CN112698055B - Parameter calibration method of accelerometer on precision centrifuge - Google Patents

Parameter calibration method of accelerometer on precision centrifuge Download PDF

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CN112698055B
CN112698055B CN202110313204.0A CN202110313204A CN112698055B CN 112698055 B CN112698055 B CN 112698055B CN 202110313204 A CN202110313204 A CN 202110313204A CN 112698055 B CN112698055 B CN 112698055B
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coordinate system
accelerometer
error
axis
shaft
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CN112698055A (en
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王常虹
夏红伟
刘庆博
任顺清
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Shenrui Technology Beijing Co ltd
Harbin Institute of Technology
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Shenrui Technology Beijing Co ltd
Harbin Institute of Technology
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    • G01—MEASURING; TESTING
    • G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
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Abstract

The invention discloses a parameter calibration method of an accelerometer on a precision centrifuge, which comprises the following steps: acquiring each static error and each dynamic error of a precision centrifuge, establishing a coordinate system according to the structure of the precision centrifuge, and calculating a pose error under the coordinate system according to each static error and each dynamic error; driving a main shaft of the precision centrifuge to rotate at a uniform angular velocity so as to generate a centripetal acceleration calibration accelerometer, and calculating specific force distribution of the centripetal acceleration, the gravitational acceleration and the Coriolis acceleration based on the pose error in the coordinate system so as to determine an accelerometer error model; and outputting the indication of six symmetrical positions of the accelerometer in three different installation modes, and calibrating a high-order term error coefficient in an accelerometer error model expression by using an addition and subtraction element method. The method can effectively improve the calibration precision of the high-order error model coefficient of the quartz accelerometer.

Description

Parameter calibration method of accelerometer on precision centrifuge
Technical Field
The invention relates to the field of centrifuge calibration, in particular to a parameter calibration method of an accelerometer on a precision centrifuge.
Background
The literature, "optimization design of accelerometer precision centrifuge test" analyzes the actual measurement noise characteristic of the accelerometer during precision centrifuge test, and indicates that the traditional optimization design method, namely the saturation D optimal test design, has the problem of engineering applicability on the basis. And then, in order to improve the applicability of the saturated D optimal experimental design and consider the compromise relationship between the experimental cost and the precision, a D optimal improved experimental design scheme is provided. According to the scheme, the saturated D optimal test spectrum points are used as basic spectrum points, other spectrum points are uniformly inserted among the basic spectrum points to reduce the influence of input acceleration deviation, the measures of the basic spectrum points and newly added spectrum points are distributed through a weighting method, and the weight is selected according to actual noise characteristics. Although the literature, "optimization design of accelerometer precision centrifuge test" performs a specific calibration test on a quartz accelerometer on a precision centrifuge, the influence of centrifuge errors on the calibration precision of error model coefficients is not considered, which may introduce additional calibration errors, and the error model coefficients of the accelerometer identified in the literature are fewer.
The document 'analysis of error calibration precision of a precision centrifuge to a quartz accelerometer' analyzes each error source of the centrifuge, accurately calculates the generated centripetal acceleration by a homogeneous transformation method, gives components of the centripetal acceleration, the gravitational acceleration and the Coriolis acceleration under an accelerometer coordinate system, and deduces a precise expression of the input acceleration of the tested accelerometer. A10-position testing method is adopted to identify the high-order coefficient of the error model, and the relationship between the calculated value of the error model coefficient and the error of the centrifuge is emphatically discussed. But quadratic error coefficient
Figure 103085DEST_PATH_IMAGE001
And cubic error coefficient
Figure 489067DEST_PATH_IMAGE002
、
Figure 940908DEST_PATH_IMAGE003
The identification is not obtained, and known dynamic and static errors are needed to correct and compensate the identification result, so that various errors of the centrifuge cannot be avoided.
Disclosure of Invention
In view of this, the present invention provides a method for calibrating parameters of an accelerometer on a precision centrifuge, including:
acquiring each static error and each dynamic error of a precision centrifuge, establishing a coordinate system according to the structure of the precision centrifuge, and calculating a pose error under the coordinate system according to each static error and each dynamic error;
driving a main shaft of the precision centrifuge to rotate at a uniform angular velocity so as to generate a centripetal acceleration calibration accelerometer, and calculating specific force distribution of the centripetal acceleration, the gravitational acceleration and the Coriolis acceleration based on the pose error in the coordinate system so as to determine an accelerometer error model;
and outputting the indication of six symmetrical positions of the accelerometer in three different installation modes, and calibrating a high-order term error coefficient in an accelerometer error model expression by using an addition and subtraction element method.
The invention relates to a parameter calibration method of an accelerometer on a precision centrifuge, which provides a precise expression of the input specific force of the centrifuge on the basis of analyzing various dynamic and static error sources of the precision centrifuge; by combining an accelerometer error model and utilizing an addition and subtraction element method to calibrate a high-order term error coefficient in an accelerometer error model expression, the dynamic error and the static error of the centrifuge can be completely eliminated by monitoring and compensating a dynamic misalignment angle and a dynamic radius under the condition that the error of the centrifuge is stable, and the calibration precision of the high-order error model coefficient of the quartz accelerometer can be effectively improved.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a schematic view of a precision centrifuge according to the present invention.
FIG. 2 is a schematic diagram of the coordinate systems of the precision centrifuge of the present invention.
Fig. 3 shows 6 symmetrical position combinations of the accelerometer of the present invention in 3 different mounting modes.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
It should be noted that, in the case of no conflict, the features in the following embodiments and examples may be combined with each other; moreover, all other embodiments that can be derived by one of ordinary skill in the art from the embodiments disclosed herein without making any creative effort fall within the scope of the present disclosure.
It is noted that various aspects of the embodiments are described below within the scope of the appended claims. It should be apparent that the aspects described herein may be embodied in a wide variety of forms and that any specific structure and/or function described herein is merely illustrative. Based on the disclosure, one skilled in the art should appreciate that one aspect described herein may be implemented independently of any other aspects and that two or more of these aspects may be combined in various ways. For example, an apparatus may be implemented and/or a method practiced using any number of the aspects set forth herein. Additionally, such an apparatus may be implemented and/or such a method may be practiced using other structure and/or functionality in addition to one or more of the aspects set forth herein.
As shown in figure 1, the precision centrifuge is provided with 3 shafting of a main shaft, a horizontal shaft and an azimuth shaft, wherein the 3 shafting have the precision position function, and the shaft end of the horizontal shaft is provided with a 360-tooth multi-tooth dividing plate which can be used for
Figure 601696DEST_PATH_IMAGE004
The precision of the positioning device is positioned to 360 positions, the main shaft system and the azimuth shaft system have the function of precise angular rate, and when the main shaft rotates in the direction of the azimuth shaft system
Figure 884910DEST_PATH_IMAGE005
At a working radius while rotating at a uniform angular rate
Figure 674749DEST_PATH_IMAGE006
Will produce
Figure 145045DEST_PATH_IMAGE007
Centripetal acceleration of (2).
The static error source of the centrifuge mainly comprises the two-dimensional verticality error of the main shaft axis
Figure 812787DEST_PATH_IMAGE008
Perpendicularity of horizontal shaft axis and main shaft axis
Figure 747245DEST_PATH_IMAGE009
Degree of intersection
Figure 209450DEST_PATH_IMAGE010
Horizontal axis and squarePerpendicularity of axis of position shaft
Figure 167042DEST_PATH_IMAGE011
Degree of intersection
Figure 372895DEST_PATH_IMAGE012
And initial zero error of azimuth axis
Figure 161859DEST_PATH_IMAGE013
Perpendicularity of working base plane for installing inertia instrument to axis of azimuth shaft
Figure 60545DEST_PATH_IMAGE014
Accelerometer mounting datum attitude error
Figure 505433DEST_PATH_IMAGE015
Eccentricity error
Figure 750863DEST_PATH_IMAGE016
And initial nulling error
Figure 659913DEST_PATH_IMAGE017
The angular position errors of the three axes of the main shaft, the horizontal shaft and the azimuth shaft are respectively
Figure 463921DEST_PATH_IMAGE018
And the like. Fig. 1 and 2 show a schematic diagram of the centrifuge and the corresponding coordinate system established.
The dynamic error source of the centrifuge mainly comprises the radial rotation error of the main shaft
Figure 661684DEST_PATH_IMAGE019
Axial play
Figure 943761DEST_PATH_IMAGE020
And rotation error of inclination angle
Figure 910580DEST_PATH_IMAGE021
Dynamic radius error
Figure 947806DEST_PATH_IMAGE022
Angle of dynamic misalignment
Figure 101707DEST_PATH_IMAGE023
Radial rotation error of horizontal axis
Figure 453054DEST_PATH_IMAGE024
Axial play
Figure 274379DEST_PATH_IMAGE025
And tilt angle gyration error
Figure 184304DEST_PATH_IMAGE026
Radial rotation error of azimuth axis
Figure 887818DEST_PATH_IMAGE027
Axial play
Figure 511698DEST_PATH_IMAGE028
Error of rotation of inclination
Figure 453109DEST_PATH_IMAGE029
And the like.
In order to conveniently research the influence of the radius error, the static error and the dynamic error of the radius are integrated,
Figure 35400DEST_PATH_IMAGE030
wherein,
Figure 226210DEST_PATH_IMAGE031
the static radius nominal value is a known quantity calibrated by a metering department, but the static test error of the radius
Figure 919359DEST_PATH_IMAGE032
Is an unknown quantity of the component (a),
Figure 184118DEST_PATH_IMAGE033
the variation of the actual working radius of the centrifuge in the running state relative to the static radius of the centrifuge is monitored by using a dual-frequency laser interferometerAngular rate
Figure 734048DEST_PATH_IMAGE034
As a function of (c).
The following coordinate system will be established:
(1) geographical coordinate system
Figure 615417DEST_PATH_IMAGE035
The axis is horizontal and pointing to the east,
Figure 846678DEST_PATH_IMAGE036
the axis is horizontally north-pointing,
Figure 998567DEST_PATH_IMAGE037
the axis refers to the sky, constituting the right hand coordinate system.
(2) Spindle sleeve coordinate system
Figure 453819DEST_PATH_IMAGE038
The pose of the spindle sleeve coordinate system relative to the geographic coordinate system is
Figure 822484DEST_PATH_IMAGE039
(3) Principal axis coordinate system
Figure 591856DEST_PATH_IMAGE040
The pose of the main shaft coordinate system relative to the main shaft sleeve coordinate system is
Figure 362366DEST_PATH_IMAGE041
Wherein
Figure 988520DEST_PATH_IMAGE042
Indicating the angle of rotation of the spindle.
(4) Horizontal axis sleeve coordinate system
Figure 844480DEST_PATH_IMAGE043
Horizontal shaft sleeve seatThe pose of the coordinate system relative to the coordinate system of the principal axis is
Figure DEST_PATH_IMAGE044
(5) Horizontal axis coordinate system
Figure 886386DEST_PATH_IMAGE045
The pose of the horizontal axis coordinate system relative to the horizontal axis shaft sleeve coordinate system is
Figure 42561DEST_PATH_IMAGE046
Wherein
Figure 308457DEST_PATH_IMAGE047
Indicating the angle of rotation of the horizontal axis.
(6) Coordinate system of azimuth axis sleeve
Figure 884669DEST_PATH_IMAGE048
The pose of the azimuth axis sleeve coordinate system relative to the horizontal axis coordinate system is
Figure 261424DEST_PATH_IMAGE049
(7) Azimuth axis coordinate system
Figure 740947DEST_PATH_IMAGE050
The position and pose of the azimuth axis coordinate system relative to the azimuth axis sleeve coordinate system are
Figure 177745DEST_PATH_IMAGE051
Wherein
Figure 539456DEST_PATH_IMAGE052
Indicating the angle of rotation of the azimuth axis.
(8) Coordinate system of working base plane
Figure 719901DEST_PATH_IMAGE053
The position and attitude of the working base plane coordinate system relative to the azimuth axis coordinate system are
Figure 788351DEST_PATH_IMAGE054
Wherein
Figure 192788DEST_PATH_IMAGE055
Is composed of
Figure 245058DEST_PATH_IMAGE056
Point to point ratio
Figure 698036DEST_PATH_IMAGE057
The point is displaced.
(9) Accelerometer coordinate system
Figure 653616DEST_PATH_IMAGE058
The position and the attitude of the accelerometer coordinate system relative to the working base plane coordinate system are
Figure 432216DEST_PATH_IMAGE059
Wherein
Figure 768519DEST_PATH_IMAGE060
Is composed of
Figure 290767DEST_PATH_IMAGE061
Point to point ratio
Figure 333810DEST_PATH_IMAGE062
The point is displaced.
All the pose errors of the centrifugal machine are regarded as small displacement and small angle. The pose of the accelerometer coordinate system relative to the geographic coordinate system is
Figure 283311DEST_PATH_IMAGE063
Wherein
Figure 44594DEST_PATH_IMAGE064
Representing a pose transformation matrix between the accelerometer coordinate system and the geographic coordinate system,
Figure 370533DEST_PATH_IMAGE065
is the relative displacement vector of the accelerometer coordinate system and the geographic coordinate system.
The position and posture of the accelerometer coordinate system relative to the principal axis coordinate system are
Figure 330399DEST_PATH_IMAGE066
Wherein
Figure 185222DEST_PATH_IMAGE067
And representing an attitude transformation matrix between the accelerometer coordinate system and the principal axis coordinate system.
The origin of the accelerometer coordinate system is expressed as
Figure 197915DEST_PATH_IMAGE068
It is available ignoring the second order small amount,
Figure DEST_PATH_IMAGE069
Figure 327545DEST_PATH_IMAGE070
Figure 345180DEST_PATH_IMAGE071
and
Figure 636484DEST_PATH_IMAGE072
will be used later to calculate the precise centripetal acceleration of the origin of the accelerometer coordinate system.
Specifically, in the parameter calibration method of the accelerometer on the precision centrifuge according to the embodiment, a calculation process of a quartz accelerometer input specific force is as follows:
when the precision centrifuge is used for calibrating acceleration timing by centripetal acceleration generated by rotation of the spindle at a uniform angular velocity, the specific force input of the accelerometer has 3 sources, namely the centripetal acceleration, the gravitational acceleration and the Coriolis acceleration, and the specific force distribution of each acceleration source can be obtained as follows:
(1) distribution of specific force generated by gravity acceleration on three axes of accelerometer to be tested
The components of the gravity acceleration on the input shaft, the pendulum shaft and the output shaft of the accelerometer to be measured are respectively
Figure 372359DEST_PATH_IMAGE073
Figure 40101DEST_PATH_IMAGE074
The specific force generated by the gravity acceleration is expressed as
Figure 708979DEST_PATH_IMAGE075
Then expressed as in the accelerometer coordinate system
Figure 436764DEST_PATH_IMAGE076
(2) Distribution of centripetal acceleration on three axes of accelerometer to be measured
According to the above, the centripetal acceleration at the origin of the accelerometer coordinates is expressed in the principal axis coordinate system
Figure 394356DEST_PATH_IMAGE077
The components of the input shaft, the pendulum shaft and the output shaft of the accelerometer to be measured are respectively
Figure 89955DEST_PATH_IMAGE078
According to formula (10):
Figure 82182DEST_PATH_IMAGE079
(3) coriolis acceleration component generated by earth rotation
The Coriolis acceleration generated by the earth rotation angular rate at the origin of the accelerometer is very small, and the calculation error caused by the centrifuge pose error is much smaller and can be ignored, so that the nominal value of the Coriolis acceleration is considered. At this time, the Coriolis acceleration expression is:
Figure 777605DEST_PATH_IMAGE080
wherein
Figure 222493DEST_PATH_IMAGE081
Is the local latitude.
In summary, the precise specific force on the three axes of the accelerometer is
Figure 966458DEST_PATH_IMAGE082
Because the influence of the rotation error term on the specific force is changed in a sine and cosine form, the whole-cycle integration can be ignored because of the change
Figure 78771DEST_PATH_IMAGE083
And
Figure 679516DEST_PATH_IMAGE084
the integral of the whole cycle is zero or can be ignored, and is calculated to obtain
Figure 877280DEST_PATH_IMAGE085
Figure 424936DEST_PATH_IMAGE086
Figure 126175DEST_PATH_IMAGE087
The accurate specific force input of the accelerometer is calculated, the accelerometer is calibrated by a 12-position method, the specific force input can be calculated by using a formula (16) through 3 mounting modes, and then a corresponding test method is designed.
Specifically, in the parameter calibration method of the accelerometer on the precision centrifuge according to the embodiment, a specific calculation process of a high-order error coefficient of the quartz accelerometer is as follows:
the quartz accelerometer error model expression takes the following form:
Figure 599620DEST_PATH_IMAGE088
wherein,
Figure 81417DEST_PATH_IMAGE089
for accelerometer output values, units: v;
Figure 432764DEST_PATH_IMAGE090
is the output equivalent of the accelerometer, in units: g;
Figure 254089DEST_PATH_IMAGE091
scale factor, unit: v/g;
Figure 399900DEST_PATH_IMAGE092
acceleration components on an input shaft, a pendulum shaft and an output shaft of the accelerometer respectively, the unit: g;
Figure 306676DEST_PATH_IMAGE093
zero offset, unit: g;
Figure 992872DEST_PATH_IMAGE094
for cross-axis sensitivity, unit: rad;
Figure 934283DEST_PATH_IMAGE095
second-order nonlinear coefficients, unit:
Figure 250995DEST_PATH_IMAGE096
；
Figure 379488DEST_PATH_IMAGE097
is the singular quadratic coefficient, unit:
Figure 574102DEST_PATH_IMAGE098
；
Figure 166758DEST_PATH_IMAGE099
third order nonlinear coefficients, in units:
Figure 919950DEST_PATH_IMAGE100
；
Figure 801318DEST_PATH_IMAGE101
for cross-coupling coefficients, the unit:
Figure 767000DEST_PATH_IMAGE102
；
Figure 417425DEST_PATH_IMAGE103
random error, unit: g.
the invention mainly aims at a test and calibration method of a quartz accelerometer high-order error model coefficient, so that a constant term and a primary term in the error model coefficient are taken as known quantities. The invention adopts 6 symmetrical positions to combine to calibrate the high-order term error coefficient in the quartz accelerometer error model expression.
The high order error model coefficients of the quartz accelerometer are identified by the 6 symmetrical position combinations shown in FIG. 3, in which
Figure 138256DEST_PATH_IMAGE104
Representing a centripetal acceleration vector. The calibrated accelerometer error model coefficients for each of the mounting positions shown in the figure are shown in table 1.
TABLE 1 relationship between symmetrical position combinations and identifiable high order error model coefficients for quartz accelerometers
Figure 506920DEST_PATH_IMAGE105
In fig. 3, 3 mounting modes are adopted totally, the paired positions 1-2, 3-4 and 7-8 are the 1 st mounting mode, at the moment, the output shaft of the accelerometer is always consistent with the axis of the azimuth axis of the centrifuge, and the horizontal axis of the centrifuge is always positioned at the position of the horizontal axis of the centrifuge
Figure 541873DEST_PATH_IMAGE106
Position, azimuth axis is at 6 positions as shown in table 1, 3 pairs of positions are obtained. The 5-6 and 9-10 positions are the 2 nd installation mode, at the moment, the input shaft of the accelerometer is always consistent with the axis of the azimuth axis of the centrifuge, and the horizontal shaft is positioned at the position of the horizontal shaft
Figure 781224DEST_PATH_IMAGE107
Position, azimuth axis in 4 positions results in 2 pairs of paired positions. The 11-12 positions are the 3 rd installation mode, at the moment, the direction of a pendulum shaft of the accelerometer is opposite to the direction of the axis of an azimuth shaft of the centrifugal machine, and a horizontal shaft is always positioned at
Figure 374754DEST_PATH_IMAGE108
Position, azimuth axis in
Figure 27452DEST_PATH_IMAGE109
These 2 positions.
According to the formula (16), the specific force input of each axis of the actual accelerometer corresponding to the 1 st to 12 th installation positions can be obtained, and during specific calculation,the specific force on the input shaft is accurate to a first order small amount, the specific force on the pendulum shaft and the output shaft is only calculated to be a nominal value, and the first order small amount is also ignored, because the coefficient related to the input specific force of the two shafts is also a small amount. In the formula (16)
Figure 334937DEST_PATH_IMAGE110
Is a known quantity for calculating the indicating output of the accelerometer
Figure 959953DEST_PATH_IMAGE111
Taking first order small quantities, dependent on other coefficients
Figure 225850DEST_PATH_IMAGE112
And taking a nominal value. To calibrate the 3 rd order error model coefficients of the accelerometer, at least 4 specific force inputs are required for each pair of positions, i.e. the principal axis is required to operate at 4 different angular rates
Figure 100265DEST_PATH_IMAGE113
And collecting a whole-cycle average of the accelerometer output. For convenience, the 12 positions are tested using a uniform structural matrix as shown in equation (16), although more angular rate points may be added.
Figure 742599DEST_PATH_IMAGE114
The specific forces of the input shaft, the swing shaft and the output shaft of the quartz accelerometer at the position 1 are respectively as follows:
Figure 222121DEST_PATH_IMAGE115
wherein
Figure 393340DEST_PATH_IMAGE116
All in units of g, the following expressions are the same.
Substituting equation (18) into equation (16), the indicated output of the quartz accelerometer at position 1 is:
Figure 958313DEST_PATH_IMAGE117
the specific forces of the input shaft, the swing shaft and the output shaft of the quartz accelerometer at the position 2 are respectively as follows:
Figure 669917DEST_PATH_IMAGE118
substituting equation (20) for equation (16), the indicated output of the quartz accelerometer at position 2 is:
Figure 770991DEST_PATH_IMAGE119
the following equations (19) and (21) are added and subtracted, respectively:
Figure 113110DEST_PATH_IMAGE120
equation (22) is a constant term of acceleration, and is composed of a primary term and a secondary term. And for equation (23) are constant, first, second and third term compositions. By combining the above analysis, the 4 speed points of the main shaft are adopted for testing, and identification can be realized
Figure 165380DEST_PATH_IMAGE121
。
Figure 680675DEST_PATH_IMAGE122
Wherein "
Figure 869211DEST_PATH_IMAGE123
"means that this term is theoretically zero or because it is a composite of many pose error terms, and need not be written out.
The formula (24) is written in matrix form
Figure 647811DEST_PATH_IMAGE124
From the least squares one can:
Figure 984114DEST_PATH_IMAGE125
in the formula (24), identification
Figure 506363DEST_PATH_IMAGE126
The item avoids the error of the centrifuge
Figure 814984DEST_PATH_IMAGE127
Thereby increasing
Figure 498906DEST_PATH_IMAGE128
The calibration accuracy of the terms.
According to the formula (23), a
Figure 56927DEST_PATH_IMAGE129
Wherein
Figure 881401DEST_PATH_IMAGE130
Figure 778950DEST_PATH_IMAGE131
From the least squares one can:
Figure 899353DEST_PATH_IMAGE132
in the observation vector
Figure 210248DEST_PATH_IMAGE133
In compensating the dynamic errorItem(s)
Figure 74299DEST_PATH_IMAGE134
，
Figure 91934DEST_PATH_IMAGE135
And a Coriolis acceleration term, wherein a pose error term of the centrifugal machine is added in the error coefficient vector
Figure 383238DEST_PATH_IMAGE136
Automatically compensating the static radius test error
Figure 915850DEST_PATH_IMAGE137
And a rotation error term and the like, thereby eliminating the influence of errors of the centrifugal machine and Coriolis acceleration and improving
Figure 318013DEST_PATH_IMAGE138
And
Figure 190154DEST_PATH_IMAGE139
the calibration accuracy of the terms.
The specific forces of the input shaft, the swing shaft and the output shaft of the quartz accelerometer at the positions 3 and 4 are respectively as follows:
Figure 419403DEST_PATH_IMAGE140
the indication output of the quartz accelerometer is calculated by substituting the equations (28) and (29) into the equation (16), respectively
Figure 173733DEST_PATH_IMAGE141
And
Figure 379586DEST_PATH_IMAGE142
and performing addition and subtraction operation to obtain the following expression:
Figure 371813DEST_PATH_IMAGE143
Figure 4919DEST_PATH_IMAGE144
this is obtained according to equation (30):
Figure 512124DEST_PATH_IMAGE145
wherein
Figure 521668DEST_PATH_IMAGE146
According to formula (31):
Figure 102822DEST_PATH_IMAGE147
wherein
Figure 172410DEST_PATH_IMAGE148
After compensating for the additional acceleration due to the dynamic misalignment angle, it can be identified
Figure 901331DEST_PATH_IMAGE149
And
Figure 714566DEST_PATH_IMAGE150
an item.
The specific forces of the input shaft, the swing shaft and the output shaft of the quartz accelerometer at the positions 5 and 6 are respectively as follows:
Figure 914341DEST_PATH_IMAGE151
the formula (34) and the formula (35) are respectively substituted into the formula (16), and the indication output of the quartz accelerometer is calculated
Figure 889251DEST_PATH_IMAGE152
And
Figure 371048DEST_PATH_IMAGE153
and performing addition and subtraction operation to obtain the following expression:
Figure 722394DEST_PATH_IMAGE154
this is obtained according to equation (36):
Figure 278141DEST_PATH_IMAGE155
wherein
Figure 423951DEST_PATH_IMAGE156
According to equation (37):
Figure 127465DEST_PATH_IMAGE157
wherein
Figure 16924DEST_PATH_IMAGE158
Also after compensating for the additional acceleration due to the dynamic misalignment angle, it can be identified
Figure 692756DEST_PATH_IMAGE159
And
Figure 71784DEST_PATH_IMAGE160
an item.
The specific forces of the input shaft, the swing shaft and the output shaft of the quartz accelerometer at the positions 7 and 8 are respectively as follows:
Figure 465857DEST_PATH_IMAGE161
Figure 406610DEST_PATH_IMAGE162
the formula (39) and the formula (40) are respectively substituted into the formula (16), and the indication output of the quartz accelerometer is calculated
Figure 202528DEST_PATH_IMAGE163
And performing addition and subtraction operation to obtain the following expression:
Figure 955721DEST_PATH_IMAGE164
this is obtained according to equation (42):
Figure 368247DEST_PATH_IMAGE165
wherein
Figure 599509DEST_PATH_IMAGE166
Accurately identify
Figure 249933DEST_PATH_IMAGE167
After coefficients, subtracting previously identified
Figure 970764DEST_PATH_IMAGE168
Can identify
Figure 339428DEST_PATH_IMAGE169
Error model coefficients.
According to formula (43):
Figure 374381DEST_PATH_IMAGE170
wherein
Figure 613732DEST_PATH_IMAGE171
The specific forces of the input shaft, the swing shaft and the output shaft of the quartz accelerometer at the positions 9 and 10 are respectively as follows:
Figure 207262DEST_PATH_IMAGE172
the formula (45) and the formula (46) are respectively substituted into the formula (16), and the indication output of the quartz accelerometer is calculated
Figure 594381DEST_PATH_IMAGE173
And performing addition and subtraction operation to obtain the following expression:
Figure 167445DEST_PATH_IMAGE174
Figure 792461DEST_PATH_IMAGE175
this is obtained according to equation (48):
Figure 58358DEST_PATH_IMAGE176
wherein
Figure 932773DEST_PATH_IMAGE177
After compensating for the effect of the dynamic misalignment angle, identification
Figure 309527DEST_PATH_IMAGE178
Then, subtract again
Figure 523471DEST_PATH_IMAGE179
Is ready to obtain
Figure 757006DEST_PATH_IMAGE180
。
According to formula (49):
Figure 321980DEST_PATH_IMAGE181
wherein
Figure 236846DEST_PATH_IMAGE182
The specific forces of the input shaft, the swing shaft and the output shaft of the quartz accelerometer at the positions 11 and 12 are respectively as follows:
Figure 337920DEST_PATH_IMAGE183
the indication output of the quartz accelerometer is calculated by substituting the expressions (51) and (52) into the expression (16)
Figure 742356DEST_PATH_IMAGE184
And
Figure 529047DEST_PATH_IMAGE185
and performing addition and subtraction operation to obtain the following expression:
Figure 247604DEST_PATH_IMAGE186
Figure 701719DEST_PATH_IMAGE187
this is obtained according to equation (54):
Figure 480319DEST_PATH_IMAGE188
wherein
Figure 551043DEST_PATH_IMAGE189
Identify out
Figure 807712DEST_PATH_IMAGE190
After that, the identified one is subtracted
Figure 116334DEST_PATH_IMAGE191
Can obtain
Figure 862573DEST_PATH_IMAGE192
An item.
According to formula (55):
Figure 889435DEST_PATH_IMAGE193
wherein
Figure 182751DEST_PATH_IMAGE194
By combining the formula proposed above, the calibration result of the high-order error term of the quartz accelerometer can be obtained as follows:
Figure 611458DEST_PATH_IMAGE195
the expression of the coefficient of the high-order error model of the quartz accelerometer can be summarized as
Figure 528598DEST_PATH_IMAGE196
As shown in fig. 2, a method for calibrating parameters of an accelerometer on a precision centrifuge according to this embodiment includes
Figure 777177DEST_PATH_IMAGE197
Obtaining error model coefficients
Figure 641228DEST_PATH_IMAGE198
The expression of the term is:
Figure 658863DEST_PATH_IMAGE199
wherein
Figure 950167DEST_PATH_IMAGE200
Representation matrix
Figure 482779DEST_PATH_IMAGE201
First, the
Figure 884942DEST_PATH_IMAGE202
Line, first
Figure 22662DEST_PATH_IMAGE203
The elements of the column. Assuming that the indicating outputs of the quartz accelerometers are independent and equal in precision, the uncertainty is
Figure 281605DEST_PATH_IMAGE204
Then, then
Figure 6241DEST_PATH_IMAGE205
The uncertainty of the term is
Figure 212094DEST_PATH_IMAGE206
Assuming that the centrifuge provides centripetal accelerations of 5g, 10g, 15g and 20g, the output of the quartz accelerometer has an uncertainty of
Figure 204321DEST_PATH_IMAGE207
Dynamic misalignment angle uncertainty
Figure 634165DEST_PATH_IMAGE208
Uncertainty of dynamic radius error
Figure 344632DEST_PATH_IMAGE209
. The uncertainty of the quadratic term and the cross quadratic term of the quartz accelerometer are respectively calculated as
Figure 88597DEST_PATH_IMAGE210
Figure 935331DEST_PATH_IMAGE212
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (6)

1. A parameter calibration method of an accelerometer on a precision centrifuge is characterized by comprising the following steps:
acquiring each static error and each dynamic error of a precision centrifuge, establishing a coordinate system according to the structure of the precision centrifuge, and calculating a pose error under the coordinate system according to each static error and each dynamic error;
driving a main shaft of the precision centrifuge to rotate at a uniform angular velocity so as to generate a centripetal acceleration calibration accelerometer, and calculating specific force distribution of the centripetal acceleration, the gravitational acceleration and the Coriolis acceleration based on the pose error in the coordinate system so as to determine an accelerometer error model;
and outputting the indication of six symmetrical positions of the accelerometer in three different installation modes, and calibrating a high-order term error coefficient in an accelerometer error model expression by using an addition and subtraction element method.
2. The method for calibrating the parameters of an accelerometer on a precision centrifuge according to claim 1, wherein the precision centrifuge comprises a main shaft, a horizontal shaft and an azimuth shaft;
the static error of the precision centrifuge comprises a two-dimensional verticality error of a spindle axis
Figure 619406DEST_PATH_IMAGE001
Perpendicularity of horizontal shaft axis and main shaft axis
Figure 940666DEST_PATH_IMAGE002
Degree of intersection
Figure 429416DEST_PATH_IMAGE003
Perpendicularity of horizontal axis and azimuth axis
Figure 759904DEST_PATH_IMAGE004
Degree of intersection
Figure 752130DEST_PATH_IMAGE005
And initial zero error of azimuth axis
Figure 916396DEST_PATH_IMAGE006
Perpendicularity of working base plane for installing inertia instrument to axis of azimuth shaft
Figure 751496DEST_PATH_IMAGE007
Accelerometer mounting datum attitude error
Figure 761041DEST_PATH_IMAGE008
Eccentricity error
Figure 997987DEST_PATH_IMAGE009
And initial nulling error
Figure 801995DEST_PATH_IMAGE010
The angular position errors of the three axes of the main shaft, the horizontal shaft and the azimuth shaft are respectively
Figure 265337DEST_PATH_IMAGE011
The dynamic error of the precision centrifuge comprises a main shaft radial rotation error
Figure 937627DEST_PATH_IMAGE012
Axial play
Figure 904446DEST_PATH_IMAGE013
And rotation error of inclination angle
Figure 535148DEST_PATH_IMAGE014
Dynamic radius error
Figure 954628DEST_PATH_IMAGE015
Angle of dynamic misalignment
Figure 571554DEST_PATH_IMAGE016
Radial rotation error of horizontal axis
Figure 517513DEST_PATH_IMAGE017
Axial play
Figure 928903DEST_PATH_IMAGE018
And tilt angle gyration error
Figure 225892DEST_PATH_IMAGE019
Radial rotation error of azimuth axis
Figure 115350DEST_PATH_IMAGE020
Axial play
Figure 181395DEST_PATH_IMAGE021
Error of rotation of inclination
Figure 29266DEST_PATH_IMAGE022
；
Error in radiusDifference (D)
Figure 423338DEST_PATH_IMAGE023
Wherein,
Figure 241121DEST_PATH_IMAGE024
the static radius nominal value is a known quantity calibrated by a metering department, and the static test error of the radius
Figure 37039DEST_PATH_IMAGE025
Is an unknown quantity of the component (a),
Figure 914865DEST_PATH_IMAGE026
the variation of the actual working radius of the precision centrifuge in the running state relative to the static radius of the centrifuge is the angular velocity of the main shaft
Figure 61813DEST_PATH_IMAGE027
As a function of (c).
3. The method for calibrating the parameters of the accelerometer on the precision centrifuge according to claim 2, wherein the establishing a coordinate system according to the structure of the precision centrifuge, and the calculating the pose errors in the coordinate system according to the static errors and the dynamic errors comprise:
establishing a geographical coordinate system
Figure 558653DEST_PATH_IMAGE028
The axis is horizontal and pointing to the east,
Figure 333711DEST_PATH_IMAGE029
the axis is horizontally north-pointing,
Figure 257805DEST_PATH_IMAGE030
the axis indicates the sky to form a right-hand coordinate system;
establishing a coordinate system of a spindle sleeve
Figure 751103DEST_PATH_IMAGE031
Obtaining the pose of the spindle sleeve coordinate system relative to the geographic coordinate system;
establishing a main shaft coordinate system
Figure 786055DEST_PATH_IMAGE032
Obtaining the pose of the main shaft coordinate system relative to the main shaft sleeve coordinate system;
establishing a horizontal axis sleeve coordinate system
Figure 822144DEST_PATH_IMAGE033
Obtaining the pose of a horizontal shaft sleeve coordinate system relative to a main shaft coordinate system;
establishing a horizontal axis coordinate system
Figure 776194DEST_PATH_IMAGE034
Obtaining the pose of the horizontal axis coordinate system relative to the horizontal axis sleeve coordinate system;
establishing an azimuth axis sleeve coordinate system
Figure 632154DEST_PATH_IMAGE035
Obtaining the pose of an azimuth axis sleeve coordinate system relative to a horizontal axis coordinate system;
establishing an azimuth axis coordinate system
Figure 861010DEST_PATH_IMAGE036
Obtaining the pose of the azimuth axis coordinate system relative to the azimuth axis sleeve coordinate system;
establishing a working base coordinate system
Figure 220447DEST_PATH_IMAGE037
Obtaining the pose of the working base plane coordinate system relative to the azimuth axis coordinate system;
establishing an accelerometer coordinate system
Figure 610978DEST_PATH_IMAGE038
Obtaining the coordinate system of the accelerometer relative to the working baseThe pose of the coordinate system, the pose of the accelerometer coordinate system relative to the geographic coordinate system, and the pose of the accelerometer coordinate system relative to the principal axis coordinate system.
4. The method for calibrating the parameters of the accelerometer on the precision centrifuge as claimed in claim 3,
the pose of the spindle sleeve coordinate system relative to the geographic coordinate system is
Figure 954234DEST_PATH_IMAGE039
The pose of the main shaft coordinate system relative to the main shaft sleeve coordinate system is
Figure 596568DEST_PATH_IMAGE040
Wherein
Figure 466304DEST_PATH_IMAGE041
Representing the angle of rotation of the spindle;
the pose of the horizontal axis shaft sleeve coordinate system relative to the main axis coordinate system is
Figure 903102DEST_PATH_IMAGE042
The pose of the horizontal axis coordinate system relative to the horizontal axis shaft sleeve coordinate system is
Figure 616146DEST_PATH_IMAGE043
Wherein
Figure 62171DEST_PATH_IMAGE044
Represents the angle of rotation of the horizontal axis;
the pose of the azimuth axis sleeve coordinate system relative to the horizontal axis coordinate system is
Figure 396201DEST_PATH_IMAGE045
The position and pose of the azimuth axis coordinate system relative to the azimuth axis sleeve coordinate system are
Figure 394112DEST_PATH_IMAGE046
Wherein
Figure 446382DEST_PATH_IMAGE047
Representing the angle of rotation of the azimuth axis;
the position and attitude of the working base plane coordinate system relative to the azimuth axis coordinate system are
Figure 430519DEST_PATH_IMAGE048
Wherein
Figure 9268DEST_PATH_IMAGE049
Is composed of
Figure 53447DEST_PATH_IMAGE050
Point to point ratio
Figure 717646DEST_PATH_IMAGE051
Point displacement;
the position and the attitude of the accelerometer coordinate system relative to the working base plane coordinate system are
Figure 239895DEST_PATH_IMAGE052
Wherein
Figure 814095DEST_PATH_IMAGE053
Is composed of
Figure 888231DEST_PATH_IMAGE054
Point to point ratio
Figure 915093DEST_PATH_IMAGE055
Point displacement;
the pose of the accelerometer coordinate system relative to the geographic coordinate system is
Figure 365665DEST_PATH_IMAGE056
Wherein
Figure 528794DEST_PATH_IMAGE057
Representing a pose transformation matrix between the accelerometer coordinate system and the geographic coordinate system,
Figure 914775DEST_PATH_IMAGE058
the relative displacement vector of the accelerometer coordinate system and the geographic coordinate system is obtained;
the position and posture of the accelerometer coordinate system relative to the principal axis coordinate system are
Figure 553567DEST_PATH_IMAGE059
Wherein
Figure 417618DEST_PATH_IMAGE060
Representing an attitude transformation matrix between an accelerometer coordinate system and a principal axis coordinate system;
the origin of the accelerometer coordinate system is expressed as
Figure 825466DEST_PATH_IMAGE061
It is available ignoring the second order small amount,
Figure 382349DEST_PATH_IMAGE062
Figure 383803DEST_PATH_IMAGE063
5. the method for calibrating the parameters of the accelerometer on the precision centrifuge as claimed in claim 1, wherein the expression of the error model of the accelerometer is as follows:
Figure 176178DEST_PATH_IMAGE064
wherein,
Figure 48320DEST_PATH_IMAGE065
outputting a value for the accelerometer;
Figure 900738DEST_PATH_IMAGE066
is the output equivalent of the accelerometer;
Figure 389488DEST_PATH_IMAGE067
is a scale factor;
Figure 719975DEST_PATH_IMAGE068
acceleration components on an input shaft, a pendulum shaft and an output shaft of the accelerometer respectively;
Figure 977781DEST_PATH_IMAGE069
is zero offset;
Figure 876467DEST_PATH_IMAGE070
cross-axis sensitivity;
Figure 445989DEST_PATH_IMAGE071
is a second-order nonlinear coefficient;
Figure 721112DEST_PATH_IMAGE072
is a singular quadratic coefficient;
Figure 958059DEST_PATH_IMAGE073
is a third order nonlinear coefficient;
Figure 762066DEST_PATH_IMAGE074
is the cross-coupling coefficient;
Figure 225409DEST_PATH_IMAGE075
-a random error;
the high-order term error coefficient comprises the second-order nonlinear coefficient, a singular second-order term coefficient, a third-order nonlinear coefficient and a cross-coupling coefficient.
6. The method for calibrating the parameters of the accelerometer on the precision centrifuge as claimed in claim 5, wherein the outputting of the indication of six symmetric positions of the accelerometer in three different installation modes, calibrating the high-order term error coefficient in the accelerometer error model expression by using the method of adding and subtracting the element comprises:
when the output shaft of the accelerometer is always consistent with the axis of the azimuth axis of the centrifuge, the horizontal axis of the centrifuge is always positioned
Figure 897699DEST_PATH_IMAGE076
Position, 3 pairs of paired positions are available, respectively: position 1 and position 2, position 3 and position 4, position 5 and position 6; when the input shaft of the accelerometer is always consistent with the axis of the azimuth axis of the centrifuge, the horizontal shaft is positioned at
Figure 864518DEST_PATH_IMAGE077
Position, 2 pairs of paired positions are available, respectively: positions 7 and 8, positions 9 and 10; when the direction of the swing shaft of the accelerometer is opposite to the direction of the axis of the azimuth shaft of the centrifuge, the horizontal shaft is always positioned at
Figure 229640DEST_PATH_IMAGE078
Position, azimuth axis in
Figure 180278DEST_PATH_IMAGE079
2 positions, respectively: position 11 and position 12;
the 12 positions adopt a uniform structural matrix as shown in a formula (17),
Figure 531625DEST_PATH_IMAGE080
identifying according to specific force of input shaft, pendulum shaft and output shaft of accelerometer at position 1 and position 2
Figure 477585DEST_PATH_IMAGE081
Items and
Figure 154554DEST_PATH_IMAGE082
an item;
identifying according to specific force of input shaft, pendulum shaft and output shaft of accelerometer at position 3 and position 4
Figure 185963DEST_PATH_IMAGE083
And
Figure 341001DEST_PATH_IMAGE084
an item;
identifying the specific force of the input shaft, the pendulum shaft and the output shaft of the accelerometer at the position 5 and the position 6
Figure 282412DEST_PATH_IMAGE085
Items and
Figure 723758DEST_PATH_IMAGE086
an item;
identifying from the specific forces of the accelerometer input, yaw and output axes at positions 7 and 8
Figure 117830DEST_PATH_IMAGE087
An item;
identifying from the specific force of the accelerometer input, yaw and output axes at positions 9 and 10
Figure 201193DEST_PATH_IMAGE088
An item;
according to the specific force of the input shaft, the pendulum shaft and the output shaft of the accelerometer at the position 11 and the position 12
Figure 997111DEST_PATH_IMAGE089
An item.
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