3 to 6, and use the least square method to fit the relationship between the corresponding output voltage V _ij and input angular velocity ω _j at each inclination angle θ _{i .} The slope between represents K _i ;

(8) It is considered that the real scale factor K of the gyroscope itself and the value of the misalignment angle δ of the input axis are stable. According to the derivation calculation formula: K _i = k·cosδ· _cosθi -k·sinδ· _sinθi , by the steps 7 Each slope obtained represents K _i , and a matrix composed of trigonometric function pairs [cosθ _i -sinθ _i ] using each inclination angle θ _i is established $h=\left[\begin{array}{cc}{h}_{11}& h_{12}\\ h_{12}& h_{\mathrm{twenty\; two}}\\ m& m\\ h_{\mathrm{no}1}& h_{\mathrm{no}2}\end{array}\right]=\left[\begin{array}{cc}\cos {\mathrm{\&theta;}}_1& -\sin {\mathrm{\&theta;}}_1\\ \cos {\mathrm{\&theta;}}_2& -\sin {\mathrm{\&theta;}}_2\\ m& m\\ \cos {\mathrm{\&theta;}}_{\mathrm{no}}& -\sin {\mathrm{\&theta;}}_{\mathrm{no}}\end{array}\right],$ Scale factor and input shaft misalignment angle coupling coefficient $x=\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]=\left[\begin{array}{c}K\&Center\; Dot;\cos \mathrm{\&delta;}\\ K\&CenterDot;\sin \mathrm{\&delta;}\end{array}\right],$ The slope indicates the matrix composed of $Z=\left[\begin{array}{c}{K}_1\\ K_2\\ m\\ K_{\mathrm{no}}\end{array}\right]$ The linear matrix model between the three was fitted by the least squares method to show the $x=\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]=\left[\begin{array}{c}K\&CenterDot;\cos \mathrm{\&delta;}\\ K\&Center\; Dot;\sin \mathrm{\&delta;}\end{array}\right]$ The stable value of ; (9) by $\left[\begin{array}{c}K\&Center\; Dot;\cos \mathrm{\&delta;}\\ K\&Center\; Dot;\sin \mathrm{\&delta;}\end{array}\right]$ The value of , solve the equation to calculate the value of the scaling factor K _one and the input shaft misalignment angle δ _one corresponding to the first state;

(10) Collect the data of state two, repeat step 2 to step 9, solve the equation and calculate the value corresponding to the scaling factor K _two of the first state and the input shaft misalignment angle δ _two ;

(11) collect the data of state three, repeat step 2 to step 9, solve the equation and calculate the value corresponding to the scaling factor K _three of the first state and the input shaft misalignment angle δ _three ;

(12) Collect the data of state four, repeat step 2 to step 9, solve the equation and calculate the value corresponding to the scale factor K _four of the first state and the input shaft misalignment angle δ _four ;

(13) Calculate the value of the gyroscope scale factor K:

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; one</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; two</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; three</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; four</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 14</span>}<span\; class="notranslate">\; )</span>$

(14) Calculate the value of the gyroscope input axis misalignment angle δ: as shown in Figure 4, the projection of the gyroscope input axis misalignment angle δ in the XOZ plane is δ _x , and the projection in the YOZ plane is δ _y , then

${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; one</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; two</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; three</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; four</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

Then the final value of the gyroscope input axis misalignment angle δ is:

$\mathrm{<span\; class="notranslate">\; \&delta;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arctan</span>}<span\; class="notranslate">\; (</span>\sqrt{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; tan</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; tan</span>}{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

Claims (2)

1. a kind of accurate decoupling test method of gyroscope scale factor and input shaft misalignment angle, it is characterized in that: test process comprises the steps: (1) Install the gyroscope so that the reference plane of the gyroscope and the turntable have an initial inclination angle θ _i , and when the gyroscope can be fixed on the turntable at different angles θ _i relative to the rotation axis of the turntable, keep the OY axis parallel to the turntable surface , this state is installation state one; (2) Under the initial _θi angle of the step (1), determine the input angular velocity, test and record the turntable in turn before it rotates, when it is stationary, when the turntable is rotating forward, when it is stationary, when the turntable is reversed, when it is stationary The average value of the gyroscope output at time; (3) change the gyroscope inclination angle θ _i value of described step (1), repeat the experiment of above-mentioned step (2); (4) Change the installation state of the gyroscope in sequence to state two, that is, rotate the gyroscope 180° clockwise in its installation plane, state three, that is, rotate 90° clockwise again, and state four, that is, rotate 180° clockwise again Afterwards, repeat the experiment of above-mentioned steps (1)-(3); (5) process the above-mentioned measured data, and obtain the value of the scale factor of the gyroscope and the misalignment angle of the input shaft; Wherein, the parameter model utilized in the data processing in step (5) does not contain small angle approximation errors, and joint processing of the data of the four states can eliminate fixture errors. The data processing specifically includes the following steps: (a) Collect the output data corresponding to the tilt angle and input angular velocity of each gyroscope under the above four installation states; (b) Under the excitation of each input angular velocity, use the average value of the output data of the gyroscope collected when the turntable is rotating, and subtract the average value of the output data when the turntable is stationary before and after the input of the angular velocity, and use it as the gyroscope when calculating the parameter model output value for calculation; (c) According to the gyroscope input-output relationship model, the slope between the output voltage and the input angular velocity is expressed at each tilt angle by using the least squares method; (d) Establish a linear matrix model about each gyroscope tilt angle, coupling coefficient, and slope representation among the three, and fit the coupling coefficient value in the whole experiment; (e) Decoupling calculations to separate the scale factor and input axis misalignment angle; (f) Combining the calculation results of the four states, eliminating the fixture error, and calculating the actual parameter value. 2. The accurate decoupling test method of a kind of gyroscope scale factor and input axis misalignment angle according to claim 1, it is characterized in that: described gyroscope tilt fixing method is: utilize inclined-plane fixture, make gyroscope Tilt and fix on a single-axis turntable to rotate; or fix the gyroscope on a three-axis turntable, and then use the inner frame of the three-axis turntable to tilt the gyroscope and rotate around the rotation axis of the outer frame of the three-axis turntable.

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