CN109782023B - Method for measuring high-order term coefficient of accelerometer through rotation modulation method - Google Patents
Method for measuring high-order term coefficient of accelerometer through rotation modulation method Download PDFInfo
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Abstract
The invention provides a method for measuring a high-order term coefficient of an accelerometer by a rotation modulation method, which comprises the following steps: (1) enabling the accelerometer to rotate at a constant speed at a first rotation frequency and collecting the output of the accelerometer as a first output; enabling the accelerometer to rotate at a constant speed at a second rotation frequency by changing the rotation frequency, collecting the output of the accelerometer as a second output, repeating the rotation for N times, and collecting N groups of accelerometer outputs under different rotation frequencies; (2) and (3) demodulating the corresponding output obtained in the step (1) by using the rotation frequency, performing low-pass filtering on the demodulated data, and fitting the low-pass filtered first-order frequency multiplication amplitude with respect to the rotation frequency to obtain a cross-coupling coefficient and a second-order nonlinear coefficient of the accelerometer. The invention utilizes the rotation modulation to modulate the high-order coefficient of the accelerometer to specific frequency, and then realizes the detection of the high-order coefficient of the high-precision accelerometer by changing the rotating speed and utilizing the dependency relationship between the high-order coefficient and the rotating speed.
Description
Technical Field
The invention belongs to the technical field of accelerometer testing, and particularly relates to a method for measuring a high-order term coefficient of an accelerometer by a rotation modulation method.
Background
The high-precision accelerometer is widely applied to the aspects of inertial navigation guidance, microseismic measurement, precision gravity measurement and the like at present, and the precision is one of key factors for determining the performance of an inertial system, so a large number of scientific researchers at home and abroad invest in the research and development work of the high-precision accelerometer, and in order to fully understand various performance parameters of the accelerometer, the test precision needs to be improved urgently.
The existing method for testing the performance parameters of the accelerometer mainly comprises a gravity field rolling method and a precision centrifugation method. The gravity field rolling method is relatively suitable for testing an accelerometer with the resolution of about 1 mu g, and uses the gravity acceleration of 1g on the earth surface as an excitation condition to incline different angles on a dividing head so as to excite each model item related to the acceleration and determine the model coefficient. Another commonly used method for measuring coefficients of higher order terms is precision centrifugation, in which an acceleration input with a high g value is provided to an input axis or a cross axis of an accelerometer by a precision centrifuge to excite the effect of the higher order terms. However, for a high-precision accelerometer with a resolution of ng magnitude, the range of the high-precision accelerometer is usually less than 1g, and the high-precision accelerometer reaches mg magnitude or even less, at this time, it is difficult to use a centrifuge to improve the effect of exciting a high-order term by an input acceleration, the precision of a dividing head often becomes a bottleneck factor for improving the test precision, and simultaneously, dynamic noise, environmental noise and the like of the precision centrifuge can become limiting factors for accurately measuring the high-order term coefficient of the accelerometer.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a method for measuring the high-order term coefficient of an accelerometer by a rotation modulation method, and aims to solve the problems that the existing accelerometer test method cannot realize the high-order term test of an ng-level accelerometer and is insensitive to environmental noise.
The invention can be applied to various high-resolution accelerometers, and is particularly suitable for testing the high-order items of the ng-grade accelerometer.
The invention provides a method for measuring a high-order term coefficient of an accelerometer by a rotation modulation method, which comprises the following steps:
(1) enabling the accelerometer to rotate at a constant speed at a first rotation frequency, and collecting the output of the accelerometer as a first output; enabling the accelerometer to rotate at a constant speed at a second rotation frequency by changing the rotation frequency, collecting the output of the accelerometer as a second output, repeating for N times, and collecting N groups of accelerometer outputs under different rotation frequencies, wherein N is an integer greater than or equal to 2;
(2) and (3) demodulating the corresponding output obtained in the step (1) by using the rotation frequency, performing low-pass filtering on the demodulated data, and fitting the low-pass filtered first-order frequency multiplication amplitude with respect to the rotation frequency to obtain a cross-coupling coefficient and a second-order nonlinear coefficient of the accelerometer.
The invention utilizes the rotation modulation to modulate the high-order coefficient of the accelerometer to specific frequency, and then realizes the detection of the high-order coefficient of the high-precision accelerometer by changing the rotating speed and utilizing the dependency relationship between the high-order coefficient and the rotating speed.
Further, before the step (1), the method further comprises the following steps: the accelerometer is arranged in a mode that a sensitive shaft is arranged along the rotation direction, an output shaft is arranged along the radial direction, and a pendulum shaft is perpendicular to the mounting table surface.
Further, in step (1), the sampling frequency at which the accelerometer output is collected is greater than the rotational frequency of the accelerometer.
Further, in step (2), the demodulation process specifically includes: different high-order item parameters are respectively demodulated through sine demodulation and cosine demodulation.
Further, the phase of the demodulated signal is aligned with the phase of the accelerometer output signal so that the sine and cosine signals in the output can be separated to separate out different higher order terms.
Still further, the cut-off frequency of the low-pass filtering is less than the rotation frequency of the accelerometer.
Further, step (3) is included after step (2): and (3) exchanging the output shaft of the accelerometer with a pendulum shaft, and repeating the steps (1) and (2) to obtain a cross coupling coefficient and a second-order nonlinear coefficient corresponding to the output shaft or the pendulum shaft of the accelerometer.
It should be noted that, when the output shaft of the accelerometer in step (1) is installed along the radial direction and rotates at a constant speed at the first rotation frequency, the cross-coupling coefficient and the second-order nonlinear coefficient corresponding to the pendulum shaft are obtained by exchanging the output shaft with the pendulum shaft in step (3).
When the pendulum shaft of the accelerometer in the step (1) is installed along the radial direction and rotates at a constant speed at the first rotation frequency, the output shaft and the pendulum shaft are exchanged in the step (3) to obtain the cross coupling coefficient and the second-order nonlinear coefficient corresponding to the output shaft.
Furthermore, in the step (3), the accelerometer rotates by 90 degrees around the sensitive shaft to realize the exchange of the output shaft and the pendulum shaft of the accelerometer, that is, the input accelerations on the output shaft and the pendulum shaft of the accelerometer during rotation are exchanged, the cross term of the sensitive shaft and the output shaft and the cross term of the sensitive shaft and the pendulum shaft are mutually exchanged on the input, and similarly, the second-order nonlinear term of the output shaft and the second-order nonlinear term of the pendulum shaft are mutually exchanged on the input, so that the corresponding coefficients of the output shaft and the pendulum shaft can be respectively tested by repeating the steps.
Compared with the prior art, the invention has the advantages that:
(1) the invention adopts a rotation-rotation speed dual modulation method, modulates output signals, environmental noise and turntable rotation noise to different frequencies by the modulation method, and only reserves target frequency (one frequency multiplication) by using a demodulation mode, namely only reserves the lower target signal and deducts the influence of the environmental noise and the turntable rotation noise, so that the anti-interference capability is strong;
(2) due to the noise limitation of the prior art, if the prior art is used for testing the high-order term of the ng-grade accelerometer, the requirement on a testing instrument is very high, and the invention can realize the test of the high-order term coefficient of the low-range high-precision accelerometer under the condition that the requirements on the environment and the performance of the turntable are relatively low.
Drawings
FIG. 1 is a flow chart of the operation of the present invention.
Fig. 2 shows the mounting of the accelerometer of the present invention.
FIG. 3 is a schematic diagram of a coordinate system and a rotation relationship according to the present invention.
FIG. 4 is a flow chart of data processing according to the present invention.
In the figure, 1 is an accelerometer, 2 is the directions of an input shaft (IA), an output shaft (OA) and a swing shaft (PA) of the accelerometer, 3 is a mounting table surface of a turntable, and 4 is the distance R from the center of mass of the accelerometer to the center of the turntable.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention utilizes the rotation modulation to modulate the high-order term coefficient of the accelerometer to specific frequency, then utilizes the dependency relationship between the high-order term coefficient and the rotation speed by changing the rotation speed to realize the detection of the high-order term coefficient of the high-precision accelerometer, and can effectively inhibit the error caused by environmental noise and accelerometer null shift.
The specific theoretical model involved in the invention is as follows: according to the test method of the single-axis pendulum type servo line accelerometer of the national military standard 1037A, the ng-grade accelerometer related by the invention is a pendulum type/flexible accelerometer, and the output of the pendulum type/flexible accelerometer can be represented by a model formula (1).
Wherein, K0Is the zero offset, K, of the accelerometer1Is a scale factor, K2Is a second order nonlinear coefficient, K5、K7Is a cross-axis second-order nonlinear coefficient, which respectively corresponds to the second-order nonlinear coefficient of the output shaft and the second-order nonlinear coefficient of the pendulum shaft, K4、K6、K8The coefficient is a cross coupling coefficient which respectively corresponds to a cross coupling coefficient of an input shaft and a pendulum shaft, a cross coupling coefficient of the input shaft and an output shaft and a cross coupling coefficient of the pendulum shaft and the output shaft, the nonlinear coefficient and the cross coupling coefficient are collectively called as a high-order term coefficient, and deltaPAnd deltaOIs the misalignment angle of the input axis relative to the input reference axis; a isI、aO、aPThe inputs applied to the accelerometer by the outside world along the input shaft, the output shaft and the pendulum shaft of the accelerometer respectively; k3For the cubic coefficient of the input acceleration, K has been ignored in this model3And other higher order coefficients.
When the accelerometer rotates on the plane with the inclination angle gamma, the input of the accelerometer on three axes is along with the rotation frequency frThere is a relationship: a isI＝gsinγsinθ，
aPGcos γ, where θ is 2 π frt is the angle formed by the sensitive axis of the accelerometer and the horizontal plane during rotation, and the output of the accelerometer under rotation modulation can be written by substituting the input of the accelerometer into formula (1):
through which it passes
And
in part can be known as K6The term, i.e. the cross-coupled term, and K5Terms, i.e. cross-axis second-order non-linear terms, which are each unique at 2 π frt is at sine-frequency multiplication and cosine-frequency multiplication and
a variable but a changed term. Obtaining a frequency multiplication amplitude U through sine and cosine demodulation and low-pass filtering, and obtaining a frequency multiplication amplitude U according to the amplitude U
Extracting coefficients in a frequency multiplication, including a cross-coupling coefficient K of the accelerometer6Cross axis of rotationSecond order nonlinear term K5By changing the installation mode of the accelerometer, the accelerometer rotates by 90 degrees around the sensitive axis, and the directions of the output shaft (O axis) and the pendulum shaft (P axis) of the accelerometer are exchanged, so that another group of cross coupling coefficients K can be obtained4Cross-axis second order nonlinear term K7。
The invention mainly aims at a test method of a high-order item of an ng-grade accelerometer, and no effective test method exists at home and abroad at present.
The method for measuring the high-order term coefficient of the accelerometer by the rotation modulation method specifically comprises the following steps:
(1) the accelerometer is arranged on a high-precision turntable, a sensitive shaft (IA) of the accelerometer is tangential to the turntable, an output shaft (OA) is radial to the turntable, and a swing shaft (PA) is perpendicular to the table surface of the turntable.
(2) And (3) enabling the accelerometer to rotate at a constant speed at a first rotating frequency, collecting the output of the accelerometer as a first output, changing the rotating frequency to enable the accelerometer to rotate at a constant speed at a second rotating frequency, collecting the output of the accelerometer as a second output, repeating the steps for N times, and collecting the outputs of N groups of accelerometers under different rotating frequencies, wherein N is more than or equal to 2.
(3) Demodulating the first output by using the first rotating frequency, obtaining a frequency multiplication amplitude under the first rotating frequency through low-pass filtering, demodulating the second output by using the second rotating frequency, obtaining a frequency multiplication amplitude under the second rotating frequency through low-pass filtering, and carrying out the processing method on the N groups of outputs. And fitting the first-order frequency multiplication amplitude under different rotation frequencies with respect to the rotation frequency to obtain coefficients related to a square term of the rotation frequency, namely a cross-coupling coefficient and a second-order nonlinear coefficient corresponding to the output shaft of the accelerometer, wherein the two parameters respectively correspond to results of sine demodulation and cosine demodulation.
(4) Changing the installation mode of the accelerometer, rotating the accelerometer by 90 degrees around the sensitive axis, exchanging the directions of the O axis and the P axis of the accelerometer, and repeating the steps (1) to (3) to obtain the cross coupling coefficient and the second-order nonlinear coefficient corresponding to the pendulum axis of the accelerometer.
The invention provides a method for measuring a high-order term coefficient of an accelerometer by a rotation modulation method. As shown in fig. 1, the specific method steps are as follows:
(1) the accelerometer is arranged on the table top of the high-precision turntable according to the installation mode shown in figure 2 to form a rigid whole, the high-precision turntable is mainly used for achieving the function of uniform rotation at different rotating speeds, and the slip ring and the circuit in the turntable can achieve the functions of transmitting and collecting signals of the accelerometer. And adjusting the base of the single-shaft turntable to be inclined at an angle gamma of 0.01 degrees with the horizontal plane, and rigidly connecting the base with a vibration isolation foundation.
The accelerometer is mounted in the way shown in fig. 2, the Input Axis (IA) of the accelerometer is tangential to the uniaxial turntable, the Output Axis (OA) is radial to the uniaxial turntable, and the distance between the sensitive mass of the accelerometer and the rotation center is denoted as R.
In FIG. 3, wherein OX is defined0Y0Z0Setting the sensitive axis of the accelerometer along OY for the initial mounting coordinate system of the accelerometer0Direction, output axis along OX0In the opposite direction of (OX)1Y1Z1Setting the axis of the single-axis turret around OX for the coordinate system of the base gamma rear accelerometer of the tilting single-axis turret1Tilt, OX2Y2Z2For accelerometers about a single-axis turntable axis of rotation OZ1The coordinate system after rotation has a rotation angle of 2 pi frt, wherein frFor the rotation frequency, t is the running time.
From the changing relationship between the coordinate systems, the coordinate system OX can be derived0Y0Z0To the coordinate system OX2Y2Z2The transformation of (a):
gravity on each axis of accelerometer (coordinate system OX)2Y2Z2) The component above is:
(2) setting the sampling frequency f of the accelerometer outputsSetting the rotation frequency f of the single-axis turntabler，frCan take different values, the sampling frequency fsMuch greater than the rotation frequency frFor example, set fs＝100Hz，fr＝[0.1,1]Hz。
(3) Enabling the accelerometer to start to rotate at a constant speed at a set rotation frequency, and outputting an output formula through the accelerometer:
the output of the accelerometer under rotational modulation can be written:
the rotation frequency is changed every t minutes until the set rotation frequency is completed.
(4) Through phase alignment, sine demodulation and cosine demodulation can be respectively carried out on the output signals of the accelerometer, and 2 pi f in the output of the accelerometer is screened outrt (including sine and cosine signals), low-pass filtering, with the cut-off frequency of the filter being much less than frThe 2 pi f related to sine demodulation and cosine demodulation under different rotating speeds can be obtained respectivelyrt is the amplitude U of one doubling of the frequency.
(5) Taking the result obtained in the step (4) as an example, the result after sine demodulation is utilized to demodulate 2 pi frA multiplied amplitude of t and the rotation frequency frFitting the dependency relationship between the two to obtain
The coefficient a of the term is the cross-coupling system of the accelerometerNumber K6As shown in fig. 4.
(6) And (3) rotating the accelerometer by 90 degrees around the sensitive axis, exchanging the directions of the output shaft of the accelerometer and the swing axis, and repeating the steps (1) to (5) to obtain a cross coupling coefficient and a second-order nonlinear coefficient corresponding to the other cross axis of the accelerometer.
The invention uses the scheme of rotation modulation to make the test experiment insensitive to the environmental noise, uses the scheme of variable rotating speed to separate the signal to be tested and the dynamic noise of the test instrument, simultaneously modulates the output signal of the accelerometer, and then uses sine demodulation and cosine demodulation to separate the nonlinear coefficient and the cross coupling coefficient of the accelerometer, namely the high-order item coefficient of the accelerometer.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (8)
1. A method for measuring the high-order coefficient of an accelerometer by a rotation modulation method is characterized by comprising the following steps:
(1) enabling the accelerometer to rotate at a constant speed at a first rotation frequency, and collecting the output of the accelerometer as a first output; enabling the accelerometer to rotate at a constant speed at a second rotation frequency by changing the rotation frequency, collecting the output of the accelerometer as a second output, repeating for N times, and collecting N groups of accelerometer outputs under different rotation frequencies, wherein N is an integer greater than or equal to 2;
(2) performing sine and cosine demodulation on the corresponding output obtained in the step (1) by using the rotation frequency, and screening out the 2 pi f in the accelerometer outputrA frequency-doubled signal of t, wherein frIs the rotation frequency, t is the running time;
and performing low-pass filtering on the demodulated data, and fitting the low-pass filtered first-order frequency multiplication amplitude with respect to the rotation frequency to obtain a cross-coupling coefficient and a second-order nonlinear coefficient of the accelerometer.
2. The method of claim 1, further comprising, prior to step (1): the accelerometer is arranged in a mode that a sensitive shaft is arranged along the rotation direction, an output shaft is arranged along the radial direction, and a pendulum shaft is perpendicular to the mounting table surface.
3. A method as claimed in claim 1 or 2, wherein in step (1), the accelerometer output is collected at a sampling frequency greater than the rotational frequency of the accelerometer.
4. The method according to claim 3, wherein in step (2), the demodulation process is specifically: different high-order item parameters are respectively demodulated through sine demodulation and cosine demodulation.
5. The method of claim 4, wherein the phase of the demodulated signal is aligned with the phase of the accelerometer output signal.
6. The method of claim 5, wherein the cut-off frequency of the low-pass filtering is less than the rotational frequency of the accelerometer.
7. The method of claim 1, further comprising step (3) after step (2): and (3) exchanging the output shaft of the accelerometer with a pendulum shaft, and repeating the steps (1) and (2) to obtain a cross coupling coefficient and a second-order nonlinear coefficient corresponding to the output shaft or the pendulum shaft of the accelerometer.
8. A method according to claim 7, wherein in step (3) the exchange of the output shaft of the accelerometer with the tilt axis is effected by rotating the accelerometer through 90 ° about the sensitive axis.
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| CN111638386A (en) * | 2020-05-25 | 2020-09-08 | 中国电子科技集团公司第二十六研究所 | Gravity field-based accelerometer scale factor nonlinearity testing method |
| CN112485331B (en) * | 2020-11-13 | 2021-09-28 | 西南交通大学 | Method for correcting influence of grain size on metal plastic damage measurement |
| CN113466492B (en) * | 2021-06-11 | 2022-07-19 | 华中科技大学 | Device and method for measuring accelerometer model parameter magnetic vector sensitivity |
| CN113777671B (en) * | 2021-08-10 | 2022-07-12 | 华中科技大学 | Magnetic field effect evaluation method, device and system of rotary gravity gradiometer |
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