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
pose
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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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Harbin Institute of Technology Shenzhen
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Shenrui Technology Beijing Co ltd
Harbin Institute of Technology Shenzhen
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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

加速度计在精密离心机上的参数标定方法Parameter calibration method of accelerometer on precision centrifuge

技术领域technical field

本发明涉及离心机标定领域，具体涉及一种加速度计在精密离心机上的参数标定方法。The invention relates to the field of centrifuge calibration, in particular to a parameter calibration method of an accelerometer on a precision centrifuge.

背景技术Background technique

文献“加速度计精密离心机试验的优化设计”分析了加速度计在精密离心机测试时的实际量测噪声特性，在此基础上指出传统的优化设计方法，即饱和D最优试验设计，存在工程适用性问题。然后为了改善饱和D最优试验设计的适用性，并且考虑到试验代价和精度的折中关系，提出了D最优改进试验设计方案。该方案将饱和D最优试验谱点作为基本谱点，在基本谱点之间均匀插入其他谱点来降低输入加速度偏差的影响，并通过加权的方法来分配基本谱点和新增谱点的测度，权值的选取依据实际的噪声特性。虽然文献“加速度计精密离心机试验的优化设计”对石英加速度计在精密离心机上进行了具体的标定试验，但没有考虑离心机误差对误差模型系数标定精度的影响，这可能会引入额外的标定误差，并且文献中所辨识的加速度计的误差模型系数较少。The document "Optimal Design of Accelerometer Precision Centrifuge Test" analyzes the actual measurement noise characteristics of accelerometers during precision centrifuge testing. Applicability issues. Then, in order to improve the applicability of the saturated D-optimal experimental design, and considering the trade-off relationship between the experimental cost and the accuracy, a D-optimal improved experimental design is proposed. In this scheme, the optimal test spectrum point of saturated D is used as the basic spectrum point, and other spectrum points are evenly inserted between the basic spectrum points to reduce the influence of input acceleration deviation, and the basic spectrum point and the new spectrum point are allocated by weighting method. The selection of weights is based on the actual noise characteristics. Although the literature "Optimized Design of Accelerometer Precision Centrifuge Experiment" conducts a specific calibration test of quartz accelerometer on a precision centrifuge, it does not consider the influence of centrifuge error on the calibration accuracy of error model coefficients, which may introduce additional calibration error, and the accelerometers identified in the literature have fewer error model coefficients.

文献“精密离心机误差对石英加速度计误差标定精度分析”分析了离心机各个误差源，用齐次变换法精确地计算了产生的向心加速度，给出了向心加速度、重力加速度和哥氏加速度在加速度计坐标系下的分量，推导了被试加速度计输入加速度的精确表达式。采用了10位置测试方法来辨识误差模型的高阶系数，着重讨论了误差模型系数的计算值与离心机误差之间的关系。但是二次项误差系数

Figure 103085DEST_PATH_IMAGE001
和三次项误差系数
Figure 489067DEST_PATH_IMAGE002
、
Figure 940908DEST_PATH_IMAGE003
未得到辨识，并且需要已知动态和静态误差对辨识结果进行修正和补偿，无法规避离心机的各项误差。The document "Analysis of Precision Centrifuge Error Calibration Accuracy of Quartz Accelerometer Error" analyzes each error source of the centrifuge, uses the homogeneous transformation method to accurately calculate the centripetal acceleration, and gives the centripetal acceleration, gravitational acceleration and Coriolis The component of the acceleration in the accelerometer coordinate system, the exact expression of the input acceleration of the tested accelerometer is derived. The 10-position test method is used to identify the higher-order coefficients of the error model, and the relationship between the calculated values of the error model coefficients and the centrifuge error is emphatically discussed. But the quadratic term error coefficient
Figure 103085DEST_PATH_IMAGE001
and cubic error coefficient
Figure 489067DEST_PATH_IMAGE002
,
Figure 940908DEST_PATH_IMAGE003
It has not been identified, and the identification results need to be corrected and compensated for known dynamic and static errors, and various errors of the centrifuge cannot be avoided.

发明内容SUMMARY OF THE INVENTION

有鉴于此，本发明提供一种加速度计在精密离心机上的参数标定方法，包括：In view of this, the present invention provides a method for calibrating parameters of an accelerometer on a precision centrifuge, including:

获取精密离心机的各静态误差以及动态误差，并根据精密离心机的结构建立坐标系，以及根据所述各静态误差以及动态误差计算所述坐标系下的位姿误差；Acquiring various static errors and dynamic errors of the precision centrifuge, establishing a coordinate system according to the structure of the precision centrifuge, and calculating the pose errors under the coordinate system according to the various static errors and dynamic errors;

驱动精密离心机的主轴以匀角速率旋转，以产生向心加速度标定加速度计，基于所述坐标系下的位姿误差计算向心加速度、重力加速度和Coriolis加速度的比力分配，以确定加速度计误差模型；The main shaft that drives the precision centrifuge rotates at a constant angular rate to generate centripetal acceleration to calibrate the accelerometer, and the specific force distribution of centripetal acceleration, gravitational acceleration and Coriolis acceleration is calculated based on the pose error in the coordinate system to determine the accelerometer error model;

对加速度计在三种不同安装方式下的六个对称位置的指示输出，利用加减消元的方法标定加速度计误差模型表达式中的高阶项误差系数。For the indication output of the six symmetrical positions of the accelerometer under three different installation methods, the method of adding and subtracting the subtraction element is used to calibrate the error coefficient of the higher-order term in the accelerometer's error model expression.

本发明一种加速度计在精密离心机上的参数标定方法，在分析精密离心机各项动、静态误差源的基础上，给出了离心机输入比力的精确表达式；结合加速度计误差模型，利用加减消元的方法标定加速度计误差模型表达式中的高阶项误差系数，在离心机误差稳定的情况下，监测和补偿动态失准角和动态半径，就可以完全消除离心机的动态误差和静态误差，可有效提高石英加速度计高阶误差模型系数的标定精度。The invention provides a method for calibrating parameters of an accelerometer on a precision centrifuge. On the basis of analyzing various dynamic and static error sources of the precision centrifuge, an accurate expression of the input specific force of the centrifuge is given; combined with the accelerometer error model, The high-order error coefficient in the accelerometer error model expression is calibrated by the method of adding and subtracting elements. When the centrifuge error is stable, the dynamic misalignment angle and dynamic radius of the centrifuge can be completely eliminated by monitoring and compensating for the dynamic misalignment angle and dynamic radius. error and static error, which can effectively improve the calibration accuracy of the high-order error model coefficients of the quartz accelerometer.

附图说明Description of drawings

为了更清楚地说明本发明实施例的技术方案，下面将对实施例中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其它的附图。In order to illustrate the technical solutions of the embodiments of the present invention more clearly, the following briefly introduces the accompanying drawings used in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained from these drawings without any creative effort.

图1为本发明精密离心机结构示意图。Fig. 1 is the structure schematic diagram of the precision centrifuge of the present invention.

图2为本发明精密离心机各个坐标系示意图。2 is a schematic diagram of each coordinate system of the precision centrifuge of the present invention.

图3为本发明加速度计3种不同安装方式下的6个对称位置组合。FIG. 3 is a combination of six symmetrical positions under three different installation modes of the accelerometer of the present invention.

具体实施方式Detailed ways

下面结合附图对本发明实施例进行详细描述。The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

需说明的是，在不冲突的情况下，以下实施例及实施例中的特征可以相互组合；并且，基于本公开中的实施例，本领域普通技术人员在没有作出创造性劳动前提下所获得的所有其他实施例，都属于本公开保护的范围。It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict; and, based on the embodiments in the present disclosure, those of ordinary skill in the art can obtain the results obtained without creative work. All other embodiments fall within the protection scope of the present disclosure.

需要说明的是，下文描述在所附权利要求书的范围内的实施例的各种方面。应显而易见，本文中所描述的方面可体现于广泛多种形式中，且本文中所描述的任何特定结构及/或功能仅为说明性的。基于本公开，所属领域的技术人员应了解，本文中所描述的一个方面可与任何其它方面独立地实施，且可以各种方式组合这些方面中的两者或两者以上。举例来说，可使用本文中所阐述的任何数目个方面来实施设备及/或实践方法。另外，可使用除了本文中所阐述的方面中的一或多者之外的其它结构及/或功能性实施此设备及/或实践此方法。It is noted that various aspects of embodiments within the scope of the appended claims are described below. 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 illustrative only. Based on this disclosure, those skilled in the art should appreciate that an 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 may be 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.

如图1所示，精密离心机有主轴、水平轴和方位轴3个轴系，3个轴系均有精密位置功能，水平轴轴端安装有360齿多齿分度盘，可以

Figure 601696DEST_PATH_IMAGE004
的精度定位到360个位置，主轴轴系与方位轴轴系均有精密角速率功能，当主轴以
Figure 884910DEST_PATH_IMAGE005
的匀角速率旋转时，在工作半径
Figure 674749DEST_PATH_IMAGE006
处，将产生
Figure 145045DEST_PATH_IMAGE007
的向心加速度。As shown in Figure 1, the precision centrifuge has three shaft systems: the main shaft, the horizontal axis and the azimuth axis, and the three shaft systems have the function of precision position.
Figure 601696DEST_PATH_IMAGE004
The accuracy of positioning can reach 360 positions, and both the spindle axis and the azimuth axis have the function of precise angular rate.
Figure 884910DEST_PATH_IMAGE005
When rotating at a uniform angular rate, the working radius
Figure 674749DEST_PATH_IMAGE006
, will produce
Figure 145045DEST_PATH_IMAGE007
centripetal acceleration.

离心机的静态误差源主要包括主轴轴线的二维铅垂度误差

Figure 812787DEST_PATH_IMAGE008
水平轴轴线与主轴轴线的垂直度
Figure 747245DEST_PATH_IMAGE009
相交度
Figure 209450DEST_PATH_IMAGE010
水平轴轴线与方位轴轴线的垂直度
Figure 167042DEST_PATH_IMAGE011
相交度
Figure 372895DEST_PATH_IMAGE012
以及方位轴的初始零位误差
Figure 161859DEST_PATH_IMAGE013
安装惯性仪表的工作基面对方位轴轴线的垂直度
Figure 60545DEST_PATH_IMAGE014
加速度计安装基面姿态误差
Figure 505433DEST_PATH_IMAGE015
偏心误差
Figure 750863DEST_PATH_IMAGE016
以及初始对零误差
Figure 659913DEST_PATH_IMAGE017
主轴、水平轴和方位轴三个轴的角位置误差分别为
Figure 463921DEST_PATH_IMAGE018
等。图1和图2标出了离心机结构简图以及建立的相应坐标系。The static error sources of the centrifuge mainly include the two-dimensional plumb error of the main shaft axis.
Figure 812787DEST_PATH_IMAGE008
The perpendicularity of the horizontal axis axis to the main axis axis
Figure 747245DEST_PATH_IMAGE009
degree of intersection
Figure 209450DEST_PATH_IMAGE010
The perpendicularity of the horizontal axis axis to the azimuth axis axis
Figure 167042DEST_PATH_IMAGE011
degree of intersection
Figure 372895DEST_PATH_IMAGE012
and the initial zero error of the azimuth axis
Figure 161859DEST_PATH_IMAGE013
The perpendicularity of the working base where the inertial instrument is installed to the axis of the azimuth axis
Figure 60545DEST_PATH_IMAGE014
Attitude error of accelerometer mounting base
Figure 505433DEST_PATH_IMAGE015
Eccentricity error
Figure 750863DEST_PATH_IMAGE016
and the initial zero-to-zero error
Figure 659913DEST_PATH_IMAGE017
The angular position errors of the main axis, the horizontal axis and the azimuth axis are respectively
Figure 463921DEST_PATH_IMAGE018
Wait. Figures 1 and 2 show a schematic diagram of the centrifuge structure and the corresponding coordinate system established.

离心机的动态误差源主要包括主轴径向回转误差

Figure 661684DEST_PATH_IMAGE019
轴向窜动
Figure 943761DEST_PATH_IMAGE020
及倾角回转误差
Figure 910580DEST_PATH_IMAGE021
动态半径误差
Figure 947806DEST_PATH_IMAGE022
动态失准角
Figure 101707DEST_PATH_IMAGE023
水平轴径向回转误差
Figure 453054DEST_PATH_IMAGE024
轴向窜动
Figure 274379DEST_PATH_IMAGE025
以及倾角回转误差
Figure 184304DEST_PATH_IMAGE026
方位轴径向回转误差
Figure 887818DEST_PATH_IMAGE027
轴向窜动
Figure 511698DEST_PATH_IMAGE028
倾角回转误差
Figure 453109DEST_PATH_IMAGE029
等。The dynamic error source of the centrifuge mainly includes the radial rotation error of the main shaft.
Figure 661684DEST_PATH_IMAGE019
Axial play
Figure 943761DEST_PATH_IMAGE020
and tilt angle error
Figure 910580DEST_PATH_IMAGE021
Dynamic radius error
Figure 947806DEST_PATH_IMAGE022
Dynamic misalignment angle
Figure 101707DEST_PATH_IMAGE023
Horizontal axis radial rotation error
Figure 453054DEST_PATH_IMAGE024
Axial play
Figure 274379DEST_PATH_IMAGE025
and the inclination rotation error
Figure 184304DEST_PATH_IMAGE026
Azimuth axis radial rotation error
Figure 887818DEST_PATH_IMAGE027
Axial play
Figure 511698DEST_PATH_IMAGE028
Tilt rotation error
Figure 453109DEST_PATH_IMAGE029
Wait.

为了方便研究半径误差的影响，将半径的静态误差与动态误差综合，

Figure 35400DEST_PATH_IMAGE030
其中，
Figure 226210DEST_PATH_IMAGE031
为静态半径标称值，是由计量部门标定出的已知量，但半径的静态测试误差
Figure 919359DEST_PATH_IMAGE032
是未知量，
Figure 184118DEST_PATH_IMAGE033
为用双频激光干涉仪监测的离心机在运行状态下的实际工作半径相对于离心机静态半径的变化量，是主轴角速率
Figure 734048DEST_PATH_IMAGE034
的函数。In order to facilitate the study of the influence of radius error, the static error and dynamic error of radius are synthesized,
Figure 35400DEST_PATH_IMAGE030
in,
Figure 226210DEST_PATH_IMAGE031
It is the nominal value of the static radius, which is a known quantity calibrated by the metrology department, but the static test error of the radius
Figure 919359DEST_PATH_IMAGE032
is the unknown quantity,
Figure 184118DEST_PATH_IMAGE033
is the change of the actual working radius of the centrifuge under the running state monitored by the dual-frequency laser interferometer relative to the static radius of the centrifuge, which is the angular velocity of the main shaft
Figure 734048DEST_PATH_IMAGE034
The function.

下面将建立如下坐标系：The following coordinate system will be established:

(1)地理坐标系

Figure 615417DEST_PATH_IMAGE035
轴水平指东，
Figure 846678DEST_PATH_IMAGE036
轴水平指北，
Figure 998567DEST_PATH_IMAGE037
轴指天，构成右手坐标系。(1) Geographical coordinate system
Figure 615417DEST_PATH_IMAGE035
The axis points to the east horizontally,
Figure 846678DEST_PATH_IMAGE036
The axis points horizontally to the north,
Figure 998567DEST_PATH_IMAGE037
The axis points to the sky, forming a right-handed coordinate system.

(2)主轴轴套坐标系

Figure 453819DEST_PATH_IMAGE038
主轴轴套坐标系相对于地理坐标系的位姿为(2) Coordinate system of spindle bushing
Figure 453819DEST_PATH_IMAGE038
The pose of the spindle sleeve coordinate system relative to the geographic coordinate system is

Figure 822484DEST_PATH_IMAGE039
Figure 822484DEST_PATH_IMAGE039

(3)主轴坐标系

Figure 591856DEST_PATH_IMAGE040
主轴坐标系相对于主轴轴套坐标系的位姿为(3) Spindle coordinate system
Figure 591856DEST_PATH_IMAGE040
The pose of the spindle coordinate system relative to the spindle sleeve coordinate system is

Figure 362366DEST_PATH_IMAGE041
Figure 362366DEST_PATH_IMAGE041

其中

Figure 988520DEST_PATH_IMAGE042
表示主轴旋转的角度。in
Figure 988520DEST_PATH_IMAGE042
Indicates the angle of rotation of the main axis.

(4)水平轴轴套坐标系

Figure 844480DEST_PATH_IMAGE043
水平轴轴套坐标系相对于主轴坐标系的位姿为(4) Coordinate system of horizontal shaft sleeve
Figure 844480DEST_PATH_IMAGE043
The pose of the horizontal axis bushing coordinate system relative to the main axis coordinate system is

Figure DEST_PATH_IMAGE044
Figure DEST_PATH_IMAGE044

(5)水平轴坐标系

Figure 886386DEST_PATH_IMAGE045
水平轴坐标系相对于水平轴轴套坐标系的位姿为(5) Horizontal axis coordinate system
Figure 886386DEST_PATH_IMAGE045
The pose of the horizontal axis coordinate system relative to the horizontal axis sleeve coordinate system is

Figure 42561DEST_PATH_IMAGE046
Figure 42561DEST_PATH_IMAGE046

其中

Figure 308457DEST_PATH_IMAGE047
表示水平轴旋转的角度。in
Figure 308457DEST_PATH_IMAGE047
Indicates the angle by which the horizontal axis is rotated.

(6)方位轴轴套坐标系

Figure 884669DEST_PATH_IMAGE048
方位轴轴套坐标系相对于水平轴坐标系的位姿为(6) Azimuth shaft sleeve coordinate system
Figure 884669DEST_PATH_IMAGE048
The pose of the azimuth axis bushing coordinate system relative to the horizontal axis coordinate system is

Figure 261424DEST_PATH_IMAGE049
Figure 261424DEST_PATH_IMAGE049

(7)方位轴坐标系

Figure 740947DEST_PATH_IMAGE050
方位轴坐标系相对于方位轴轴套坐标系的位姿为(7) Azimuth axis coordinate system
Figure 740947DEST_PATH_IMAGE050
The pose of the azimuth axis coordinate system relative to the azimuth axis bushing coordinate system is

Figure 177745DEST_PATH_IMAGE051
Figure 177745DEST_PATH_IMAGE051

其中

Figure 539456DEST_PATH_IMAGE052
表示方位轴旋转的角度。in
Figure 539456DEST_PATH_IMAGE052
Indicates the angle by which the azimuth axis is rotated.

(8)工作基面坐标系

Figure 719901DEST_PATH_IMAGE053
工作基面坐标系相对于方位轴坐标系的位姿为(8) Work base coordinate system
Figure 719901DEST_PATH_IMAGE053
The pose of the working base coordinate system relative to the azimuth axis coordinate system is

Figure 788351DEST_PATH_IMAGE054
Figure 788351DEST_PATH_IMAGE054

其中

Figure 192788DEST_PATH_IMAGE055
为
Figure 245058DEST_PATH_IMAGE056
点相对
Figure 698036DEST_PATH_IMAGE057
点位移。in
Figure 192788DEST_PATH_IMAGE055
for
Figure 245058DEST_PATH_IMAGE056
point relative
Figure 698036DEST_PATH_IMAGE057
point displacement.

(9)加速度计坐标系

Figure 653616DEST_PATH_IMAGE058
加速度计坐标系相对于工作基面坐标系的位姿为(9) Accelerometer coordinate system
Figure 653616DEST_PATH_IMAGE058
The pose of the accelerometer coordinate system relative to the working base coordinate system is

Figure 432216DEST_PATH_IMAGE059
Figure 432216DEST_PATH_IMAGE059

其中

Figure 768519DEST_PATH_IMAGE060
为
Figure 290767DEST_PATH_IMAGE061
点相对
Figure 333810DEST_PATH_IMAGE062
点位移。in
Figure 768519DEST_PATH_IMAGE060
for
Figure 290767DEST_PATH_IMAGE061
point relative
Figure 333810DEST_PATH_IMAGE062
point displacement.

以上离心机的各个位姿误差均视为小位移和小角度。加速度计坐标系相对于地理坐标系的位姿为Each of the above centrifuge position and orientation errors are regarded as small displacements and small angles. The pose of the accelerometer coordinate system relative to the geographic coordinate system is

Figure 283311DEST_PATH_IMAGE063
Figure 283311DEST_PATH_IMAGE063

其中

Figure 44594DEST_PATH_IMAGE064
表示加速度计坐标系与地理坐标系之间的姿态变换矩阵，
Figure 370533DEST_PATH_IMAGE065
为加速度计坐标系与地理坐标系的相对位移矢量。in
Figure 44594DEST_PATH_IMAGE064
represents the attitude transformation matrix between the accelerometer coordinate system and the geographic coordinate system,
Figure 370533DEST_PATH_IMAGE065
is the relative displacement vector between the accelerometer coordinate system and the geographic coordinate system.

加速度计坐标系相对于主轴坐标系的位姿为The pose of the accelerometer coordinate system relative to the spindle coordinate system is

Figure 330399DEST_PATH_IMAGE066
Figure 330399DEST_PATH_IMAGE066

其中

Figure 185222DEST_PATH_IMAGE067
表示加速度计坐标系与主轴坐标系之间的姿态变换矩阵。in
Figure 185222DEST_PATH_IMAGE067
Represents the attitude transformation matrix between the accelerometer coordinate system and the spindle coordinate system.

加速度计坐标系原点在主轴坐标系下表示为

Figure 197915DEST_PATH_IMAGE068
忽略二阶小量后可得，
Figure DEST_PATH_IMAGE069
Figure 327545DEST_PATH_IMAGE070
The origin of the accelerometer coordinate system is expressed in the spindle coordinate system as
Figure 197915DEST_PATH_IMAGE068
After ignoring the second-order epsilon, it can be obtained,
Figure DEST_PATH_IMAGE069
Figure 327545DEST_PATH_IMAGE070

Figure 345180DEST_PATH_IMAGE071
和
Figure 636484DEST_PATH_IMAGE072
将在后文用来计算加速度计坐标系原点的精确向心加速度。
Figure 345180DEST_PATH_IMAGE071
and
Figure 636484DEST_PATH_IMAGE072
It will be used later to calculate the exact centripetal acceleration at the origin of the accelerometer coordinate system.

具体地，本实施例所涉及的一种加速度计在精密离心机上的参数标定方法，石英加速度计输入比力的计算过程为：Specifically, in the method for calibrating parameters of an accelerometer on a precision centrifuge involved in this embodiment, the calculation process of the input specific force of the quartz accelerometer is as follows:

精密离心机当主轴以匀角速率旋转产生的向心加速度标定加速度计时，加速度计的比力输入有3个来源，即向心加速度、重力加速度、Coriolis加速度，可以得出各个加速度来源的比力分配为：When the centripetal acceleration generated by the rotation of the main shaft at a constant angular rate of the precision centrifuge calibrates the accelerometer, the specific force input of the accelerometer has three sources, namely centripetal acceleration, gravitational acceleration, and Coriolis acceleration, and the specific force of each acceleration source can be obtained. Assigned as:

（1）重力加速度产生的比力在被测加速度计三个轴上的分配(1) The distribution of the specific force generated by the acceleration of gravity on the three axes of the measured accelerometer

设重力加速度在被测加速度计输入轴、摆轴和输出轴上的分量分别为

Figure 372359DEST_PATH_IMAGE073
Figure 40101DEST_PATH_IMAGE074
重力加速度产生的比力在地理坐标系下表示为
Figure 708979DEST_PATH_IMAGE075
，则在加速度计坐标系下表示为Let the components of gravitational acceleration on the input axis, pendulum axis and output axis of the measured accelerometer be respectively
Figure 372359DEST_PATH_IMAGE073
Figure 40101DEST_PATH_IMAGE074
The specific force produced by the acceleration of gravity is expressed in the geographic coordinate system as
Figure 708979DEST_PATH_IMAGE075
, then in the accelerometer coordinate system, it is expressed as

Figure 436764DEST_PATH_IMAGE076
Figure 436764DEST_PATH_IMAGE076

（2）向心加速度在被测加速度计三个轴上的分配(2) Distribution of centripetal acceleration on the three axes of the measured accelerometer

根据上面所述，加速度计坐标原点处的向心加速度在主轴坐标系下表示为

Figure 394356DEST_PATH_IMAGE077
，它被测加速度计输入轴、摆轴和输出轴上的分量分别为
Figure 89955DEST_PATH_IMAGE078
根据式(10)可得：According to the above, the centripetal acceleration at the origin of the accelerometer coordinate is expressed as
Figure 394356DEST_PATH_IMAGE077
, the components on the input axis, pendulum axis and output axis of the measured accelerometer are respectively
Figure 89955DEST_PATH_IMAGE078
According to formula (10), we can get:

Figure 82182DEST_PATH_IMAGE079
Figure 82182DEST_PATH_IMAGE079

（3）地球自转产生的Coriolis加速度分量(3) Coriolis acceleration component generated by the Earth's rotation

在加速度计原点处由地球自转角速率产生的Coriolis加速度很小，由离心机位姿误差引起的计算误差要小得多，可以忽略不计，因此考虑Coriolis加速度的标称值即可。此时，Coriolis加速度表达式为：The Coriolis acceleration generated by the angular rate of the Earth's rotation 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 the nominal value of the Coriolis acceleration can be considered. At this point, the Coriolis acceleration expression is:

Figure 777605DEST_PATH_IMAGE080
Figure 777605DEST_PATH_IMAGE080

其中

Figure 222493DEST_PATH_IMAGE081
为当地纬度。in
Figure 222493DEST_PATH_IMAGE081
is the local latitude.

综上可得加速度计三个轴上的精密比力为In summary, the precise specific force on the three axes of the accelerometer can be obtained as

Figure 966458DEST_PATH_IMAGE082
Figure 966458DEST_PATH_IMAGE082

因为回转误差项对于比力的影响呈正弦、余弦形式的变化，采用整周积分时可以忽略，因含

Figure 78771DEST_PATH_IMAGE083
和
Figure 679516DEST_PATH_IMAGE084
的整周积分为零，亦可忽略，经计算得Because the influence of the rotation error term on the specific force changes in the form of sine and cosine, it can be ignored when the integral cycle is used.
Figure 78771DEST_PATH_IMAGE083
and
Figure 679516DEST_PATH_IMAGE084
The integral of the whole week is zero, which can also be ignored. After calculation, we get

Figure 877280DEST_PATH_IMAGE085
Figure 877280DEST_PATH_IMAGE085

Figure 424936DEST_PATH_IMAGE086
Figure 424936DEST_PATH_IMAGE086

Figure 126175DEST_PATH_IMAGE087
Figure 126175DEST_PATH_IMAGE087

计算了加速度计的精确的比力输入，下面将用12位置法标定加速度计，可通过3种安装方式，利用公式（16）计算比力输入，再设计相应的试验方法。The precise specific force input of the accelerometer is calculated. The 12-position method will be used to calibrate the accelerometer. The specific force input can be calculated by formula (16) through three installation methods, and then the corresponding test method is designed.

具体地，本实施例所涉及的一种加速度计在精密离心机上的参数标定方法，石英加速度计高阶误差系数的具体计算过程为：Specifically, in a method for calibrating parameters of an accelerometer on a precision centrifuge involved in this embodiment, the specific calculation process of the high-order error coefficient of a quartz accelerometer is as follows:

石英加速度计误差模型表达式采用如下形式：The quartz accelerometer error model expression takes the following form:

Figure 599620DEST_PATH_IMAGE088
Figure 599620DEST_PATH_IMAGE088

其中，

Figure 81417DEST_PATH_IMAGE089
为加速度计输出值，单位：V；in,
Figure 81417DEST_PATH_IMAGE089
is the output value of the accelerometer, unit: V;

Figure 432764DEST_PATH_IMAGE090
为加速度计的输出当量，单位：g；
Figure 432764DEST_PATH_IMAGE090
is the output equivalent of the accelerometer, unit: g;

Figure 254089DEST_PATH_IMAGE091
为标度因数，单位：V/g；
Figure 254089DEST_PATH_IMAGE091
is the scale factor, unit: V/g;

Figure 399900DEST_PATH_IMAGE092
分别为加速度计输入轴，摆轴和输出轴上的加速度分量，单位：g；
Figure 399900DEST_PATH_IMAGE092
are the acceleration components on the input shaft, pendulum shaft and output shaft of the accelerometer, unit: g;

Figure 306676DEST_PATH_IMAGE093
为零偏，单位：g；
Figure 306676DEST_PATH_IMAGE093
Zero offset, unit: g;

Figure 992872DEST_PATH_IMAGE094
为交叉轴敏感度，单位：rad；
Figure 992872DEST_PATH_IMAGE094
is the cross-axis sensitivity, unit: rad;

Figure 934283DEST_PATH_IMAGE095
为二阶非线性系数，单位：
Figure 250995DEST_PATH_IMAGE096
；
Figure 934283DEST_PATH_IMAGE095
is the second-order nonlinear coefficient, unit:
Figure 250995DEST_PATH_IMAGE096
;

Figure 379488DEST_PATH_IMAGE097
为奇异二次项系数，单位：
Figure 574102DEST_PATH_IMAGE098
；
Figure 379488DEST_PATH_IMAGE097
is the singular quadratic term coefficient, unit:
Figure 574102DEST_PATH_IMAGE098
;

Figure 166758DEST_PATH_IMAGE099
为三阶非线性系数，单位：
Figure 919950DEST_PATH_IMAGE100
；
Figure 166758DEST_PATH_IMAGE099
is the third-order nonlinear coefficient, unit:
Figure 919950DEST_PATH_IMAGE100
;

Figure 801318DEST_PATH_IMAGE101
为交叉耦合系数，单位：
Figure 767000DEST_PATH_IMAGE102
；
Figure 801318DEST_PATH_IMAGE101
is the cross-coupling coefficient, unit:
Figure 767000DEST_PATH_IMAGE102
;

Figure 417425DEST_PATH_IMAGE103
随机误差，单位：g。
Figure 417425DEST_PATH_IMAGE103
Random error, unit: g.

本发明主要针对石英加速度计高阶误差模型系数的测试与标定方法，因此，误差模型系数中的常值项和一次项当作已知量。本发明将采用6个对称位置组合来标定石英加速度计误差模型表达式中的高阶项误差系数。The present invention is mainly aimed at the testing and calibration method of the high-order error model coefficients of the quartz accelerometer. Therefore, the constant value items and the first-order items in the error model coefficients are regarded as known quantities. The present invention will use 6 symmetrical position combinations to calibrate the error coefficient of the higher order term in the error model expression of the quartz accelerometer.

通过图3所示6个对称位置组合来辨识石英加速度计的高阶误差模型系数，其中

Figure 138256DEST_PATH_IMAGE104
表示向心加速度矢量。图中所示的各个安装位置所对应的能标定的加速度计误差模型系数如表1所示。The higher-order error model coefficients of the quartz accelerometer are identified by the combination of the six symmetrical positions shown in Figure 3, where
Figure 138256DEST_PATH_IMAGE104
represents the centripetal acceleration vector. The accelerometer error model coefficients that can be calibrated corresponding to each installation position shown in the figure are shown in Table 1.

表1对称位置组合与石英加速度计可辨识高阶误差模型系数的关系Table 1 The relationship between the symmetrical position combination and the identifiable higher-order error model coefficients of the quartz accelerometer

Figure 506920DEST_PATH_IMAGE105
Figure 506920DEST_PATH_IMAGE105

图3中总共采用3种安装方式，成对位置1-2，3-4，7-8是第1种安装方式，此时加速度计的输出轴始终与离心机的方位轴轴线一致，离心机的水平轴始终处于

Figure 541873DEST_PATH_IMAGE106
位置，方位轴处于如表1所示的6个位置，可获得3对成对位置。5-6，9-10位置为第2种安装方式，此时加速度计的输入轴始终与离心机的方位轴轴线一致，水平轴处于
Figure 781224DEST_PATH_IMAGE107
位置，方位轴处于4个位置可获得2对成对位置。11-12位置为第3种安装方式，此时加速度计的摆轴与离心机的方位轴轴线方向相反，水平轴始终处于
Figure 374754DEST_PATH_IMAGE108
位置，方位轴处于
Figure 27452DEST_PATH_IMAGE109
这2个位置。A total of 3 installation methods are used in Figure 3. The paired positions 1-2, 3-4, and 7-8 are the first installation methods. At this time, the output shaft of the accelerometer is always consistent with the azimuth axis of the centrifuge. The horizontal axis of is always in
Figure 541873DEST_PATH_IMAGE106
position, the azimuth axis is in 6 positions as shown in Table 1, and 3 pairs of paired positions can be obtained. Positions 5-6 and 9-10 are the second installation methods. At this time, the input shaft of the accelerometer is always consistent with the azimuth axis of the centrifuge, and the horizontal axis is in the position of the centrifuge.
Figure 781224DEST_PATH_IMAGE107
position, the azimuth axis is in 4 positions to obtain 2 paired positions. The 11-12 position is the third installation method. At this time, the pendulum axis of the accelerometer is in the opposite direction to the azimuth axis of the centrifuge, and the horizontal axis is always in
Figure 374754DEST_PATH_IMAGE108
position, the azimuth axis is at
Figure 27452DEST_PATH_IMAGE109
these 2 locations.

根据式（16），可以得出第1~12安装位置对应的实际加速度计各轴的比力输入，具体计算时，输入轴上的比力精确到一阶小量，摆轴与输出轴上的比力只计算标称值，一阶小量也忽略，因为与这两个轴的输入比力相关的系数也是小量。公式（16）中的

Figure 334937DEST_PATH_IMAGE110
是已知量，用于计算加速度计的指示输出
Figure 959953DEST_PATH_IMAGE111
取到一阶小量，与其它系数相关的
Figure 225850DEST_PATH_IMAGE112
取标称值即可。要标定到加速度计的3阶误差模型系数，至少每个成对位置需要4个比力输入，即要求主轴运行于4个不同角速率
Figure 100265DEST_PATH_IMAGE113
，并采集加速度计的输出的整周均值。为方便起见，12位置采用统一的结构矩阵如公式（16）所示，当然也可以增加更多的角速率点进行测试。According to formula (16), the specific force input of each axis of the actual accelerometer corresponding to the 1st to 12th installation positions can be obtained. In the specific calculation, the specific force on the input shaft is accurate to a first-order small amount, and the pendulum shaft and the output shaft are Only the nominal value is calculated for the specific force of , and the first-order small quantities are ignored, because the coefficients related to the input specific forces of these two axes are also small quantities. in formula (16)
Figure 334937DEST_PATH_IMAGE110
is a known quantity used to calculate the indicated output of the accelerometer
Figure 959953DEST_PATH_IMAGE111
Take the first-order small quantity, which is related to other coefficients
Figure 225850DEST_PATH_IMAGE112
Just take the nominal value. To calibrate to the accelerometer's 3rd order error model coefficients, at least 4 specific force inputs are required for each paired position, i.e. the spindle is required to operate at 4 different angular rates
Figure 100265DEST_PATH_IMAGE113
, and collect the weekly mean of the output of the accelerometer. For convenience, the 12-position adopts a unified structure matrix as shown in formula (16). Of course, more angular rate points can be added for testing.

Figure 742599DEST_PATH_IMAGE114
Figure 742599DEST_PATH_IMAGE114

位置1上石英加速度计输入轴、摆轴和输出轴的比力分别为：The specific forces of the input shaft, pendulum shaft and output shaft of the quartz accelerometer at position 1 are:

Figure 222121DEST_PATH_IMAGE115
Figure 222121DEST_PATH_IMAGE115

其中

Figure 393340DEST_PATH_IMAGE116
均以g为单位，以下表达式相同。in
Figure 393340DEST_PATH_IMAGE116
All are in g, and the following expressions are the same.

将式(18)代入到式（16），石英加速度计在位置1的指示输出为：Substituting equation (18) into equation (16), the indicated output of the quartz accelerometer at position 1 is:

Figure 958313DEST_PATH_IMAGE117
Figure 958313DEST_PATH_IMAGE117

位置2上石英加速度计输入轴、摆轴和输出轴的比力分别为：The specific forces of the input shaft, pendulum shaft and output shaft of the quartz accelerometer at position 2 are:

Figure 669917DEST_PATH_IMAGE118
Figure 669917DEST_PATH_IMAGE118

将式(20)代入式（16），石英加速度计在位置2的指示输出为：Substituting equation (20) into equation (16), the indicated output of the quartz accelerometer at position 2 is:

Figure 770991DEST_PATH_IMAGE119
Figure 770991DEST_PATH_IMAGE119

分别将式(19)和式(21)相加和相减得到：Adding and subtracting equations (19) and (21) respectively, we get:

Figure 113110DEST_PATH_IMAGE120
Figure 113110DEST_PATH_IMAGE120

对于式（22）为加速度的常数项，一次项和二次项组成。对于式（23）为常数项、一次项、二次项和三次项组成。综合以上分析，采用主轴4个速率点进行测试，可以辨识

Figure 165380DEST_PATH_IMAGE121
。For equation (22), it is the constant term of acceleration, consisting of a first-order term and a quadratic term. For formula (23), it consists of constant term, first-order term, quadratic term and cubic term. Based on the above analysis, the 4 speed points of the spindle are used for testing, which can be identified
Figure 165380DEST_PATH_IMAGE121
.

Figure 680675DEST_PATH_IMAGE122
Figure 680675DEST_PATH_IMAGE122

其中“

Figure 869211DEST_PATH_IMAGE123
”表示此项理论上为零或者因为是很多位姿误差项的合成，而又没有必要写出。in"
Figure 869211DEST_PATH_IMAGE123
"Indicates that this item is theoretically zero or because it is a synthesis of many pose error terms, and there is no need to write it out.

式(24)写成矩阵形式为Equation (24) can be written in matrix form as

Figure 647811DEST_PATH_IMAGE124
Figure 647811DEST_PATH_IMAGE124

根据最小二乘可得：According to least squares, we can get:

Figure 984114DEST_PATH_IMAGE125
Figure 984114DEST_PATH_IMAGE125

在式(24)中，辨识

Figure 506363DEST_PATH_IMAGE126
项规避了离心机误差
Figure 814984DEST_PATH_IMAGE127
，从而提高了
Figure 498906DEST_PATH_IMAGE128
项的标定精度。In equation (24), identify
Figure 506363DEST_PATH_IMAGE126
term avoids centrifuge errors
Figure 814984DEST_PATH_IMAGE127
, thereby increasing the
Figure 498906DEST_PATH_IMAGE128
The calibration accuracy of the item.

根据式(23)可得According to formula (23), we can get

Figure 56927DEST_PATH_IMAGE129
Figure 56927DEST_PATH_IMAGE129

其中in

Figure 881401DEST_PATH_IMAGE130
Figure 881401DEST_PATH_IMAGE130

Figure 778950DEST_PATH_IMAGE131
Figure 778950DEST_PATH_IMAGE131

根据最小二乘可得：According to least squares, we can get:

Figure 899353DEST_PATH_IMAGE132
Figure 899353DEST_PATH_IMAGE132

在观测向量

Figure 210248DEST_PATH_IMAGE133
中补偿了动态误差项
Figure 74299DEST_PATH_IMAGE134
，
Figure 91934DEST_PATH_IMAGE135
和Coriolis加速度项，在误差系数向量中加入了离心机的位姿误差项
Figure 383238DEST_PATH_IMAGE136
，自动补偿了静态半径测试误差
Figure 915850DEST_PATH_IMAGE137
以及回转误差项等，消除了离心机误差和Coriolis加速度的影响，从而提高了
Figure 318013DEST_PATH_IMAGE138
和
Figure 190154DEST_PATH_IMAGE139
项的标定精度。in the observation vector
Figure 210248DEST_PATH_IMAGE133
compensated for the dynamic error term in
Figure 74299DEST_PATH_IMAGE134
,
Figure 91934DEST_PATH_IMAGE135
and Coriolis acceleration term, adding the centrifuge's pose error term to the error coefficient vector
Figure 383238DEST_PATH_IMAGE136
, which automatically compensates the static radius test error
Figure 915850DEST_PATH_IMAGE137
As well as the rotation error term, etc., the influence of centrifuge error and Coriolis acceleration is eliminated, thereby improving the
Figure 318013DEST_PATH_IMAGE138
and
Figure 190154DEST_PATH_IMAGE139
The calibration accuracy of the item.

位置3和4上石英加速度计输入轴、摆轴和输出轴的比力分别为：The specific forces of the input shaft, pendulum shaft and output shaft of the quartz accelerometer at positions 3 and 4 are:

Figure 419403DEST_PATH_IMAGE140
Figure 419403DEST_PATH_IMAGE140

将式（28）和式（29）分别代入到式（16）中，计算出石英加速度计的指示输出

Figure 173733DEST_PATH_IMAGE141
和
Figure 379586DEST_PATH_IMAGE142
，并进行加减消元运算，得到以下表达式：Substitute Equation (28) and Equation (29) into Equation (16) respectively to calculate the indication output of the quartz accelerometer
Figure 173733DEST_PATH_IMAGE141
and
Figure 379586DEST_PATH_IMAGE142
, and perform addition, subtraction, and subtraction operations to obtain the following expression:

Figure 371813DEST_PATH_IMAGE143
Figure 371813DEST_PATH_IMAGE143

Figure 4919DEST_PATH_IMAGE144
Figure 4919DEST_PATH_IMAGE144

根据式（30）可得：According to formula (30), we can get:

Figure 512124DEST_PATH_IMAGE145
Figure 512124DEST_PATH_IMAGE145

其中in

Figure 521668DEST_PATH_IMAGE146
Figure 521668DEST_PATH_IMAGE146

根据式（31）可得：According to formula (31), we can get:

Figure 102822DEST_PATH_IMAGE147
Figure 102822DEST_PATH_IMAGE147

其中in

Figure 172410DEST_PATH_IMAGE148
Figure 172410DEST_PATH_IMAGE148

补偿掉动态失准角所产生的附加加速度后，可以辨识出

Figure 901331DEST_PATH_IMAGE149
和
Figure 714566DEST_PATH_IMAGE150
项。After compensating for the additional acceleration caused by the dynamic misalignment angle, it can be identified
Figure 901331DEST_PATH_IMAGE149
and
Figure 714566DEST_PATH_IMAGE150
item.

位置5和6上石英加速度计输入轴、摆轴和输出轴的比力分别为：The specific forces of the input shaft, pendulum shaft and output shaft of the quartz accelerometer at positions 5 and 6 are:

Figure 914341DEST_PATH_IMAGE151
Figure 914341DEST_PATH_IMAGE151

将式（34）和式（35）分别代入到式（16）中，计算出石英加速度计的指示输出

Figure 889251DEST_PATH_IMAGE152
和
Figure 371048DEST_PATH_IMAGE153
，并进行加减消元运算，得到以下表达式：Substitute Equation (34) and Equation (35) into Equation (16) respectively to calculate the indication output of the quartz accelerometer
Figure 889251DEST_PATH_IMAGE152
and
Figure 371048DEST_PATH_IMAGE153
, and perform addition, subtraction, and subtraction operations to obtain the following expression:

Figure 722394DEST_PATH_IMAGE154
Figure 722394DEST_PATH_IMAGE154

根据式（36）可得：According to formula (36), we can get:

Figure 278141DEST_PATH_IMAGE155
Figure 278141DEST_PATH_IMAGE155

其中in

Figure 423951DEST_PATH_IMAGE156
Figure 423951DEST_PATH_IMAGE156

根据式(37)可得：According to formula (37), we can get:

Figure 127465DEST_PATH_IMAGE157
Figure 127465DEST_PATH_IMAGE157

其中in

Figure 16924DEST_PATH_IMAGE158
Figure 16924DEST_PATH_IMAGE158

同样补偿掉动态失准角所产生的附加加速度后，可以辨识出

Figure 692756DEST_PATH_IMAGE159
和
Figure 71784DEST_PATH_IMAGE160
项。Also after compensating for the additional acceleration caused by the dynamic misalignment angle, it can be identified that
Figure 692756DEST_PATH_IMAGE159
and
Figure 71784DEST_PATH_IMAGE160
item.

位置7和8上石英加速度计输入轴、摆轴和输出轴的比力分别为：The specific forces of the input shaft, pendulum shaft and output shaft of the quartz accelerometer at positions 7 and 8 are:

Figure 465857DEST_PATH_IMAGE161
Figure 465857DEST_PATH_IMAGE161

Figure 406610DEST_PATH_IMAGE162
Figure 406610DEST_PATH_IMAGE162

将式（39）和式（40）分别代入到式（16）中，计算出石英加速度计的指示输出

Figure 202528DEST_PATH_IMAGE163
，并进行加减消元运算，得到以下表达式：Substitute Equation (39) and Equation (40) into Equation (16) respectively to calculate the indication output of the quartz accelerometer
Figure 202528DEST_PATH_IMAGE163
, and perform addition, subtraction, and subtraction operations to obtain the following expression:

Figure 955721DEST_PATH_IMAGE164
Figure 955721DEST_PATH_IMAGE164

根据式（42）可得：According to formula (42), we can get:

Figure 368247DEST_PATH_IMAGE165
Figure 368247DEST_PATH_IMAGE165

其中in

Figure 599509DEST_PATH_IMAGE166
Figure 599509DEST_PATH_IMAGE166

精确辨识出

Figure 249933DEST_PATH_IMAGE167
系数后，再减去以前辨识的
Figure 970764DEST_PATH_IMAGE168
，可以辨识
Figure 339428DEST_PATH_IMAGE169
误差模型系数。accurately identified
Figure 249933DEST_PATH_IMAGE167
After the coefficient, subtract the previously identified
Figure 970764DEST_PATH_IMAGE168
, can be identified
Figure 339428DEST_PATH_IMAGE169
Error model coefficients.

根据式（43）可得：According to formula (43), we can get:

Figure 374381DEST_PATH_IMAGE170
Figure 374381DEST_PATH_IMAGE170

其中in

Figure 613732DEST_PATH_IMAGE171
Figure 613732DEST_PATH_IMAGE171

位置9和10上石英加速度计输入轴、摆轴和输出轴的比力分别为：The specific forces of the input, pendulum, and output shafts of the quartz accelerometer at positions 9 and 10 are:

Figure 207262DEST_PATH_IMAGE172
Figure 207262DEST_PATH_IMAGE172

将式（45）和式（46）分别代入到式（16）中，计算出石英加速度计的指示输出

Figure 594381DEST_PATH_IMAGE173
，并进行加减消元运算，得到以下表达式：Substitute Equation (45) and Equation (46) into Equation (16) respectively to calculate the indication output of the quartz accelerometer
Figure 594381DEST_PATH_IMAGE173
, and perform addition, subtraction, and subtraction operations to obtain the following expression:

Figure 167445DEST_PATH_IMAGE174
Figure 167445DEST_PATH_IMAGE174

Figure 792461DEST_PATH_IMAGE175
Figure 792461DEST_PATH_IMAGE175

根据式（48）可得：According to formula (48), we can get:

Figure 58358DEST_PATH_IMAGE176
Figure 58358DEST_PATH_IMAGE176

其中in

Figure 932773DEST_PATH_IMAGE177
Figure 932773DEST_PATH_IMAGE177

补偿动态失准角的影响之后，辨识

Figure 309527DEST_PATH_IMAGE178
后，再减去
Figure 523471DEST_PATH_IMAGE179
即可得
Figure 757006DEST_PATH_IMAGE180
。After compensating for the effect of dynamic misalignment angle, identify
Figure 309527DEST_PATH_IMAGE178
, then subtract
Figure 523471DEST_PATH_IMAGE179
available
Figure 757006DEST_PATH_IMAGE180
.

根据式（49）可得：According to formula (49), we can get:

Figure 321980DEST_PATH_IMAGE181
Figure 321980DEST_PATH_IMAGE181

其中in

Figure 236846DEST_PATH_IMAGE182
Figure 236846DEST_PATH_IMAGE182

位置11和12上石英加速度计输入轴、摆轴和输出轴的比力分别为：The specific forces of the input shaft, pendulum shaft and output shaft of the quartz accelerometer at positions 11 and 12 are:

Figure 337920DEST_PATH_IMAGE183
Figure 337920DEST_PATH_IMAGE183

将式(51)和式(52)分别代入到式(16)中，计算出石英加速度计的指示输出

Figure 742356DEST_PATH_IMAGE184
和
Figure 529047DEST_PATH_IMAGE185
，并进行加减消元运算，得到以下表达式：Substitute Equation (51) and Equation (52) into Equation (16) respectively to calculate the indication output of the quartz accelerometer
Figure 742356DEST_PATH_IMAGE184
and
Figure 529047DEST_PATH_IMAGE185
, and perform addition, subtraction, and subtraction operations to obtain the following expression:

Figure 247604DEST_PATH_IMAGE186
Figure 247604DEST_PATH_IMAGE186

Figure 701719DEST_PATH_IMAGE187
Figure 701719DEST_PATH_IMAGE187

根据式（54）可得：According to formula (54), we can get:

Figure 480319DEST_PATH_IMAGE188
Figure 480319DEST_PATH_IMAGE188

其中in

Figure 551043DEST_PATH_IMAGE189
Figure 551043DEST_PATH_IMAGE189

辨识出

Figure 807712DEST_PATH_IMAGE190
后，再减去辨识出的
Figure 116334DEST_PATH_IMAGE191
即可得到
Figure 862573DEST_PATH_IMAGE192
项。identify
Figure 807712DEST_PATH_IMAGE190
After that, subtract the identified
Figure 116334DEST_PATH_IMAGE191
can get
Figure 862573DEST_PATH_IMAGE192
item.

根据式（55）可得：According to formula (55), we can get:

Figure 889435DEST_PATH_IMAGE193
Figure 889435DEST_PATH_IMAGE193

其中in

Figure 182751DEST_PATH_IMAGE194
Figure 182751DEST_PATH_IMAGE194

综合前面推出的公式，可得石英加速度计高阶误差项的标定结果如下：Combining the formulas introduced above, the calibration results of the high-order error term of the quartz accelerometer can be obtained as follows:

Figure 611458DEST_PATH_IMAGE195
Figure 611458DEST_PATH_IMAGE195

可归纳出石英加速度计高阶误差模型系数的表达式为The expression of the high-order error model coefficients of the quartz accelerometer can be summarized as

Figure 528598DEST_PATH_IMAGE196
Figure 528598DEST_PATH_IMAGE196

如图2所示，本实施例所涉及的一种加速度计在精密离心机上的参数标定方法，令

Figure 777177DEST_PATH_IMAGE197
，可得误差模型系数
Figure 641228DEST_PATH_IMAGE198
项的表达式为：As shown in FIG. 2, a method for calibrating parameters of an accelerometer on a precision centrifuge involved in this embodiment is as follows:
Figure 777177DEST_PATH_IMAGE197
, the error model coefficients can be obtained
Figure 641228DEST_PATH_IMAGE198
The expression for the term is:

Figure 658863DEST_PATH_IMAGE199
Figure 658863DEST_PATH_IMAGE199

其中

Figure 950167DEST_PATH_IMAGE200
表示矩阵
Figure 482779DEST_PATH_IMAGE201
第
Figure 884942DEST_PATH_IMAGE202
行，第
Figure 22662DEST_PATH_IMAGE203
列的元素。假设石英加速度计的指示输出独立且精度相等，其不确定度为
Figure 281605DEST_PATH_IMAGE204
，那么
Figure 6241DEST_PATH_IMAGE205
项的不确定度为in
Figure 950167DEST_PATH_IMAGE200
representation matrix
Figure 482779DEST_PATH_IMAGE201
the first
Figure 884942DEST_PATH_IMAGE202
OK, No.
Figure 22662DEST_PATH_IMAGE203
element of the column. Assuming that the indicated outputs of the quartz accelerometer are independent and of equal accuracy, the uncertainty is
Figure 281605DEST_PATH_IMAGE204
,So
Figure 6241DEST_PATH_IMAGE205
The uncertainty of the term is

Figure 212094DEST_PATH_IMAGE206
Figure 212094DEST_PATH_IMAGE206

假设离心机提供5g，10g，15g和20g的向心加速度，石英加速度计的输出的不确定度为

Figure 204321DEST_PATH_IMAGE207
，动态失准角不确定度
Figure 634165DEST_PATH_IMAGE208
，动态半径误差的不确定度
Figure 344632DEST_PATH_IMAGE209
。经计算可得，石英加速度计的二次项和交叉二次项的不确定度分别为
Figure 88597DEST_PATH_IMAGE210
Figure 935331DEST_PATH_IMAGE212
Assuming centripetal accelerations of 5g, 10g, 15g and 20g are provided by the centrifuge, the uncertainty of the output of the quartz accelerometer is
Figure 204321DEST_PATH_IMAGE207
, the dynamic misalignment angle uncertainty
Figure 634165DEST_PATH_IMAGE208
, the uncertainty of the dynamic radius error
Figure 344632DEST_PATH_IMAGE209
. After calculation, the uncertainty of the quadratic term and the cross quadratic term of the quartz accelerometer are respectively
Figure 88597DEST_PATH_IMAGE210
Figure 935331DEST_PATH_IMAGE212

以上所述，仅为本发明的具体实施方式，但本发明的保护范围并不局限于此，任何熟悉本技术领域的技术人员在本发明揭露的技术范围内，可轻易想到的变化或替换，都应涵盖在本发明的保护范围之内。因此，本发明的保护范围应以权利要求的保护范围为准。The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art who is familiar with the technical scope disclosed by the present invention can easily think of changes or substitutions. All should be included within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims (6)

1.一种加速度计在精密离心机上的参数标定方法，其特征在于，包括：1. a parameter calibration method of an accelerometer on a precision centrifuge, is characterized in that, comprises: 获取精密离心机的各静态误差以及动态误差，并根据精密离心机的结构建立坐标系，以及根据所述各静态误差以及动态误差计算所述坐标系下的位姿误差；Acquiring various static errors and dynamic errors of the precision centrifuge, establishing a coordinate system according to the structure of the precision centrifuge, and calculating the pose errors under the coordinate system according to the various static errors and dynamic errors; 驱动精密离心机的主轴以匀角速率旋转，以产生向心加速度标定加速度计，基于所述坐标系下的位姿误差计算向心加速度、重力加速度和Coriolis加速度的比力分配，以确定加速度计误差模型；The main shaft that drives the precision centrifuge rotates at a constant angular rate to generate centripetal acceleration to calibrate the accelerometer, and the specific force distribution of centripetal acceleration, gravitational acceleration and Coriolis acceleration is calculated based on the pose error in the coordinate system to determine the accelerometer error model; 对加速度计在三种不同安装方式下的六个对称位置的指示输出，利用加减消元的方法标定加速度计误差模型表达式中的高阶项误差系数。For the indication output of the six symmetrical positions of the accelerometer under three different installation methods, the method of adding and subtracting the subtraction element is used to calibrate the error coefficient of the higher-order term in the accelerometer's error model expression. 2.根据权利要求1所述的加速度计在精密离心机上的参数标定方法，其特征在于，所述精密离心机包括主轴、水平轴和方位轴；2. The method for calibrating parameters of an accelerometer on a precision centrifuge according to claim 1, wherein the precision centrifuge comprises a main shaft, a horizontal axis and an azimuth axis; 所述精密离心机的静态误差包括主轴轴线的二维铅垂度误差
Figure 619406DEST_PATH_IMAGE001
水平轴轴线与主轴轴线的垂直度
Figure 940666DEST_PATH_IMAGE002
相交度
Figure 429416DEST_PATH_IMAGE003
水平轴轴线与方位轴轴线的垂直度
Figure 759904DEST_PATH_IMAGE004
相交度
Figure 752130DEST_PATH_IMAGE005
以及方位轴的初始零位误差
Figure 916396DEST_PATH_IMAGE006
安装惯性仪表的工作基面对方位轴轴线的垂直度
Figure 751496DEST_PATH_IMAGE007
加速度计安装基面姿态误差
Figure 761041DEST_PATH_IMAGE008
偏心误差
Figure 997987DEST_PATH_IMAGE009
以及初始对零误差
Figure 801995DEST_PATH_IMAGE010
主轴、水平轴和方位轴三个轴的角位置误差分别为
Figure 265337DEST_PATH_IMAGE011
The static error of the precision centrifuge includes the two-dimensional plumb error of the main shaft axis
Figure 619406DEST_PATH_IMAGE001
The perpendicularity of the horizontal axis axis to the main axis axis
Figure 940666DEST_PATH_IMAGE002
degree of intersection
Figure 429416DEST_PATH_IMAGE003
The perpendicularity of the horizontal axis axis to the azimuth axis axis
Figure 759904DEST_PATH_IMAGE004
degree of intersection
Figure 752130DEST_PATH_IMAGE005
and the initial zero error of the azimuth axis
Figure 916396DEST_PATH_IMAGE006
The perpendicularity of the working base where the inertial instrument is installed to the axis of the azimuth axis
Figure 751496DEST_PATH_IMAGE007
Attitude error of accelerometer mounting base
Figure 761041DEST_PATH_IMAGE008
Eccentricity error
Figure 997987DEST_PATH_IMAGE009
and the initial zero-to-zero error
Figure 801995DEST_PATH_IMAGE010
The angular position errors of the main axis, the horizontal axis and the azimuth axis are respectively
Figure 265337DEST_PATH_IMAGE011
 所述精密离心机的动态误差包括主轴径向回转误差
Figure 937627DEST_PATH_IMAGE012
轴向窜动
Figure 904446DEST_PATH_IMAGE013
及倾角回转误差
Figure 535148DEST_PATH_IMAGE014
动态半径误差
Figure 954628DEST_PATH_IMAGE015
动态失准角
Figure 571554DEST_PATH_IMAGE016
水平轴径向回转误差
Figure 517513DEST_PATH_IMAGE017
轴向窜动
Figure 928903DEST_PATH_IMAGE018
以及倾角回转误差
Figure 225892DEST_PATH_IMAGE019
方位轴径向回转误差
Figure 115350DEST_PATH_IMAGE020
，轴向窜动
Figure 181395DEST_PATH_IMAGE021
倾角回转误差
Figure 29266DEST_PATH_IMAGE022
；The dynamic error of the precision centrifuge includes the radial rotation error of the main shaft
Figure 937627DEST_PATH_IMAGE012
Axial play
Figure 904446DEST_PATH_IMAGE013
and tilt angle error
Figure 535148DEST_PATH_IMAGE014
Dynamic radius error
Figure 954628DEST_PATH_IMAGE015
Dynamic misalignment angle
Figure 571554DEST_PATH_IMAGE016
Horizontal axis radial rotation error
Figure 517513DEST_PATH_IMAGE017
Axial play
Figure 928903DEST_PATH_IMAGE018
and the inclination rotation error
Figure 225892DEST_PATH_IMAGE019
Azimuth axis radial rotation error
Figure 115350DEST_PATH_IMAGE020
, the axial movement
Figure 181395DEST_PATH_IMAGE021
Tilt rotation error
Figure 29266DEST_PATH_IMAGE022
; 半径误差
Figure 423338DEST_PATH_IMAGE023
其中，
Figure 241121DEST_PATH_IMAGE024
为静态半径标称值，是由计量部门标定出的已知量，半径的静态测试误差
Figure 37039DEST_PATH_IMAGE025
是未知量，
Figure 914865DEST_PATH_IMAGE026
为用双频激光干涉仪监测的精密离心机在运行状态下的实际工作半径相对于离心机静态半径的变化量，是主轴角速率
Figure 61813DEST_PATH_IMAGE027
的函数。radius error
Figure 423338DEST_PATH_IMAGE023
in,
Figure 241121DEST_PATH_IMAGE024
It is the nominal value of the static radius, which is a known quantity calibrated by the metrology department, and the static test error of the radius
Figure 37039DEST_PATH_IMAGE025
is the unknown quantity,
Figure 914865DEST_PATH_IMAGE026
It is the variation of the actual working radius of the precision centrifuge under the running state monitored by the dual-frequency laser interferometer relative to the static radius of the centrifuge, which is the angular velocity of the main shaft.
Figure 61813DEST_PATH_IMAGE027
The function. 3.根据权利要求2所述的加速度计在精密离心机上的参数标定方法，其特征在于，所述根据精密离心机的结构建立坐标系，以及根据所述各静态误差以及动态误差计算所述坐标系下的位姿误差包括：3. the parameter calibration method of the accelerometer according to claim 2 on the precision centrifuge, it is characterized in that, described establishing coordinate system according to the structure of precision centrifuge, and calculating described coordinate according to described each static error and dynamic error The pose errors under the system include: 建立地理坐标系
Figure 558653DEST_PATH_IMAGE028
轴水平指东，
Figure 333711DEST_PATH_IMAGE029
轴水平指北，
Figure 257805DEST_PATH_IMAGE030
轴指天，构成右手坐标系；Create a geographic coordinate system
Figure 558653DEST_PATH_IMAGE028
The axis points to the east horizontally,
Figure 333711DEST_PATH_IMAGE029
The axis points horizontally to the north,
Figure 257805DEST_PATH_IMAGE030
The axis points to the sky, forming a right-handed coordinate system; 建立主轴轴套坐标系
Figure 751103DEST_PATH_IMAGE031
得到主轴轴套坐标系相对于地理坐标系的位姿；Establishing the spindle bushing coordinate system
Figure 751103DEST_PATH_IMAGE031
Obtain the pose of the spindle sleeve coordinate system relative to the geographic coordinate system; 建立主轴坐标系
Figure 786055DEST_PATH_IMAGE032
得到主轴坐标系相对于主轴轴套坐标系的位姿；Establish the main axis coordinate system
Figure 786055DEST_PATH_IMAGE032
Obtain the pose of the spindle coordinate system relative to the spindle sleeve coordinate system; 建立水平轴轴套坐标系
Figure 822144DEST_PATH_IMAGE033
得到水平轴轴套坐标系相对于主轴坐标系的位姿；Establish the coordinate system of the horizontal axis sleeve
Figure 822144DEST_PATH_IMAGE033
Obtain the pose of the horizontal axis sleeve coordinate system relative to the main axis coordinate system; 建立水平轴坐标系
Figure 776194DEST_PATH_IMAGE034
得到水平轴坐标系相对于水平轴轴套坐标系的位姿；Create a horizontal axis coordinate system
Figure 776194DEST_PATH_IMAGE034
Obtain the pose of the horizontal axis coordinate system relative to the horizontal axis bushing coordinate system; 建立方位轴轴套坐标系
Figure 632154DEST_PATH_IMAGE035
得到方位轴轴套坐标系相对于水平轴坐标系的位姿；Establishing the azimuth axis bushing coordinate system
Figure 632154DEST_PATH_IMAGE035
Obtain the pose of the azimuth axis sleeve coordinate system relative to the horizontal axis coordinate system; 建立方位轴坐标系
Figure 861010DEST_PATH_IMAGE036
得到方位轴坐标系相对于方位轴轴套坐标系的位姿；Establish the azimuth axis coordinate system
Figure 861010DEST_PATH_IMAGE036
Obtain the pose of the azimuth axis coordinate system relative to the azimuth axis bushing coordinate system; 建立工作基面坐标系
Figure 220447DEST_PATH_IMAGE037
得到工作基面坐标系相对于方位轴坐标系的位姿；Establish work base coordinate system
Figure 220447DEST_PATH_IMAGE037
Obtain the pose of the working base coordinate system relative to the azimuth axis coordinate system; 建立加速度计坐标系
Figure 610978DEST_PATH_IMAGE038
得到加速度计坐标系相对于工作基面坐标系的位姿、加速度计坐标系相对于地理坐标系的位姿、加速度计坐标系相对于主轴坐标系的位姿。Create the accelerometer coordinate system
Figure 610978DEST_PATH_IMAGE038
Obtain the pose of the accelerometer coordinate system relative to the working base 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 spindle coordinate system. 4.根据权利要求3所述的加速度计在精密离心机上的参数标定方法，其特征在于，4. the parameter calibration method of the accelerometer according to claim 3 on the precision centrifuge, is characterized in that, 主轴轴套坐标系相对于地理坐标系的位姿为The pose of the spindle sleeve coordinate system relative to the geographic coordinate system is
Figure 954234DEST_PATH_IMAGE039
Figure 954234DEST_PATH_IMAGE039
 主轴坐标系相对于主轴轴套坐标系的位姿为The pose of the spindle coordinate system relative to the spindle sleeve coordinate system is
Figure 596568DEST_PATH_IMAGE040
Figure 596568DEST_PATH_IMAGE040
 其中
Figure 466304DEST_PATH_IMAGE041
表示主轴旋转的角度；in
Figure 466304DEST_PATH_IMAGE041
Indicates the rotation angle of the main shaft; 水平轴轴套坐标系相对于主轴坐标系的位姿为The pose of the horizontal axis bushing coordinate system relative to the main axis coordinate system is
Figure 903102DEST_PATH_IMAGE042
Figure 903102DEST_PATH_IMAGE042
 水平轴坐标系相对于水平轴轴套坐标系的位姿为The pose of the horizontal axis coordinate system relative to the horizontal axis sleeve coordinate system is
Figure 616146DEST_PATH_IMAGE043
Figure 616146DEST_PATH_IMAGE043
 其中
Figure 62171DEST_PATH_IMAGE044
表示水平轴旋转的角度；in
Figure 62171DEST_PATH_IMAGE044
Indicates the angle of rotation of the horizontal axis; 方位轴轴套坐标系相对于水平轴坐标系的位姿为The pose of the azimuth axis bushing coordinate system relative to the horizontal axis coordinate system is
Figure 396201DEST_PATH_IMAGE045
Figure 396201DEST_PATH_IMAGE045
 方位轴坐标系相对于方位轴轴套坐标系的位姿为The pose of the azimuth axis coordinate system relative to the azimuth axis bushing coordinate system is
Figure 394112DEST_PATH_IMAGE046
Figure 394112DEST_PATH_IMAGE046
 其中
Figure 446382DEST_PATH_IMAGE047
表示方位轴旋转的角度；in
Figure 446382DEST_PATH_IMAGE047
Indicates the angle of rotation of the azimuth axis; 工作基面坐标系相对于方位轴坐标系的位姿为The pose of the working base coordinate system relative to the azimuth axis coordinate system is
Figure 430519DEST_PATH_IMAGE048
Figure 430519DEST_PATH_IMAGE048
 其中
Figure 9268DEST_PATH_IMAGE049
为
Figure 53447DEST_PATH_IMAGE050
点相对
Figure 717646DEST_PATH_IMAGE051
点位移；in
Figure 9268DEST_PATH_IMAGE049
for
Figure 53447DEST_PATH_IMAGE050
point relative
Figure 717646DEST_PATH_IMAGE051
point displacement; 加速度计坐标系相对于工作基面坐标系的位姿为The pose of the accelerometer coordinate system relative to the working base coordinate system is
Figure 239895DEST_PATH_IMAGE052
Figure 239895DEST_PATH_IMAGE052
 其中
Figure 814095DEST_PATH_IMAGE053
为
Figure 888231DEST_PATH_IMAGE054
点相对
Figure 915093DEST_PATH_IMAGE055
点位移；in
Figure 814095DEST_PATH_IMAGE053
for
Figure 888231DEST_PATH_IMAGE054
point relative
Figure 915093DEST_PATH_IMAGE055
point displacement; 加速度计坐标系相对于地理坐标系的位姿为The pose of the accelerometer coordinate system relative to the geographic coordinate system is
Figure 365665DEST_PATH_IMAGE056
Figure 365665DEST_PATH_IMAGE056
 其中
Figure 528794DEST_PATH_IMAGE057
表示加速度计坐标系与地理坐标系之间的姿态变换矩阵，
Figure 914775DEST_PATH_IMAGE058
为加速度计坐标系与地理坐标系的相对位移矢量；in
Figure 528794DEST_PATH_IMAGE057
represents the attitude transformation matrix between the accelerometer coordinate system and the geographic coordinate system,
Figure 914775DEST_PATH_IMAGE058
is the relative displacement vector between the accelerometer coordinate system and the geographic coordinate system; 加速度计坐标系相对于主轴坐标系的位姿为The pose of the accelerometer coordinate system relative to the spindle coordinate system is
Figure 553567DEST_PATH_IMAGE059
Figure 553567DEST_PATH_IMAGE059
 其中
Figure 417618DEST_PATH_IMAGE060
表示加速度计坐标系与主轴坐标系之间的姿态变换矩阵；in
Figure 417618DEST_PATH_IMAGE060
Represents the attitude transformation matrix between the accelerometer coordinate system and the spindle coordinate system; 加速度计坐标系原点在主轴坐标系下表示为
Figure 825466DEST_PATH_IMAGE061
忽略二阶小量后可得，
Figure 382349DEST_PATH_IMAGE062
Figure 383803DEST_PATH_IMAGE063
The origin of the accelerometer coordinate system is expressed in the spindle coordinate system as
Figure 825466DEST_PATH_IMAGE061
After ignoring the second-order epsilon, it can be obtained,
Figure 382349DEST_PATH_IMAGE062
Figure 383803DEST_PATH_IMAGE063
 5.根据权利要求1所述的加速度计在精密离心机上的参数标定方法，其特征在于，所述加速度计误差模型的表达式为：5. the parameter calibration method of accelerometer according to claim 1 on precision centrifuge is characterized in that, the expression of described accelerometer error model is:
Figure 176178DEST_PATH_IMAGE064
Figure 176178DEST_PATH_IMAGE064
 其中，
Figure 48320DEST_PATH_IMAGE065
为加速度计输出值；in,
Figure 48320DEST_PATH_IMAGE065
is the output value of the accelerometer;
Figure 900738DEST_PATH_IMAGE066
为加速度计的输出当量；
Figure 900738DEST_PATH_IMAGE066
is the output equivalent of the accelerometer;
Figure 389488DEST_PATH_IMAGE067
为标度因数；
Figure 389488DEST_PATH_IMAGE067
is the scale factor;
Figure 719975DEST_PATH_IMAGE068
分别为加速度计输入轴，摆轴和输出轴上的加速度分量；
Figure 719975DEST_PATH_IMAGE068
are the acceleration components on the input shaft, pendulum shaft and output shaft of the accelerometer, respectively;
Figure 977781DEST_PATH_IMAGE069
为零偏；
Figure 977781DEST_PATH_IMAGE069
zero bias;
Figure 876467DEST_PATH_IMAGE070
为交叉轴敏感度；
Figure 876467DEST_PATH_IMAGE070
is the cross-axis sensitivity;
Figure 445989DEST_PATH_IMAGE071
为二阶非线性系数；
Figure 445989DEST_PATH_IMAGE071
is the second-order nonlinear coefficient;
Figure 721112DEST_PATH_IMAGE072
为奇异二次项系数；
Figure 721112DEST_PATH_IMAGE072
is the singular quadratic term coefficient;
Figure 958059DEST_PATH_IMAGE073
为三阶非线性系数；
Figure 958059DEST_PATH_IMAGE073
is the third-order nonlinear coefficient;
Figure 762066DEST_PATH_IMAGE074
为交叉耦合系数；
Figure 762066DEST_PATH_IMAGE074
is the cross-coupling coefficient;
Figure 225409DEST_PATH_IMAGE075
—随机误差；
Figure 225409DEST_PATH_IMAGE075
-Random error; 所述高阶项误差系数包括所述二阶非线性系数、奇异二次项系数、三阶非线性系数以及交叉耦合系数。The higher-order term error coefficients include the second-order nonlinear coefficients, singular quadratic term coefficients, third-order nonlinear coefficients, and cross-coupling coefficients. 6.根据权利要求5所述的加速度计在精密离心机上的参数标定方法，其特征在于，所述对加速度计在三种不同安装方式下的六个对称位置的指示输出，利用加减消元的方法标定加速度计误差模型表达式中的高阶项误差系数包括：6. The method for calibrating parameters of an accelerometer on a precision centrifuge according to claim 5, wherein the indication output of the six symmetrical positions of the accelerometer under three different installation modes is performed by adding and subtracting elements. The method of calibrating the higher-order term error coefficients in the accelerometer error model expression includes: 当加速度计的输出轴始终与离心机的方位轴轴线一致，离心机的水平轴始终处于
Figure 897699DEST_PATH_IMAGE076
位置，可获得3对成对位置，分别为：位置1与位置2、位置3与位置4、位置5与位置6；当加速度计的输入轴始终与离心机的方位轴轴线一致，水平轴处于
Figure 864518DEST_PATH_IMAGE077
位置，可获得2对成对位置，分别为：位置7与位置8、位置9与位置10；当加速度计的摆轴与离心机的方位轴轴线方向相反，水平轴始终处于
Figure 229640DEST_PATH_IMAGE078
位置，方位轴处于
Figure 180278DEST_PATH_IMAGE079
2个位置，分别为：位置11与位置12；When the output shaft of the accelerometer is always consistent with the azimuth axis of the centrifuge, the horizontal axis of the centrifuge is always in
Figure 897699DEST_PATH_IMAGE076
position, three pairs of positions can be obtained, namely: 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 azimuth axis of the centrifuge, the horizontal axis is at
Figure 864518DEST_PATH_IMAGE077
position, two pairs of positions can be obtained, namely: position 7 and position 8, position 9 and position 10; when the pendulum axis of the accelerometer is opposite to the azimuth axis of the centrifuge, the horizontal axis is always in
Figure 229640DEST_PATH_IMAGE078
position, the azimuth axis is at
Figure 180278DEST_PATH_IMAGE079
2 positions, namely: position 11 and position 12; 12个位置采用统一的结构矩阵如式(17)所示，The 12 positions adopt a unified structure matrix as shown in formula (17),
Figure 531625DEST_PATH_IMAGE080
Figure 531625DEST_PATH_IMAGE080
 根据位置1和位置2上加速度计输入轴、摆轴和输出轴的比力辨识出
Figure 477585DEST_PATH_IMAGE081
项和
Figure 154554DEST_PATH_IMAGE082
项；It is identified from the ratio of the accelerometer input shaft, pendulum shaft and output shaft at position 1 and position 2
Figure 477585DEST_PATH_IMAGE081
item and
Figure 154554DEST_PATH_IMAGE082
item; 根据位置3和位置4上加速度计输入轴、摆轴和输出轴的比力辨识出
Figure 185963DEST_PATH_IMAGE083
和
Figure 341001DEST_PATH_IMAGE084
项；It is identified from the ratio of the accelerometer input shaft, pendulum shaft and output shaft at positions 3 and 4
Figure 185963DEST_PATH_IMAGE083
and
Figure 341001DEST_PATH_IMAGE084
item; 根据位置5和位置6上加速度计输入轴、摆轴和输出轴的比力辨识出
Figure 282412DEST_PATH_IMAGE085
项和
Figure 723758DEST_PATH_IMAGE086
项；According to the specific force of the accelerometer input shaft, pendulum shaft and output shaft at position 5 and position 6
Figure 282412DEST_PATH_IMAGE085
item and
Figure 723758DEST_PATH_IMAGE086
item; 根据位置7和位置8上加速度计输入轴、摆轴和输出轴的比力辨识出
Figure 117830DEST_PATH_IMAGE087
项；It is identified from the ratio of the accelerometer input shaft, pendulum shaft and output shaft at positions 7 and 8.
Figure 117830DEST_PATH_IMAGE087
item; 根据位置9和位置10上加速度计输入轴、摆轴和输出轴的比力辨识出
Figure 201193DEST_PATH_IMAGE088
项；It is identified from the ratio of the accelerometer input shaft, pendulum shaft and output shaft at positions 9 and 10.
Figure 201193DEST_PATH_IMAGE088
item; 根据位置11和位置12上加速度计输入轴、摆轴和输出轴的比力辨识出
Figure 997111DEST_PATH_IMAGE089
项。According to the specific force of the accelerometer input shaft, pendulum shaft and output shaft at position 11 and position 12
Figure 997111DEST_PATH_IMAGE089
item.
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