CN113156166A - Symmetry melting and elimination test method of quartz accelerometer on precision centrifuge - Google Patents
Symmetry melting and elimination test method of quartz accelerometer on precision centrifuge Download PDFInfo
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Abstract
The invention provides a symmetry melting and elimination test method of a quartz accelerometer on a precision centrifuge, belonging to the field of calibration of centrifuges. The method comprises the following specific steps: the method comprises the following steps: establishing a coordinate system according to the structure of the precision centrifuge and calculating a pose error; step two: when a spindle of the precision centrifuge rotates at a uniform angular velocity to generate centripetal acceleration calibration acceleration timing, calculating the specific force distribution of the centripetal acceleration, the gravity accelerometer and the Coriolis acceleration; step three: giving out an error model expression of the quartz accelerometer according to the content of the second step; step four: and calibrating a high-order term error coefficient in the quartz accelerometer error model expression by adopting 6 symmetrical position combinations and a method of adding and subtracting a damping element. The method can completely eliminate the dynamic error and the static error of the centrifuge by monitoring and compensating the dynamic misalignment angle and the dynamic radius under the condition of stable error of the centrifuge, and can effectively improve the calibration precision of the high-order error model coefficient of the quartz accelerometer.
Description
Technical Field
The invention relates to a symmetry melting and elimination test method of a quartz accelerometer on a precision centrifuge, belonging to the field of calibration of centrifuges.
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. However, the quadratic error coefficient KOO and the cubic error coefficients KPPP and KOOO are not identified, 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
The invention aims to solve the problems in the prior art, and further provides a method for testing the symmetric melting and extinction of a quartz accelerometer on a precision centrifuge.
The purpose of the invention is realized by the following technical scheme:
a method for testing the symmetry melting and elimination of a quartz accelerometer on a precision centrifuge comprises the following steps:
the method comprises the following steps: establishing a coordinate system according to the structure of the precision centrifuge and calculating a pose error;
step two: when a spindle of the precision centrifuge rotates at a uniform angular velocity to generate centripetal acceleration calibration acceleration timing, calculating the specific force distribution of the centripetal acceleration, the gravity accelerometer and the Coriolis acceleration;
step three: giving out an error model expression of the quartz accelerometer according to the content of the second step;
step four: and calibrating a high-order term error coefficient in the quartz accelerometer error model expression by adopting 6 symmetrical position combinations and a method of adding and subtracting a damping element.
The invention relates to a method for testing the symmetry melting and elimination of a quartz accelerometer on a precision centrifuge, wherein the precision centrifuge comprises 3 shafting of a main shaft, a horizontal shaft and an azimuth shaft;
the static error source of the centrifuge includes the two-dimensional sag error Delta theta of the spindle axisx0、Δθy0(ii) a Perpendicularity delta lambda of horizontal shaft axis and main shaft axisy2Angle of intersection Δ dy2(ii) a Perpendicularity delta lambda of horizontal axis and azimuth axisy3Angle of intersection Δ dy3And initial zero error of azimuth axis Δ λx3(ii) a Perpendicularity Delta theta of working base surface for installing inertia instrument to axis of azimuth shaftx4、Δθy4(ii) a Accelerometer mounting base plane attitude error delta thetax5、Δθy5Eccentricity error Δ x5、Δy5And initial nulling error Δ θz5(ii) a Angular position errors of the main shaft, the horizontal shaft and the azimuth shaft are respectively delta alpha, delta beta and delta gamma;
the dynamic error source of the centrifuge comprises a main shaft radial rotation error delta x1(α)、Δy1(α), axial play Δ z1(alpha) and Tilt gyration error Delta thetax1(α)、Δθy1(α); dynamic radius error Δ Rd(ii) a Dynamic misalignment angle Δ λyd(Ω)、Δλzd(Ω); radial revolution error deltay of horizontal axis2(β)、Δz2(β), axial play Δ x2(beta) and Tilt gyration error Delta thetay2(β)、Δθz2(β); azimuth axis radial rotation error Deltax3(γ)、Δy3(gamma), axial play Δ z3(γ), tilt angle rotation error Δ θx3(γ)、Δθy3(γ)；
Radius error R ═ R0+ΔRd+ΔRsWherein R is0The static radius nominal value is a known quantity calibrated by a metering department, and the static test error Delta R of the radiussIs an unknown quantity, Δ RdAnd (omega) is the variation of the actual working radius of the centrifuge in the running state relative to the static radius of the centrifuge, which is monitored by using the dual-frequency laser interferometer and is a function of the angular velocity omega of the main shaft.
The invention relates to a method for testing the symmetry melting and elimination of a quartz accelerometer on a precision centrifuge, which comprises the following steps of establishing a coordinate system according to the structure of the precision centrifuge and calculating a pose error:
(1) geographic coordinate system o1-x1y1z1，o1x1Axis is horizontal and pointing east, o1y1Axis horizontal north-seeking, o1z1The axis indicates the sky to form a right-hand coordinate system;
(2) coordinate system o of spindle sleeve2t-x2t y2t z2tThe pose of the spindle sleeve coordinate system relative to the geographic coordinate system is
(3) Principal axis coordinate system o2-x2y2z2The pose of the main shaft coordinate system relative to the main shaft sleeve coordinate system is
Wherein α ═ Ω t denotes the angle of spindle rotation;
(4) water (W)Coordinate system o of flat shaft sleeve3t-x3ty3tz3tThe pose of the horizontal axis shaft sleeve coordinate system relative to the main axis coordinate system is
(5) Horizontal axis coordinate system o3-x3y3z3The pose of the horizontal axis coordinate system relative to the horizontal axis shaft sleeve coordinate system is
Wherein β represents the angle of rotation of the horizontal axis;
(6) coordinate system o of azimuth axis sleeve4t-x4ty4tz4tThe pose of the azimuth axis sleeve coordinate system relative to the horizontal axis coordinate system is
(7) Azimuth axis coordinate system o4-x4y4z4The position and attitude of the azimuth axis coordinate system relative to the azimuth axis sleeve coordinate system are
Wherein γ represents the angle of rotation of the azimuth axis;
(8) coordinate system o of the working base5-x5y5z5The position and attitude of the working base plane coordinate system relative to the azimuth axis coordinate system are
Wherein L is o5Point relative to4Point displacement;
(9) accelerometer coordinate system o6-x6y6z6The position and attitude of the accelerometer coordinate system relative to the working base coordinate system are
Wherein l is o6Point relative to5Point displacement;
the pose of the accelerometer coordinate system relative to the geographic coordinate system is
Wherein
Representing the attitude transformation matrix, P, between the accelerometer coordinate system and the geographic coordinate system1The 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
Wherein
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 P under the principal axis coordinate system2＝[px(Ω) py(Ω) pz(Ω)]TNeglecting the second order fractional amount, which is available, px(Ω)＝R0+ΔRs+ΔRd(Ω)+Δx2(β)+Δx3(γ)+Δx5 cosγ -Δy5 sinγ，py(Ω)＝Δdy2+Δy2(β)+[Δy3(γ)+Δdy3]cosβ-Δz3(γ)sinβ+(Δx5 sinγ +Δy5 cosγ)cosβ-(L+l)sinβ-(L+l)cosβΔβ。
The invention relates to a method for testing the symmetry melting and elimination of a quartz accelerometer on a precision centrifuge, which comprises the following steps that in the second step, the spindle of the precision centrifuge rotates at a uniform angular velocity to generate centripetal acceleration calibration acceleration timing, and the specific force distribution of the centripetal acceleration, the gravity accelerometer and the Coriolis acceleration is calculated 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 aIg、 apg、aOgThe specific force generated by the gravity acceleration is represented as [ 00 g ] in the geographic coordinate system]TThen expressed as in the accelerometer coordinate system
(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 as [ -P ] in the principal axis coordinate systemx(Ω)Ω2 -Py(Ω)Ω2 0]TThe components of the input shaft, the pendulum shaft and the output shaft of the accelerometer to be measured are respectively aIΩ、aPΩ、aOΩFrom equation (10) we can obtain:
(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, and at the moment, the Coriolis acceleration expression is as follows:
wherein
The local latitude is;
in summary, the precise specific force on the three axes of the accelerometer can be obtained as
The influence of the rotation error term on the specific force is changed in a sine and cosine form, the whole-cycle integral is ignored, and the whole-cycle integral containing cos omega t and sin omega t is zero or can be ignored, and the change is calculated to obtain the rotation error term
The invention discloses a method for testing the symmetry melting and elimination of a quartz accelerometer on a precision centrifuge, wherein the error model expression of the quartz accelerometer is as follows:
wherein E is the accelerometer output, unit: v;
asis the output equivalent of the accelerometer, in units: g;
KIscale factor, unit: v/g;
aI、ap、aOacceleration components on an input shaft, a pendulum shaft and an output shaft of the accelerometer respectively, the unit: g;
KFzero offset, unit: g;
KO、KPis cross-axis sensitivityThe unit: rad;
KII、KPP、KOOsecond-order nonlinear coefficients, unit: g/g2；
KoqIs the singular quadratic coefficient, unit: g/g2；
KIII、KPPP、KOOOThird order nonlinear coefficients, in units: g/g3；
KIP、KIO、KPOFor cross-coupling coefficients, the unit: g/g2；
ε -random error, unit: g.
the invention discloses a method for testing the symmetry melting and elimination of a quartz accelerometer on a precision centrifuge, which comprises the following steps:
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 at 0 degree, and 3 pairs of paired positions can be obtained; when the input shaft of the accelerometer is consistent with the axis of the azimuth axis of the centrifuge all the time, and the horizontal shaft is at the position of 0 degree or 180 degrees, 2 pairs of paired positions can be obtained; 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 at the 0-degree position, and the azimuth shaft is at 135-degree and 315-degree 2 positions;
the 12 positions adopt a unified structural matrix as shown in a formula (17),
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:
wherein a isI，apAnd aOAll in g;
substituting equation (18) into the quartz accelerometer error model expression (16), the indicated output of the quartz accelerometer at position 1 is:
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:
substituting equation (20) into the quartz accelerometer error model expression (16), the indicated output of the quartz accelerometer at position 2 is:
the following equations (19) and (21) are added and subtracted, respectively:
for equation (22), constant terms, first order terms and second order terms of acceleration are used; for equation (23), constant, first, second, and third terms; k can be identified by adopting 4 speed points of the main shaft for testingoq、KII、KIII：
Where "xxx" indicates 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
Y1+2＝ΦK1+2+ε (25)
From the least squares one can:
K1+2＝(ΦTΦ)-1ΦTY1+2 (26)
in the formula (24), K is recognizedIIAn item;
according to the formula (23), a
Y1-2＝ΦK1-2+ε (27)
Wherein
From the least squares one can:
K1-2＝(ΦTΦ)-1ΦTY1-2
compensating for dynamic misalignment angle delta lambda measured by an autocollimatoryd(Ωi) Dynamic radius error Δ R measured by a dual-frequency interferometric laserd(Ωi) The generated additional acceleration and Coriolis acceleration terms identify KoqTerm and KIIIAn item;
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:
respectively substituting the formula and the formula into the formula, and calculating the indication output a of the quartz accelerometerind3And aind4And performing an add-subtract-cancel operation to obtainThe following expressions:
according to formula (31):
Y3+4＝ΦK3+4+ε (33)
wherein
This is obtained according to equation (32):
Y3-4＝ΦK3-4+ε (34)
wherein
K is identified after compensating for the additional acceleration caused by the dynamic misalignment angle measured by the autocollimatorPPAnd KPPPAn 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:
respectively substituting the formula and the formula into the formula, and calculating the indication output a of the quartz accelerometerind5And aind6And performing addition and subtraction operation to obtain the following expression:
according to equation (37):
Y5+6＝ΦK5+6+ε (39)
wherein
This is obtained according to equation (38):
Y5-6＝ΦK5-6+ε (40)
wherein
K is identified after compensating for the additional acceleration caused by the dynamic misalignment angle measured by the autocollimatorOOTerm and KOOOAn 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:
respectively substituting the formula and the formula into the formula, and calculating the indication output a of the quartz accelerometerind7And aind8And performing addition and subtraction operation to obtain the following expression:
according to formula (43):
Y7+8＝ΦK7+8+ε (45)
wherein
Accurately identify KII+KPP+KIPAfter the coefficients, the identified K is subtractedII、KPPIdentify KIPError model coefficients;
this is obtained according to equation (44):
Y7-8＝ΦK7-8+ε (46)
wherein
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:
respectively substituting the formula and the formula into the formula, and calculating the indication output a of the quartz accelerometerind9And aind10And performing addition and subtraction operation to obtain the following expression:
according to formula (49):
Y9+10＝ΦK9+10+ε (51)
wherein
K is identified after compensating for the additional acceleration caused by the dynamic misalignment angle measured by the autocollimatorOO+KPP+KOPCoefficient, then subtract KOO、KPPTo obtain KOP；
This is obtained according to equation (50):
Y9-10＝ΦK9-10+ε (52)
wherein
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:
respectively substituting the formula and the formula into the formula, and calculating the indication output a of the quartz accelerometerind11And aind12And performing addition and subtraction operation to obtain the following expression:
according to formula (55):
Y11+12＝ΦK11+12+ε (57)
wherein
Identify KII+KOO+KIOThen, the identified K is subtractedII、KOOObtaining KIOAn item;
this is obtained according to equation (56):
Y11-12＝ΦK11-12+ε (58)
wherein
According to the above formula, the calibration result of the high-order error term of the quartz accelerometer is as follows:
KII＝K1+2(3)，Koq＝K1-2(3)，KIII＝K1-2(4)；
KPP＝K3+4(3)，KPPP＝K3-4(4)；
KOO＝K5+6(3)，KOOO＝K5-6(4)；
(KII+KPP+KIP)/2＝K7+8(3)，Koq/2＝K7-8(3)，
(KOO+KPP+KOP)/2＝K9+10(3)，
(KII+KOO+KIO)/2＝K11+12(3)，Koq/2＝K11-12(3)，
then the expression of the coefficients of the high order error model of the quartz accelerometer is as follows:
the invention relates to a method for testing the symmetry melting and elimination of a quartz accelerometer on a precision centrifuge, which provides an accurate expression of the input specific force of the centrifuge on the basis of analyzing various dynamic and static error sources of the precision centrifuge; a test method for symmetrical elimination of the quartz accelerometer on the precision centrifuge is provided by combining a quartz accelerometer error model, an identification model of a high-order error model of the quartz accelerometer is established by adopting the combination of two symmetrical installation positions and a method of adding and subtracting elimination elements, and a high-order error model coefficient of the quartz accelerometer is identified by utilizing a least square method. Under the condition that the error of the centrifuge is stable, the dynamic misalignment angle and the dynamic radius are monitored and compensated, so that the dynamic error and the static error of the centrifuge can be completely eliminated, and the calibration precision of the high-order error model coefficient of the quartz accelerometer can be effectively improved.
Drawings
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
The invention will be described in further detail below with reference to the accompanying drawings: the present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation is given, but the scope of the present invention is not limited to the following embodiments.
The first embodiment is as follows: as shown in fig. 1-2, in the method for testing the symmetric ablation of a quartz accelerometer on a precision centrifuge according to the present embodiment, the transformation between the main error source and the coordinate system of the precision centrifuge is:
as shown in figure 1, the precision centrifuge is provided with a main shaft, 3 shafting of a horizontal shaft and an azimuth shaft, the 3 shafting all have the precision position function, a 360-tooth multi-tooth dividing plate is arranged at the shaft end of the horizontal shaft, the horizontal shaft can be positioned to 360 positions with +/-3' precision, the main shaft shafting and the azimuth shaft all have the precision angular rate function, when the main shaft rotates at the uniform angular rate of omega, R omega is generated at the position of a working radius R2Centripetal acceleration of (2).
The static error source of the centrifuge mainly comprises a two-dimensional verticality error delta theta of a main shaft axisx0、Δθy0(ii) a Perpendicularity delta lambda of horizontal shaft axis and main shaft axisy2Angle of intersection Δ dy2(ii) a Perpendicularity delta lambda of horizontal axis and azimuth axisy3Angle of intersection Δ dy3And initial zero error of azimuth axis Δ λx3(ii) a Perpendicularity Delta theta of working base surface for installing inertia instrument to axis of azimuth shaftx4、Δθy4(ii) a Accelerometer mounting base plane attitude error delta thetax5、Δθy5Eccentricity error Δ x5、Δy5And initial nulling error Δ θz5(ii) a The angular position errors of the three axes of the main axis, the horizontal axis and the azimuth axis are respectively delta alpha, delta beta, delta gamma 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 a main shaft radial rotation error delta x1(α)、Δy1(α), axial play Δ z1(alpha) and Tilt gyration error Delta thetax1(α)、Δθy1(α); dynamic radius error Δ Rd(ii) a Dynamic misalignment angle Δ λyd(Ω)、Δλzd(Ω); radial revolution error deltay of horizontal axis2(β)、Δz2(β), axial play Δ x2(beta) and Tilt gyration error Delta thetay2(β)、Δθz2(β); azimuth axis radial rotation error Deltax3(γ)、Δy3(gamma), axial play Δ z3(γ), tilt angle rotation error Δ θx3(γ)、Δθy3And (. gamma.) are used.
In order to conveniently research the influence of radius errors, the static errors and the dynamic errors of the radius are integrated, wherein R is R0+ΔRd+ΔRsWherein R is0The static radius nominal value is a known quantity calibrated by a metering department, but the static test error of the radius is delta RsIs an unknown quantity, Δ RdAnd (omega) is the variation of the actual working radius of the centrifuge in the running state relative to the static radius of the centrifuge, which is monitored by using the dual-frequency laser interferometer and is a function of the angular velocity omega of the main shaft.
The following coordinate system will be established:
(1) geographic coordinate system o1-x1y1z1，o1x1Axis is horizontal and pointing east, o1y1Axis horizontal north-seeking, o1z1The axis refers to the sky, constituting the right hand coordinate system.
(2) Coordinate system o of spindle sleeve2t-x2t y2t z2t. The pose of the spindle sleeve coordinate system relative to the geographic coordinate system is
(3) Principal axis coordinate system o2-x2y2z2. The pose of the main shaft coordinate system relative to the main shaft sleeve coordinate system is
Where α ═ Ω t denotes the angle of spindle rotation.
(4) Horizontal axis sleeve coordinate system o3t-x3ty3tz3t. Horizontal axisThe pose of the sleeve coordinate system relative to the principal axis coordinate system is
(5) Horizontal axis coordinate system o3-x3y3z3. The pose of the horizontal axis coordinate system relative to the horizontal axis shaft sleeve coordinate system is
Where β represents the angle of rotation of the horizontal axis.
(6) Coordinate system o of azimuth axis sleeve4t-x4ty4tz4t. The position of the azimuth axis-sleeve coordinate system relative to the horizontal axis coordinate system is
(7) Azimuth axis coordinate system o4-x4y4z4. The position and pose of the azimuth axis coordinate system relative to the azimuth axis sleeve coordinate system are
Where γ represents the angle of rotation of the azimuth axis.
(8) Coordinate system o of the working base5-x5y5z5. The position and attitude of the working base plane coordinate system relative to the azimuth axis coordinate system are
Wherein L is o5Point relative to4The point is displaced.
(9) Accelerometer coordinate system o6-x6y6z6. The position and the attitude of the accelerometer coordinate system relative to the working base plane coordinate system are
Wherein l is o6Point relative to5The 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
Wherein
Representing the attitude transformation matrix, P, between the accelerometer coordinate system and the geographic coordinate system1Is 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
Wherein
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 P under the principal axis coordinate system2＝[px(Ω) py(Ω) pz(Ω)]TNeglecting the second order fractional amount, which is available, px(Ω)＝R0+ΔRs+ΔRd(Ω)+Δx2(β)+Δx3(γ)+Δx5 cosγ -Δy5 sinγ，py(Ω)＝Δdy2+Δy2(β)+[Δy3(γ)+Δdy3]cosβ-Δz3(γ)sinβ+(Δx5 sinγ +Δy5 cosγ)cosβ-(L+l)sinβ-(L+l)cosβΔβ。px(omega) and py(Ω) will be used later to calculate the precise centripetal acceleration of the origin of the accelerometer coordinate system.
Example two: in the method for testing the symmetric ablation of the quartz accelerometer on the precision centrifuge, the calculation process of the input specific force of the quartz accelerometer comprises the following steps:
when a main shaft of the precision centrifuge rotates at a uniform angular rate to generate centripetal acceleration calibration acceleration timing, the specific force input of the accelerometer has 3 sources, namely centripetal acceleration, a gravity accelerometer and 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 aIg、 apg、aOgThe specific force generated by the gravity acceleration is represented as [ 00 g ] in the geographic coordinate system]TThen expressed as in the accelerometer coordinate system
(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 as [ -P ] in the principal axis coordinate systemx(Ω)Ω2 -Py(Ω)Ω2 0]TThe components of the input shaft, the pendulum shaft and the output shaft of the accelerometer to be measured are respectively aIΩ、aPΩ、aOΩFrom equation (10) we can obtain:
(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:
wherein
Is the local latitude.
In summary, the precise specific force on the three axes of the accelerometer is
Because the influence of the rotation error term on the specific force is changed in sine and cosine forms, the whole-cycle integral can be ignored, and the whole-cycle integral containing cos omega t and sin omega t is zero or can be ignored, and the change can be calculated
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 through 3 mounting modes, and then a corresponding test method is designed.
Example three: the embodiment relates to a method for testing the symmetry melting and elimination of a quartz accelerometer on a precision centrifuge, which is characterized in that the specific calculation process of the method for calibrating the symmetry melting and elimination of the high-order error coefficient of the quartz accelerometer is as follows:
the quartz accelerometer error model expression takes the following form:
wherein E is the accelerometer output, unit: v;
asis the output equivalent of the accelerometer, in units: g;
KIscale factor, unit: v/g;
aI、ap、aOacceleration components on an input shaft, a pendulum shaft and an output shaft of the accelerometer respectively, the unit: g;
KFzero offset, unit: g;
KO、KPfor cross-axis sensitivity, unit: rad;
KII、KPP、KOOsecond-order nonlinear coefficients, unit: g/g2；
KoqIs the singular quadratic coefficient, unit: g/g2；
KIII、KPPP、KOOOThird order nonlinear coefficients, in units: g/g3；
KIP、KIO、KPOFor cross-coupling coefficients, the unit: g/g2；
ε -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 error model expression of the quartz accelerometer.
The high order error model coefficients of the quartz accelerometer are identified by the 6 symmetrical position combinations shown in fig. 3, where a represents the 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
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 this time, the output shaft of the accelerometer is always consistent with the axis of the azimuth axis of the centrifuge, the horizontal shaft of the centrifuge is always at the 0-degree position, the azimuth axis is at the 6 positions shown in table 1, and 3 pairs of paired positions can be obtained. The 5-6, 9-10 positions are the 2 nd installation mode, and the input shaft of the accelerometer is always consistent with the axis of the azimuth axis of the centrifuge, the horizontal shaft is in the 0 degree or 180 degree position, and the azimuth axis is in 4 positions, so that 2 pairs of paired positions can be obtained. The 11-12 position is the 3 rd installation mode, and the direction of the pendulum shaft of the accelerometer is opposite to the axis direction of the azimuth shaft of the centrifuge, the horizontal shaft is always at the 0-degree position, and the azimuth shaft is at 2 positions of 135 degrees and 315 degrees.
According to the formula, the specific force input of each axis of the actual accelerometer corresponding to the 1 st to 12 th installation positions can be obtained, during specific calculation, the specific force on the input axis is accurate to a first-order small amount, the specific force on the swing axis and the output axis only calculates a nominal value, and the first-order small amount is also ignored, because the coefficient related to the input specific force of the two axes is also a small amount. K in the formulaIIs a known quantity, is used for calculating the indicating output a of the accelerometers，aITake a first order fractional amount, a related to other coefficientsI、aO、aPAnd (4) 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 paired position, i.e. to
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:
wherein a isI，apAnd aOAll 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:
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:
substituting equation (20) into equation (16), the indicated output of the quartz accelerometer at position 2 is:
the following equations (19) and (21) are added and subtracted, respectively:
for equation (22), the constant term, the first term and the second term of the acceleration areAnd (4) item composition. For equation (23), there are constant, first, second and third terms. By combining the above analysis, the K can be identified by testing with 4 speed points of the main shaftoq、KII、KIII。
Where "xxx" indicates 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
Y1+2＝ΦK1+2+ε (25)
From the least squares one can:
K1+2＝(ΦTΦ)-1ΦTY1+2 (26)
in the formula (24), K is recognizedIIThe item avoids the error [ Delta x ] of the centrifuge3(π)-Δx3(0)]/2-Δx5Thereby increasing KIIThe calibration accuracy of the terms.
According to the formula (23), a
Y1-2＝ΦK1-2+ε (27)
Wherein
From the least squares one can:
K1-2＝(ΦTΦ)-1ΦTY1-2 (28)
in the observation vector Y1-2In compensating for the dynamic error term delta lambdayd(Ωi)，ΔRd(Ωi) And a Coriolis acceleration term in the error coefficient vectorAdding a pose error term delta lambda of the centrifugal machiney2，Δλy3Automatically compensating the static radius test error delta RsAnd a rotation error term and the like, and eliminates the influence of errors of the centrifugal machine and Coriolis acceleration, thereby improving KoqAnd KIIIThe 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:
respectively substituting the formula and the formula into the formula, and calculating the indication output a of the quartz accelerometerind3And aind4And performing addition and subtraction operation to obtain the following expression:
according to formula (31):
Y3+4＝ΦK3+4+ε (33)
wherein
This is obtained according to equation (32):
Y3-4＝ΦK3-4+ε (34)
wherein
K can be identified by compensating for the additional acceleration due to the dynamic misalignment anglePPAnd KPPPAn 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:
respectively substituting the formula and the formula into the formula, and calculating the indication output a of the quartz accelerometerind5And aind6And performing addition and subtraction operation to obtain the following expression:
according to equation (37):
Y5+6＝ΦK5+6+ε (39)
wherein
This is obtained according to equation (38):
Y5-6＝ΦK5-6+ε (40)
wherein
K can be identified by also compensating for the additional acceleration due to the dynamic misalignment angleOOAnd KOOOAn 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:
respectively substituting the formula and the formula into the formula, and calculating the indication output a of the quartz accelerometerind7And aind8And performing addition and subtraction operation to obtain the following expression:
according to formula (43):
Y7+8＝ΦK7+8+ε (45)
wherein
Accurately identify KII+KPP+KIPAfter the coefficients, the previously identified K is subtractedII、KPPCan identify KIPError model coefficients.
This is obtained according to equation (44):
Y7-8＝ΦK7-8+ε (46)
wherein
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:
respectively substituting the formula and the formula into the formula, and calculating the indication output a of the quartz accelerometerind9And aind10And performing addition and subtraction operation to obtain the following expression:
according to formula (49):
Y9+10＝ΦK9+10+ε (51)
wherein
After compensating for the effect of the dynamic misalignment angle, K is identifiedOO+KPP+KOPThen, subtract KOO、KPPTo obtain KOP。
This is obtained according to equation (50):
Y9-10＝ΦK9-10+ε (52)
wherein
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:
respectively substituting the formula and the formula into the formula, and calculating the indication output a of the quartz accelerometerind11And aind12And performing addition and subtraction operation to obtain the following expression:
according to formula (55):
Y11+12＝ΦK11+12+ε (57)
wherein
Identify KII+KOO+KIOThen, the identified K is subtractedII、KOOObtaining KIOAn item.
This is obtained according to equation (56):
Y11-12＝ΦK11-12+ε (58)
wherein
By combining the formula proposed above, the calibration result of the high-order error term of the quartz accelerometer can be obtained as follows:
KII＝K1+2(3)，Koq＝K1-2(3)，KIII＝K1-2(4)；
KPP＝K3+4(3)，KPPP＝K3-4(4)；
KOO＝K5+6(3)，KOOO＝K5-6(4)；
(KII+KPP+KIP)/2＝K7+8(3)，Koq/2＝K7-8(3)，
(KOO+KPP+KOP)/2＝K9+10(3)，
(KII+KOO+KIO)/2＝K11+12(3)，Koq/2＝K11-12(3)，
the expression of the coefficient of the high-order error model of the quartz accelerometer can be summarized as
Example four: as shown in fig. 2, in the method for testing the symmetric melting and extinction of a quartz accelerometer on a precision centrifuge according to the present embodiment, let a ═ Φ (Φ)TΦ)-1ΦTAn error model coefficient K is obtained from equation (24)IIThe expression of the term is:
wherein A isijRepresenting the elements of matrix a at row i and column j. Assuming that the indicating outputs of the quartz accelerometers are independent and equal in precision, the uncertainty is
Then KIIThe uncertainty of the term is
Assuming that the centrifuge provides centripetal accelerations of 5g, 10g, 15g and 20g, the uncertainty in the output of the quartz accelerometer is σa＝10-6g, dynamic misalignment angle uncertainty σλ0.04 ″, uncertainty of dynamic radius error
The uncertainty of the quadratic term and the cross quadratic term of the quartz accelerometer are respectively calculated as
The above description is only a preferred embodiment of the present invention, and these embodiments are based on different implementations of the present invention, and 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 method for testing the symmetry melting and elimination of a quartz accelerometer on a precision centrifuge is characterized by comprising the following steps:
the method comprises the following steps: establishing a coordinate system according to the structure of the precision centrifuge and calculating a pose error;
step two: when a spindle of the precision centrifuge rotates at a uniform angular velocity to generate centripetal acceleration calibration acceleration timing, calculating the specific force distribution of the centripetal acceleration, the gravity accelerometer and the Coriolis acceleration;
step three: giving out an error model expression of the quartz accelerometer according to the content of the second step;
step four: and calibrating a high-order term error coefficient in the quartz accelerometer error model expression by adopting 6 symmetrical position combinations and a method of adding and subtracting a damping element.
2. The method for testing the symmetry melting and elimination of the quartz accelerometer on the precision centrifuge as claimed in claim 1, wherein the precision centrifuge comprises 3 shafting of a main shaft, a horizontal shaft and an azimuth shaft;
the static error source of the centrifuge includes the two-dimensional sag error Delta theta of the spindle axisx0、Δθy0(ii) a Perpendicularity delta lambda of horizontal shaft axis and main shaft axisy2Angle of intersection Δ dy2(ii) a Perpendicularity delta lambda of horizontal axis and azimuth axisy3Angle of intersection Δ dy3And initial zero error of azimuth axis Δ λx3(ii) a Working base plane to azimuth axis for installing inertia instrumentPerpendicularity delta theta of axisx4、Δθy4(ii) a Accelerometer mounting base plane attitude error delta thetax5、Δθy5Eccentricity error Δ x5、Δy5And initial nulling error Δ θz5(ii) a Angular position errors of the main shaft, the horizontal shaft and the azimuth shaft are respectively delta alpha, delta beta and delta gamma;
the dynamic error source of the centrifuge comprises a main shaft radial rotation error delta x1(α)、Δy1(α), axial play Δ z1(alpha) and Tilt gyration error Delta thetax1(α)、Δθy1(α); dynamic radius error Δ Rd(ii) a Dynamic misalignment angle Δ λyd(Ω)、Δλzd(Ω); radial revolution error deltay of horizontal axis2(β)、Δz2(β), axial play Δ x2(beta) and Tilt gyration error Delta thetay2(β)、Δθz2(β); azimuth axis radial rotation error Deltax3(γ)、Δy3(gamma), axial play Δ z3(γ), tilt angle rotation error Δ θx3(γ)、Δθy3(γ)；
Radius error R ═ R0+ΔRd+ΔRsWherein R is0The static radius nominal value is a known quantity calibrated by a metering department, and the static test error Delta R of the radiussIs an unknown quantity, Δ RdAnd (omega) is the variation of the actual working radius of the centrifuge in the running state relative to the static radius of the centrifuge, which is monitored by using the dual-frequency laser interferometer and is a function of the angular velocity omega of the main shaft.
3. The method for testing the symmetry melting and elimination of the quartz accelerometer on the precision centrifuge as claimed in claim 1, wherein the establishing of the coordinate system and the calculation of the pose error according to the structure of the precision centrifuge specifically comprises:
(1) geographic coordinate system o1-x1y1z1，o1x1Axis is horizontal and pointing east, o1y1Axis horizontal north-seeking, o1z1The axis indicates the sky to form a right-hand coordinate system;
(2) coordinate system o of spindle sleeve2t-x2ty2tz2tThe pose of the spindle sleeve coordinate system relative to the geographic coordinate system is
(3) Principal axis coordinate system o2-x2y2z2The pose of the main shaft coordinate system relative to the main shaft sleeve coordinate system is
Wherein α ═ Ω t denotes the angle of spindle rotation;
(4) horizontal axis sleeve coordinate system o3t-x3ty3tz3tThe pose of the horizontal axis shaft sleeve coordinate system relative to the main axis coordinate system is
(5) Horizontal axis coordinate system o3-x3y3z3The pose of the horizontal axis coordinate system relative to the horizontal axis shaft sleeve coordinate system is
Wherein β represents the angle of rotation of the horizontal axis;
(6) coordinate system o of azimuth axis sleeve4t-x4ty4tz4tThe pose of the azimuth axis sleeve coordinate system relative to the horizontal axis coordinate system is
(7) Azimuth axis coordinate system o4-x4y4z4The position and attitude of the azimuth axis coordinate system relative to the azimuth axis sleeve coordinate system are
Wherein γ represents the angle of rotation of the azimuth axis;
(8) coordinate system o of the working base5-x5y5z5The position and attitude of the working base plane coordinate system relative to the azimuth axis coordinate system are
Wherein L is o5Point relative to4Point displacement;
(9) accelerometer coordinate system o6-x6y6z6The position and attitude of the accelerometer coordinate system relative to the working base coordinate system are
Wherein l is o6Point relative to5Point displacement;
the pose of the accelerometer coordinate system relative to the geographic coordinate system is
Wherein
Representing the attitude transformation matrix, P, between the accelerometer coordinate system and the geographic coordinate system1The 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
Wherein
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 P under the principal axis coordinate system2＝[px(Ω) py(Ω) pz(Ω)]TNeglecting the second order fractional amount, which is available, px(Ω)＝R0+ΔRs+ΔRd(Ω)+Δx2(β)+Δx3(γ)+Δx5cosγ-Δy5sinγ，py(Ω)＝Δdy2+Δy2(β)+[Δy3(γ)+Δdy3]cosβ-Δz3(γ)sinβ+(Δx5sinγ+Δy5cosγ)cosβ-(L+l)sinβ-(L+l)cosβΔβ。
4. The method for testing the symmetry melting and elimination of the quartz accelerometer on the precision centrifuge as claimed in claim 1, wherein the second step is that the spindle of the precision centrifuge rotates at a uniform angular rate to generate centripetal acceleration calibration acceleration timing, and the specific force distribution for calculating the centripetal acceleration, the gravity accelerometer and the Coriolis acceleration is 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 aIg、apg、aOgThe specific force generated by the gravity acceleration is represented as [ 00 g ] in the geographic coordinate system]TThen expressed as in the accelerometer coordinate system
(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 as [ -P ] in the principal axis coordinate systemx(Ω)Ω2-Py(Ω)Ω2 0]TThe components of the input shaft, the pendulum shaft and the output shaft of the accelerometer to be measured are respectively aIΩ、aPΩ、aOΩFrom equation (10) we can obtain:
(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, and at the moment, the Coriolis acceleration expression is as follows:
wherein
The local latitude is;
in summary, the precise specific force on the three axes of the accelerometer can be obtained as
The influence of the rotation error term on the specific force is changed in a sine and cosine form, the whole-cycle integral can be ignored, and the whole-cycle integral containing cos omega t and sin omega t is zero or can be ignored, and the change can be calculated
5. The method for testing the symmetry melting and elimination of the quartz accelerometer on the precision centrifuge as claimed in claim 1, wherein the error model expression of the quartz accelerometer is as follows:
wherein E is the accelerometer output, unit: v;
asis the output equivalent of the accelerometer, in units: g;
KIscale factor, unit: v/g;
aI、ap、aOacceleration components on an input shaft, a pendulum shaft and an output shaft of the accelerometer respectively, the unit: g;
KFzero offset, unit: g;
KO、KPfor cross-axis sensitivity, unit: rad;
KII、KPP、KOOsecond-order nonlinear coefficients, unit: g/g2；
KoqIs the singular quadratic coefficient, unit: g/g2；
KIII、KPPP、KOOOThird order nonlinear coefficients, in units: g/g3；
KIP、KIO、KPOFor cross-coupling coefficients, the unit: g/g2；
ε -random error, unit: g.
6. the method for testing the symmetric melting and elimination of the quartz accelerometer on the precision centrifuge as claimed in claim 1, wherein the step four is specifically as follows:
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 at 0 degree, and 3 pairs of paired positions can be obtained; when the input shaft of the accelerometer is consistent with the axis of the azimuth axis of the centrifuge all the time, and the horizontal shaft is at the position of 0 degree or 180 degrees, 2 pairs of paired positions can be obtained; 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 at the 0-degree position, and the azimuth shaft is at 135-degree and 315-degree 2 positions;
the 12 positions adopt a unified structural matrix as shown in a formula (17),
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:
wherein a isI，apAnd aOAll in g;
substituting equation (18) into the quartz accelerometer error model expression (16), the indicated output of the quartz accelerometer at position 1 is:
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:
substituting equation (20) into the quartz accelerometer error model expression (16), the indicated output of the quartz accelerometer at position 2 is:
the following equations (19) and (21) are added and subtracted, respectively:
for equation (22), constant terms, first order terms and second order terms of acceleration are used; for equation (23), constant, first, second, and third terms; k can be identified by adopting 4 speed points of the main shaft for testingoq、KII、KIII：
Where "xxx" indicates 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
Y1+2＝ΦK1+2+ε (25)
From the least squares one can:
K1+2＝(ΦTΦ)-1ΦTY1+2 (26)
in the formula (24), K is recognizedIIAn item;
according to the formula (23), a
Y1-2＝ΦK1-2+ε (27)
Wherein
From the least squares one can:
K1-2＝(ΦTΦ)-1ΦTY1-2
compensating for dynamic misalignment angle delta lambda measured by an autocollimatoryd(Ωi) Dynamic radius error Δ R measured by a dual-frequency interferometric laserd(Ωi) The generated additional acceleration and Coriolis acceleration terms identify KoqTerm and KIIIAn item;
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:
the indication output a of the quartz accelerometer is calculated by substituting the formula (15) and the formula (16) into the formulaeind3And aind4And performing addition and subtraction operation to obtain the following expression:
according to formula (31):
Y3+4＝ΦK3+4+ε (33)
wherein
This is obtained according to equation (32):
Y3+4＝ΦK3+4+ε (34)
wherein
K is identified after compensating for the additional acceleration caused by the dynamic misalignment angle measured by the autocollimatorPPAnd KPPPAn 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:
the indication output a of the quartz accelerometer is calculated by substituting the formula (21) and the formula (22) into the formulaeind5And aind6And performing addition and subtraction operation to obtain the following expression:
according to equation (37):
Y5+6＝ΦK5+6+ε (39)
wherein
This is obtained according to equation (38):
Y5-6＝ΦK5-6+ε (40)
wherein
K is identified after compensating for the additional acceleration caused by the dynamic misalignment angle measured by the autocollimatorOOTerm and KOOOAn 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:
the indication output a of the quartz accelerometer is calculated by substituting the equations (27) and (28) into the equations, respectivelyind7And aind8And performing addition and subtraction operation to obtain the following expression:
according to formula (43):
Y7+8＝ΦK7+8+ε (45)
wherein
Accurately identify KII+KPP+KIPAfter the coefficients, the identified K is subtractedII、KPPIdentify KIPError model coefficients;
this is obtained according to equation (44):
Y7-8＝ΦK7-8+ε (46)
wherein
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:
the indication output a of the quartz accelerometer is calculated by substituting the equations (33) and (34) into the equations, respectivelyind9And aind10And performing addition and subtraction operation to obtain the following expression:
according to formula (49):
Y9+10＝ΦK9+10+ε (51)
wherein
K is identified after compensating for the additional acceleration caused by the dynamic misalignment angle measured by the autocollimatorOO+KPP+KOPCoefficient, then subtract KOO、KPPTo obtain KOP；
This is obtained according to equation (50):
Y9-10＝ΦK9-10+ε (52)
wherein
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:
the indication output a of the quartz accelerometer is calculated by substituting the formula (39) and the formula (40) into the formulaeind11And aind12And performing addition and subtraction operation to obtain the following expression:
according to formula (55):
Y11+12＝ΦK11+12+ε (57)
wherein
Identify KII+KOO+KIOThen, the identified K is subtractedII、KOOObtaining KIOAn item;
this is obtained according to equation (56):
Y11-12＝ΦK11-12+ε (58)
wherein
According to the above formula, the calibration result of the high-order error term of the quartz accelerometer is as follows:
KII＝K1+2 (3)，Koq＝K1-2 (3)，KIII＝K1-2 (4)；
KPP＝K3+4 (3)，KPPP＝K3-4 (4)；
KOO＝K5+6 (3)，KOOO＝K5-6 (4)；
(KII+KOO+KIO)/2＝K11+12 (3)，Koq/2＝K11-12 (3)，
then the expression of the coefficients of the high order error model of the quartz accelerometer is as follows:
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| CN113804221A (en) * | 2021-10-14 | 2021-12-17 | 天津科技大学 | Method for calibrating centrifugal machine accelerometer combination based on model observation method |
| CN113804221B (en) * | 2021-10-14 | 2023-10-03 | 天津科技大学 | Centrifugal machine accelerometer combined calibration method based on model observation method |
| CN114034885B (en) * | 2021-11-11 | 2024-04-26 | 哈尔滨工业大学 | Method for testing gyroscopic accelerometer on double-shaft centrifuge based on full-error analysis |
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