CN103983281A - Coaxial error analysis evaluation and compensation method of active type half-strapdown system - Google Patents

Abstract

The invention relates to a half-strapdown inertial measurement technology, and in particular relates to a coaxial error analysis evaluation and compensation method of an active type half-strapdown system, aiming at solving the problems that the whole structure strength, the stability, the less spin accuracy and the measurement accuracy of the active type half-strapdown system are influenced by the coaxial error of the active type half-strapdown system. The coaxial error analysis evaluation and compensation method of the active type half-strapdown system is realized by adopting the steps of (1) analyzing and evaluating the coaxial error of an outer cylinder of the active type half-strapdown system; (2) carrying out dynamic calibration and compensation on the coaxial error angle of an inner cylinder of the active type half-strapdown system; and (3) unifying the reference axis of the active type half-strapdown system. The coaxial error analysis evaluation and compensation method is suitable for the accurate measurement of high spin ammunition flight attitude.

Description

Active half strapdown system coaxiality error analytical evaluation and compensation method

Technical field

The present invention relates to half quick-connecting inertia measurement technology, specifically a kind of active half strapdown system coaxiality error analytical evaluation and compensation method.

Background technology

The accurate measurement that height revolves ammunition flight attitude is one of core of rotation ammunition research, is also the basis of ammunition guidanceization.High along the axial rotating speed of bullet when height revolves ammunition flight, generally can reach 20r/s, even higher.Under this kind high rotating speed environment, traditional Strapdown Inertial Units measuring method is difficult to keep compared with lofty stance measuring accuracy under high rotating speed environment, and it is limited that simple dependence improvement algorithm improves measuring accuracy effect, can not meet the requirement of modern operation to its precision.The proposition with the active half strapdown micro-inertial measuring system of " revolving every only turning " function efficiently solves the mismatch problem of micro-inertia device range and precision under high rotating speed environment.The structure of active half strapdown system comprises urceolus, inner core, MIMU (micro inertial measurement unit), one-level speed governing gyro, secondary speed governing gyro, control module, subtracts and revolve motor, bearing, shaft coupling etc.Wherein, urceolus and the high body that the revolves ammunition installation that is connected.One end of inner core by shaft coupling with subtract the rotating shaft of revolving motor and be connected, the other end is chimeric by bearing and outer tube inner wall.MIMU is fixedly installed in inner core, for measuring the high ammunition flight attitude that revolves.One-level speed governing gyro is fixedly installed in urceolus, for measuring the high body rotating speed that revolves ammunition.Secondary speed governing gyro is fixedly installed in inner core, for measuring inner cylinder rotating angular speed.Control module drives to subtract according to the measurement result of one-level speed governing gyro and secondary speed governing gyro revolves motor and carries out reverse rotation, subtract and revolve motor and drive MIMU to carry out reverse rotation by inner core, make MIMU static or micro-the revolving of relative inertness coordinate system in the axial direction, realize thus " revolving every only turning " function, thereby make MIMU under high rotating speed environment, keep higher measuring accuracy.In actual applications, because all parts of active half strapdown system all needs independent processing, the various errors that exist in manufacturing process system certainly will cause all parts all to produce mismachining tolerance.And all parts assembling is being formed after active half strapdown system, above-mentioned mismachining tolerance just shows as the coaxiality error of active half strapdown system.The coaxiality error of active half strapdown system can be divided into urceolus coaxiality error and inner core coaxiality error.Wherein, urceolus coaxiality error can make the part-structure that departs from benchmark in active half strapdown system make conical motion, and the unbalanced stressed meeting that conical motion produces causes the Assembly interface of active half strapdown system to wear and tear, thereby not only the overall construction intensity to active half strapdown system and stability cause damage, even cause active half strapdown system to occur to burst and collapse.Inner core coaxiality error can make the rotating speed of urceolus and inner core inconsistent on the one hand, now will directly cause inner core to subtract using one-level speed governing gyro Output rusults as basis for estimation revolving not thorough, affect subtracting of active half strapdown system and revolve precision, on the other hand can be directly for measurement result be introduced error, directly cause thus MIMU to produce measuring error, thereby affect the measuring accuracy of active half strapdown system.In sum, the coaxiality error of active half strapdown system not only affects overall construction intensity and the stability of active half strapdown system, and affects subtracting of active half strapdown system and revolve precision and measuring accuracy.Based on this, be necessary a kind of active half strapdown system coaxiality error analytical evaluation and compensation method of invention, affect to solve the coaxiality error of active half strapdown system active half strapdown system overall construction intensity, stability, subtract the problem of revolving precision and measuring accuracy.

Summary of the invention

The present invention affect in order to solve the coaxiality error of active half strapdown system active half strapdown system overall construction intensity, stability, subtract the problem of revolving precision and measuring accuracy, a kind of active half strapdown system coaxiality error analytical evaluation and compensation method is provided.

The present invention adopts following technical scheme to realize: active half strapdown system coaxiality error analytical evaluation and compensation method, and the method is to adopt following steps to realize:

1) analytical evaluation of the urceolus coaxiality error of active half strapdown system; Specifically comprise the steps:

1.1) active half strapdown system is installed in two top going up of dividing head, and ensures that the central axis of urceolus base of active half strapdown system and the shaft axis of dividing head overlap; Using the central axis of urceolus base as urceolus datum axis;

1.2) height of supposing urceolus base is h, by urceolus base by being highly divided into individual sampled cross-section; For each sampled cross-section of urceolus base, 5 ° of every rotations of dividing head are once sampled, and carry out altogether 72 samplings; Suppose j the sampled cross-section for urceolus base, sampled data when dividing head carries out the i time sampling is K _ij(r _ij, θ _ij, z _j); The least square center of supposing j sampled cross-section of urceolus base is O _j(a _j, b _j, z _j); According to the sampled data of dividing head, solve the least square center of each sampled cross-section of urceolus base; Solution formula is as follows:

$\left.\begin{array}{c}{a}_j=\frac{2}{m}\mathrm{\Σ}{r}_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}\\ b_j=\frac{2}{m}\mathrm{\Σ}{r}_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ z_j=z_j\end{array}\right\}---\left(1\right);$

In formula (1): i=1,2 ... 72; m=72; for positive integer; r _ijfor the radius value of j sampled cross-section of urceolus base; θ _ijfor j the sampled cross-section for urceolus base, the angle value rotating when dividing head carries out the i time sampling; z _jfor j sampled cross-section of urceolus base is along the coordinate figure of urceolus datum axis;

1.3) height of supposing all the other structures of urceolus is H, by all the other structures of urceolus by being highly divided into individual sampled cross-section; For each sampled cross-section of all the other structures of urceolus, 5 ° of every rotations of dividing head are once sampled, and carry out altogether 72 samplings; Suppose J the sampled cross-section for urceolus base, sampled data when dividing head carries out the I time sampling is M _iJ(r _iJ, θ _iJ, z _j); The least square center of supposing J sampled cross-section of urceolus base is O _j(a _j, b _j, z _j); According to the sampled data of dividing head, solve the least square center of each sampled cross-section of all the other structures of urceolus; Solution formula is as follows:

$\left.\begin{array}{c}{a}_J=\frac{2}{M}\mathrm{\Σ}{r}_{\mathrm{IJ}}\cos {\mathrm{\θ}}_{\mathrm{IJ}}\\ b_J=\frac{2}{M}\mathrm{\Σ}{r}_{\mathrm{IJ}}\sin {\mathrm{\θ}}_{\mathrm{IJ}}\\ z_J=z_J\end{array}\right\}---\left(2\right);$

In formula (2): I=1,2 ... 72; m=72; for positive integer; r _iJfor the radius value of J sampled cross-section of all the other structures of urceolus; θ _iJfor J the sampled cross-section for all the other structures of urceolus, the angle value rotating when dividing head carries out the I time sampling; z _jfor J sampled cross-section of all the other structures of urceolus is along the coordinate figure of urceolus datum axis;

1.4) suppose urceolus datum axis by coordinate plane XOY and intersect at it an A (x ₀, y ₀, 0); One group of direction number supposing urceolus datum axis is (l', k', 1); According to the least square center of each sampled cross-section of urceolus base, solve an A (x ₀, y ₀, 0) and direction number S=(l', k', 1); Solution formula is as follows:

$\left.\begin{array}{c}{x}_0=\frac{8}{h}\underset{j=1}{\overset{\frac{h}{8}}{\mathrm{\Σ}}}{a}_j\\ y_0=\frac{8}{h}\underset{j=1}{\overset{\frac{h}{8}}{\mathrm{\Σ}}}{b}_j\\ l^{\′}\text{=}\underset{j=1}{\overset{\frac{h}{8}}{\mathrm{\Σ}}}{a}_j{z}_j/\underset{j=1}{\overset{\frac{h}{8}}{\mathrm{\Σ}}}{z}_j^2\\ k^{\′}=\underset{j=1}{\overset{\frac{h}{8}}{\mathrm{\Σ}}}{b}_j{z}_j/\underset{j=1}{\overset{\frac{h}{8}}{\mathrm{\Σ}}}{z}_j^2\end{array}\right\}---\left(3\right);$

In formula (3): for positive integer;

1.5) according to an A (x ₀, y ₀, 0), the least square center of each sampled cross-section of direction number (l', k', 1), all the other structures of urceolus, solve the least square center of each sampled cross-section of all the other structures of urceolus to the distance of urceolus datum axis; Solution formula is as follows:

$e_J=\frac{|(O_J-A)\×S|}{\left|S\right|}---\left(4\right);$

O _J＝{a _J,b _J,z _J} (5)；

A＝{x ₀,y ₀,0} (6)；

S＝(l',k',1) (7)；

In formula (4)-(7): e _jfor the least square center O of J sampled cross-section of all the other structures of urceolus _j(a _j, b _j, z _j) to the distance of urceolus datum axis; O _jfor the least square center of J sampled cross-section of urceolus base; A is that urceolus datum axis is by the joining of coordinate plane XOY; S is one group of direction number of urceolus datum axis;

1.6) distance to urceolus datum axis according to the least square center of each sampled cross-section of all the other structures of urceolus, solves the urceolus coaxiality error of active half strapdown system; Solution formula is as follows:

In formula (8): for the urceolus coaxiality error of active half strapdown system; e _jfor the least square center O of J sampled cross-section of all the other structures of urceolus _j(a _j, b _j, z _j) to the distance of urceolus datum axis;

1.7) the concentricity tolerance maximal value of the urceolus coaxiality error of active half strapdown system and regulation is compared; If the urceolus coaxiality error of active half strapdown system is less than the concentricity tolerance maximal value of regulation, think that the urceolus coaxiality error of active half strapdown system, in allowed band, completes the analytical evaluation of the urceolus coaxiality error of active half strapdown system thus;

2) dynamic calibration and the compensation at the inner core coaxiality error angle of active half strapdown system; Specifically comprise the steps:

2.1) because the inner core of active half strapdown system has radially characteristic freely, suppose that it is inner core datum axis that subtracting of active half strapdown system revolved machine shaft axis, and the angle between the Z axis axis of MIMU and inner core datum axis is called to inner core coaxiality error angle;

2.2), under the condition existing at inner core coaxiality error angle, active half strapdown system is fixed on high-speed rotating equipment; In the range ability of MIMU, control high-speed rotating equipment and drive active half strapdown system to be rotated with set angle speed, MIMU is output angle speed thus; According to the angular speed of MIMU output, calibrate the inner core coaxiality error angle of active half strapdown system; Calibration formula is as follows:

$\mathrm{\θ}=\arctan \frac{\sqrt{w_y^2+w_z^2}}{w_x}---\left(9\right);$

In formula (9): θ is the inner core coaxiality error angle of active half strapdown system; w _xfor the angular speed of MIMU output is at the component of the X-axis of MIMU; w _yfor the angular speed of MIMU output is at the component of the Y-axis of MIMU; w _zfor the angular speed of MIMU output is at the component of the Z axis of MIMU;

2.3) according to the inner core coaxiality error angle of active half strapdown system, the angular speed of MIMU output is compensated, complete thus dynamic calibration and the compensation at the inner core coaxiality error angle of active half strapdown system; Compensation formula is as follows:

$\left\{\begin{array}{c}{w}_x=w\cos \\ w_y=-w\sin \mathrm{\θ}\sin \left(\mathrm{wt}\right)\\ w_z=-w\sin \mathrm{\θ}\cos \left(\mathrm{wt}\right)\end{array}\right.---\left(10\right);$

In formula (10): w _xfor the angular speed of MIMU output is at the component of the X-axis of MIMU; w _yfor the angular speed of MIMU output is at the component of the Y-axis of MIMU; w _zfor the angular speed of MIMU output is at the component of the Z axis of MIMU; θ is the inner core coaxiality error angle of active half strapdown system; W is the set angle speed of high-speed rotating equipment;

3) unification of the datum axis of active half strapdown system; Specifically comprise the steps:

3.1) central axis of supposing urceolus base is urceolus datum axis, supposes to subtract that to revolve machine shaft axis be inner core datum axis; In the physical construction installation process of active half strapdown system, because the central axis of urceolus base revolves machine shaft axis and can not accomplish to overlap completely with subtracting, and the inside fixed form of active half strapdown system is embedded fastening installation, the angle between urceolus datum axis and inner core datum axis is certain value, and this angle is called to datum line angle;

3.2) active half strapdown system is fixed on high-speed rotating equipment; In the range ability of MIMU, control high-speed rotating equipment drive active half strapdown system to be rotated with set angle speed, MIMU thus output shaft to angular speed; Measure the urceolus turning rate of active half strapdown system by the one-level speed governing gyro of active half strapdown system; According to axial angle speed and the urceolus turning rate of MIMU output, solve the datum line angle of active half strapdown system; Solution formula is as follows:

W ₀=w _outward-w _in(11);

W _in=w _outwardcos φ (12);

In formula (11)-(13): for the axial angle speed of MIMU output; w _outwardfor urceolus turning rate; w _infor inner cylinder rotating angular speed, φ is the datum line angle of active half strapdown system;

3.3) control module by active half strapdown system is set as φ by subtracting the elementary angle of twist speed of revolving motor with the ratio of the feedback angular speed of one-level speed governing gyro, complete thus the unification of the datum axis of active half strapdown system, thereby realized analytical evaluation and the compensation of active half strapdown system entirety coaxiality error.

A kind of active half strapdown system coaxiality error analytical evaluation of the present invention and compensation method are according to the design feature of active half strapdown system, by following three aspects:, the coaxiality error of active half strapdown system is carried out to analytical evaluation and compensation: one, carries out analytical evaluation by top mensuration to the urceolus coaxiality error of active half strapdown system.Its two, by inner core coaxiality error model, dynamic calibration and compensation are carried out in the inner core coaxiality error angle of active half strapdown system.Its three, by solving datum line angle, the datum axis of active half strapdown system is unified.In sum, a kind of active half strapdown system coaxiality error analytical evaluation of the present invention and compensation method are by carrying out analytical evaluation and compensation to the coaxiality error of active half strapdown system, not only effectively ensure overall construction intensity and the stability of active half strapdown system, and effectively ensured that subtracting of active half strapdown system revolve precision and measuring accuracy.

The coaxiality error that the present invention efficiently solves active half strapdown system affect active half strapdown system overall construction intensity, stability, subtract the problem of revolving precision and measuring accuracy, the accurate measurement that is applicable to height and revolves ammunition flight attitude.

Embodiment

Active half strapdown system coaxiality error analytical evaluation and compensation method, the method is to adopt following steps to realize:

1) analytical evaluation of the urceolus coaxiality error of active half strapdown system; Specifically comprise the steps:

1.1) active half strapdown system is installed in two top going up of dividing head, and ensures that the central axis of urceolus base of active half strapdown system and the shaft axis of dividing head overlap; Using the central axis of urceolus base as urceolus datum axis;

1.2) height of supposing urceolus base is h, by urceolus base by being highly divided into individual sampled cross-section; For each sampled cross-section of urceolus base, 5 ° of every rotations of dividing head are once sampled, and carry out altogether 72 samplings; Suppose j the sampled cross-section for urceolus base, sampled data when dividing head carries out the i time sampling is K _ij(r _ij, θ _ij, z _j); The least square center of supposing j sampled cross-section of urceolus base is O _j(a _j, b _j, z _j); According to the sampled data of dividing head, solve the least square center of each sampled cross-section of urceolus base; Solution formula is as follows:

$\left.\begin{array}{c}{a}_j=\frac{2}{m}\mathrm{\Σ}{r}_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}\\ b_j=\frac{2}{m}\mathrm{\Σ}{r}_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ z_j=z_j\end{array}\right\}---\left(1\right);$

In formula (1): i=1,2 ... 72; m=72; for positive integer; r _ijfor the radius value of j sampled cross-section of urceolus base; θ _ijfor j the sampled cross-section for urceolus base, the angle value rotating when dividing head carries out the i time sampling; z _jfor j sampled cross-section of urceolus base is along the coordinate figure of urceolus datum axis;

1.3) height of supposing all the other structures of urceolus is H, by all the other structures of urceolus by being highly divided into individual sampled cross-section; For each sampled cross-section of all the other structures of urceolus, 5 ° of every rotations of dividing head are once sampled, and carry out altogether 72 samplings; Suppose J the sampled cross-section for urceolus base, sampled data when dividing head carries out the I time sampling is M _iJ(r _iJ, θ _iJ, z _j); The least square center of supposing J sampled cross-section of urceolus base is O _j(a _j, b _j, z _j); According to the sampled data of dividing head, solve the least square center of each sampled cross-section of all the other structures of urceolus; Solution formula is as follows:

$\left.\begin{array}{c}{a}_J=\frac{2}{M}\mathrm{\Σ}{r}_{\mathrm{IJ}}\cos {\mathrm{\θ}}_{\mathrm{IJ}}\\ b_J=\frac{2}{M}\mathrm{\Σ}{r}_{\mathrm{IJ}}\sin {\mathrm{\θ}}_{\mathrm{IJ}}\\ z_J=z_J\end{array}\right\}---\left(2\right);$

In formula (2): I=1,2 ... 72; m=72; for positive integer; r _iJfor the radius value of J sampled cross-section of all the other structures of urceolus; θ _iJfor J the sampled cross-section for all the other structures of urceolus, the angle value rotating when dividing head carries out the I time sampling; z _jfor J sampled cross-section of all the other structures of urceolus is along the coordinate figure of urceolus datum axis;

1.4) suppose urceolus datum axis by coordinate plane XOY and intersect at it an A (x ₀, y ₀, 0); One group of direction number supposing urceolus datum axis is (l', k', 1); According to the least square center of each sampled cross-section of urceolus base, solve an A (x ₀, y ₀, 0) and direction number S=(l', k', 1); Solution formula is as follows:

$\left.\begin{array}{c}{x}_0=\frac{8}{h}\underset{j=1}{\overset{\frac{h}{8}}{\mathrm{\Σ}}}{a}_j\\ y_0=\frac{8}{h}\underset{j=1}{\overset{\frac{h}{8}}{\mathrm{\Σ}}}{b}_j\\ l^{\′}\text{=}\underset{j=1}{\overset{\frac{h}{8}}{\mathrm{\Σ}}}{a}_j{z}_j/\underset{j=1}{\overset{\frac{h}{8}}{\mathrm{\Σ}}}{z}_j^2\\ k^{\′}=\underset{j=1}{\overset{\frac{h}{8}}{\mathrm{\Σ}}}{b}_j{z}_j/\underset{j=1}{\overset{\frac{h}{8}}{\mathrm{\Σ}}}{z}_j^2\end{array}\right\}---\left(3\right);$

In formula (3): for positive integer;

1.5) according to an A (x ₀, y ₀, 0), the least square center of each sampled cross-section of direction number (l', k', 1), all the other structures of urceolus, solve the least square center of each sampled cross-section of all the other structures of urceolus to the distance of urceolus datum axis; Solution formula is as follows:

$e_J=\frac{|(O_J-A)\×S|}{\left|S\right|}---\left(4\right);$

O _J＝{a _J,b _J,z _J} (5)；

A＝{x ₀,y ₀,0} (6)；

S＝(l',k',1) (7)；

In formula (4)-(7): e _jfor the least square center O of J sampled cross-section of all the other structures of urceolus _j(a _j, b _j, z _j) to the distance of urceolus datum axis; O _jfor the least square center of J sampled cross-section of urceolus base; A is that urceolus datum axis is by the joining of coordinate plane XOY; S is one group of direction number of urceolus datum axis;

1.6) distance to urceolus datum axis according to the least square center of each sampled cross-section of all the other structures of urceolus, solves the urceolus coaxiality error of active half strapdown system; Solution formula is as follows:

In formula (8): for the urceolus coaxiality error of active half strapdown system; e _jfor the least square center O of J sampled cross-section of all the other structures of urceolus _j(a _j, b _j, z _j) to the distance of urceolus datum axis;

1.7) the concentricity tolerance maximal value of the urceolus coaxiality error of active half strapdown system and regulation is compared; If the urceolus coaxiality error of active half strapdown system is less than the concentricity tolerance maximal value of regulation, think that the urceolus coaxiality error of active half strapdown system, in allowed band, completes the analytical evaluation of the urceolus coaxiality error of active half strapdown system thus;

2) dynamic calibration and the compensation at the inner core coaxiality error angle of active half strapdown system; Specifically comprise the steps:

2.1) because the inner core of active half strapdown system has radially characteristic freely, suppose that it is inner core datum axis that subtracting of active half strapdown system revolved machine shaft axis, and the angle between the Z axis axis of MIMU and inner core datum axis is called to inner core coaxiality error angle;

2.2), under the condition existing at inner core coaxiality error angle, active half strapdown system is fixed on high-speed rotating equipment; In the range ability of MIMU, control high-speed rotating equipment and drive active half strapdown system to be rotated with set angle speed, MIMU is output angle speed thus; According to the angular speed of MIMU output, calibrate the inner core coaxiality error angle of active half strapdown system; Calibration formula is as follows:

$\mathrm{\θ}=\arctan \frac{\sqrt{w_y^2+w_z^2}}{w_x}---\left(9\right);$

In formula (9): θ is the inner core coaxiality error angle of active half strapdown system; w _xfor the angular speed of MIMU output is at the component of the X-axis of MIMU; w _yfor the angular speed of MIMU output is at the component of the Y-axis of MIMU; w _zfor the angular speed of MIMU output is at the component of the Z axis of MIMU;

2.3) according to the inner core coaxiality error angle of active half strapdown system, the angular speed of MIMU output is compensated, complete thus dynamic calibration and the compensation at the inner core coaxiality error angle of active half strapdown system; Compensation formula is as follows:

$\left\{\begin{array}{c}{w}_x=w\cos \\ w_y=-w\sin \mathrm{\θ}\sin \left(\mathrm{wt}\right)\\ w_z=-w\sin \mathrm{\θ}\cos \left(\mathrm{wt}\right)\end{array}\right.---\left(10\right);$

In formula (10): w _xfor the angular speed of MIMU output is at the component of the X-axis of MIMU; w _yfor the angular speed of MIMU output is at the component of the Y-axis of MIMU; w _zfor the angular speed of MIMU output is at the component of the Z axis of MIMU; θ is the inner core coaxiality error angle of active half strapdown system; W is the set angle speed of high-speed rotating equipment;

3) unification of the datum axis of active half strapdown system; Specifically comprise the steps:

3.1) central axis of supposing urceolus base is urceolus datum axis, supposes to subtract that to revolve machine shaft axis be inner core datum axis; In the physical construction installation process of active half strapdown system, because the central axis of urceolus base revolves machine shaft axis and can not accomplish to overlap completely with subtracting, and the inside fixed form of active half strapdown system is embedded fastening installation, the angle between urceolus datum axis and inner core datum axis is certain value, and this angle is called to datum line angle;

3.2) active half strapdown system is fixed on high-speed rotating equipment; In the range ability of MIMU, control high-speed rotating equipment drive active half strapdown system to be rotated with set angle speed, MIMU thus output shaft to angular speed; Measure the urceolus turning rate of active half strapdown system by the one-level speed governing gyro of active half strapdown system; According to axial angle speed and the urceolus turning rate of MIMU output, solve the datum line angle of active half strapdown system; Solution formula is as follows:

W ₀=w _outward-w _in(11);

W _in=w _outwardcos φ (12);

In formula (11)-(13): for the axial angle speed of MIMU output; w _outwardfor urceolus turning rate; w _infor inner cylinder rotating angular speed, φ is the datum line angle of active half strapdown system;

3.3) control module by active half strapdown system is set as φ by subtracting the elementary angle of twist speed of revolving motor with the ratio of the feedback angular speed of one-level speed governing gyro, complete thus the unification of the datum axis of active half strapdown system, thereby realized analytical evaluation and the compensation of active half strapdown system entirety coaxiality error.

Claims (1)

1. active half strapdown system coaxiality error analytical evaluation and a compensation method, is characterized in that: the method is to adopt following steps to realize:

1) analytical evaluation of the urceolus coaxiality error of active half strapdown system; Specifically comprise the steps:

1.1) active half strapdown system is installed in two top going up of dividing head, and ensures that the central axis of urceolus base of active half strapdown system and the shaft axis of dividing head overlap; Using the central axis of urceolus base as urceolus datum axis;

1.2) height of supposing urceolus base is h, by urceolus base by being highly divided into individual sampled cross-section; For each sampled cross-section of urceolus base, 5 ° of every rotations of dividing head are once sampled, and carry out altogether 72 samplings; Suppose j the sampled cross-section for urceolus base, sampled data when dividing head carries out the i time sampling is K _ij(r _ij, θ _ij, z _j); The least square center of supposing j sampled cross-section of urceolus base is O _j(a _j, b _j, z _j); According to the sampled data of dividing head, solve the least square center of each sampled cross-section of urceolus base; Solution formula is as follows:

$\left.\begin{array}{c}{a}_j=\frac{2}{m}\mathrm{\Σ}{r}_{\mathrm{ij}}\cos {\mathrm{\θ}}_{\mathrm{ij}}\\ b_j=\frac{2}{m}\mathrm{\Σ}{r}_{\mathrm{ij}}\sin {\mathrm{\θ}}_{\mathrm{ij}}\\ z_j=z_j\end{array}\right\}---\left(1\right);$

In formula (1): i=1,2 ... 72; for positive integer; r _ijfor the radius value of j sampled cross-section of urceolus base; θ _ijfor j the sampled cross-section for urceolus base, the angle value rotating when dividing head carries out the i time sampling; z _jfor j sampled cross-section of urceolus base is along the coordinate figure of urceolus datum axis;

1.3) height of supposing all the other structures of urceolus is H, by all the other structures of urceolus by being highly divided into individual sampled cross-section; For each sampled cross-section of all the other structures of urceolus, 5 ° of every rotations of dividing head are once sampled, and carry out altogether 72 samplings; Suppose J the sampled cross-section for urceolus base, sampled data when dividing head carries out the I time sampling is M _iJ(r _iJ, θ _iJ, z _j); The least square center of supposing J sampled cross-section of urceolus base is O _j(a _j, b _j, z _j); According to the sampled data of dividing head, solve the least square center of each sampled cross-section of all the other structures of urceolus; Solution formula is as follows:

$\left.\begin{array}{c}{a}_J=\frac{2}{M}\mathrm{\Σ}{r}_{\mathrm{IJ}}\cos {\mathrm{\θ}}_{\mathrm{IJ}}\\ b_J=\frac{2}{M}\mathrm{\Σ}{r}_{\mathrm{IJ}}\sin {\mathrm{\θ}}_{\mathrm{IJ}}\\ z_J=z_J\end{array}\right\}---\left(2\right);$

In formula (2): m=72; for positive integer; r _iJfor the radius value of J sampled cross-section of all the other structures of urceolus; θ _iJfor J the sampled cross-section for all the other structures of urceolus, the angle value rotating when dividing head carries out the I time sampling; z _jfor J sampled cross-section of all the other structures of urceolus is along the coordinate figure of urceolus datum axis;

1.4) suppose urceolus datum axis by coordinate plane XOY and intersect at it an A (x ₀, y ₀, 0); One group of direction number supposing urceolus datum axis is (l', k', 1); According to the least square center of each sampled cross-section of urceolus base, solve an A (x ₀, y ₀, 0) and direction number S=(l', k', 1); Solution formula is as follows:

$\left.\begin{array}{c}{x}_0=\frac{8}{h}\underset{j=1}{\overset{\frac{h}{8}}{\mathrm{\Σ}}}{a}_j\\ y_0=\frac{8}{h}\underset{j=1}{\overset{\frac{h}{8}}{\mathrm{\Σ}}}{b}_j\\ l^{\′}\text{=}\underset{j=1}{\overset{\frac{h}{8}}{\mathrm{\Σ}}}{a}_j{z}_j/\underset{j=1}{\overset{\frac{h}{8}}{\mathrm{\Σ}}}{z}_j^2\\ k^{\′}=\underset{j=1}{\overset{\frac{h}{8}}{\mathrm{\Σ}}}{b}_j{z}_j/\underset{j=1}{\overset{\frac{h}{8}}{\mathrm{\Σ}}}{z}_j^2\end{array}\right\}---\left(3\right);$

In formula (3): for positive integer;

1.5) according to an A (x ₀, y ₀, 0), the least square center of each sampled cross-section of direction number (l', k', 1), all the other structures of urceolus, solve the least square center of each sampled cross-section of all the other structures of urceolus to the distance of urceolus datum axis; Solution formula is as follows:

$e_J=\frac{|(O_J-A)\×S|}{\left|S\right|}---\left(4\right);$

O _J＝{a _J,b _J,z _J} (5)；

A＝{x ₀,y ₀,0} (6)；

S＝(l',k',1) (7)；

In formula (4)-(7): e _jfor the least square center O of J sampled cross-section of all the other structures of urceolus _j(a _j, b _j, z _j) to the distance of urceolus datum axis; O _jfor the least square center of J sampled cross-section of urceolus base; A is that urceolus datum axis is by the joining of coordinate plane XOY; S is one group of direction number of urceolus datum axis;

1.6) distance to urceolus datum axis according to the least square center of each sampled cross-section of all the other structures of urceolus, solves the urceolus coaxiality error of active half strapdown system; Solution formula is as follows:

In formula (8): for the urceolus coaxiality error of active half strapdown system; e _jfor the least square center O of J sampled cross-section of all the other structures of urceolus _j(a _j, b _j, z _j) to the distance of urceolus datum axis;

1.7) the concentricity tolerance maximal value of the urceolus coaxiality error of active half strapdown system and regulation is compared; If the urceolus coaxiality error of active half strapdown system is less than the concentricity tolerance maximal value of regulation, think that the urceolus coaxiality error of active half strapdown system, in allowed band, completes the analytical evaluation of the urceolus coaxiality error of active half strapdown system thus;

2) dynamic calibration and the compensation at the inner core coaxiality error angle of active half strapdown system; Specifically comprise the steps:

2.1) because the inner core of active half strapdown system has radially characteristic freely, suppose that it is inner core datum axis that subtracting of active half strapdown system revolved machine shaft axis, and the angle between the Z axis axis of MIMU and inner core datum axis is called to inner core coaxiality error angle;

2.2), under the condition existing at inner core coaxiality error angle, active half strapdown system is fixed on high-speed rotating equipment; In the range ability of MIMU, control high-speed rotating equipment and drive active half strapdown system to be rotated with set angle speed, MIMU is output angle speed thus; According to the angular speed of MIMU output, calibrate the inner core coaxiality error angle of active half strapdown system; Calibration formula is as follows:

$\mathrm{\θ}=\arctan \frac{\sqrt{w_y^2+w_z^2}}{w_x}---\left(9\right);$

In formula (9): θ is the inner core coaxiality error angle of active half strapdown system; w _xfor the angular speed of MIMU output is at the component of the X-axis of MIMU; w _yfor the angular speed of MIMU output is at the component of the Y-axis of MIMU; w _zfor the angular speed of MIMU output is at the component of the Z axis of MIMU;

2.3) according to the inner core coaxiality error angle of active half strapdown system, the angular speed of MIMU output is compensated, complete thus dynamic calibration and the compensation at the inner core coaxiality error angle of active half strapdown system; Compensation formula is as follows:

$\left\{\begin{array}{c}{w}_x=w\cos \\ w_y=-w\sin \mathrm{\θ}\sin \left(\mathrm{wt}\right)\\ w_z=-w\sin \mathrm{\θ}\cos \left(\mathrm{wt}\right)\end{array}\right.---\left(10\right);$

In formula (10): w _xfor the angular speed of MIMU output is at the component of the X-axis of MIMU; w _yfor the angular speed of MIMU output is at the component of the Y-axis of MIMU; w _zfor the angular speed of MIMU output is at the component of the Z axis of MIMU; θ is the inner core coaxiality error angle of active half strapdown system; W is the set angle speed of high-speed rotating equipment;

3) unification of the datum axis of active half strapdown system; Specifically comprise the steps:

3.1) central axis of supposing urceolus base is urceolus datum axis, supposes to subtract that to revolve machine shaft axis be inner core datum axis; In the physical construction installation process of active half strapdown system, because the central axis of urceolus base revolves machine shaft axis and can not accomplish to overlap completely with subtracting, and the inside fixed form of active half strapdown system is embedded fastening installation, the angle between urceolus datum axis and inner core datum axis is certain value, and this angle is called to datum line angle;

3.2) active half strapdown system is fixed on high-speed rotating equipment; In the range ability of MIMU, control high-speed rotating equipment drive active half strapdown system to be rotated with set angle speed, MIMU thus output shaft to angular speed; Measure the urceolus turning rate of active half strapdown system by the one-level speed governing gyro of active half strapdown system; According to axial angle speed and the urceolus turning rate of MIMU output, solve the datum line angle of active half strapdown system; Solution formula is as follows:

W ₀=w _outward-w _in(11);

W _in=w _outwardcos φ (12);

In formula (11)-(13): for the axial angle speed of MIMU output; w _outwardfor urceolus turning rate; w _infor inner cylinder rotating angular speed, φ is the datum line angle of active half strapdown system;

3.3) control module by active half strapdown system is set as φ by subtracting the elementary angle of twist speed of revolving motor with the ratio of the feedback angular speed of one-level speed governing gyro, complete thus the unification of the datum axis of active half strapdown system, thereby realized analytical evaluation and the compensation of active half strapdown system entirety coaxiality error.