CN104197955A - Full-automatic triaxial air bearing table micro-interference force moment measurement system and method - Google Patents

Abstract

The invention discloses a full-automatic triaxial air bearing table micro-interference force moment measurement system and a method. The full-automatic triaxial air bearing table micro-interference force moment measurement system comprises an air floating ball and a ball socket, wherein a gyroscope is arranged on the air floating ball for measuring angular velocities omega m in three directions, three balancing mass blocks m1, m2 and m3 and a jet system are arranged on the air floating ball, the rotational inertia matrix of a system formed by the air floating ball, the gyroscope, the mass blocks and the jet system under coordinates of air floating ball is a 3*3 matrix Ia, the air floating ball can generate initial angular velocity by the jet system, the angular velocity omega m of the air floating ball during rotation can be measured by the gyroscope, and the interference force moments in three directions can be calculated according to Ia. According to the full-automatic triaxial air bearing table micro-interference force moment measurement system and the method, the interference problem between a bearing of the air floating ball and the ball socket can be effectively solved through nutation formed by a symmetrical structure during rotation entirely, and the interference force moment of the bearing of the air floating ball can be measured in a small-angle range.

Description

The full-automatic micro-disturbance torque measuring system of three-axis air-bearing table and method

Technical field

The present invention relates to measure the disturbance torque of trace level, relate to more specifically the needs such as a kind of three-axis air-bearing table and accurately measure all directions disturbance torque, the situation that has mechanical interference when single shaft is measured simultaneously, is difficult to measurement.

Background technology

Three-axis air-bearing table, as effective ground checkout equipment of development high precision spacecraft, checking posture control system and backoff algorithm, need to accurately be measured the disturbance torque of its all directions.The general basis of engineering practice now measure longitudinal disturbance torque, but due to disturbance torque T _dmagnitude very little, the precision of the angle measurement speed of the instrument of the angle measurement speed classes such as gyro is limited, during by this kind of method measurements interference moment, need to, through the integration of long period, just can measure due to T _dthe variation of the ω causing, and then be reflected to T _dupper, but because integral time is very long, air supporting ball need to turn over very large angle, and so this kind of method is also inapplicable on horizontal both direction, otherwise air supporting ball will strike on ball-and-socket.The means effectively that there is no in engineering at present solve problems, and the disturbance torque of generally giving tacit consent to three directions is consistent, lacks test figure support.

Summary of the invention

The present invention is directed to above-mentioned deficiency of the prior art, provide a kind of full-automatic micro-disturbance torque measuring system of three-axis air-bearing table and method, for measuring the size of the disturbance torque in three rotational freedom directions of three-axis air-bearing table air-floating ball bearing.This system and method, while utilizing full rotation, the nutating that symmetrical structure forms, can solve the interference problem between air-floating ball bearing and ball-and-socket effectively, can realize the disturbance torque of measuring air-floating ball bearing in low-angle scope.

For achieving the above object, the technical solution adopted in the present invention is as follows:

A kind of full-automatic micro-disturbance torque measuring system of three-axis air-bearing table, comprises air supporting ball and ball-and-socket, a gyro is installed on described air supporting ball, for measuring the angular velocity omega of three directions _m, three trim mass m are installed on air supporting ball ₁, m ₂, m ₃and gas ejecting system, the moment of inertia matrix of the system that described air supporting ball, gyro, mass and gas ejecting system form under air supporting spherical coordinates is the matrix I of 3 × 3 _a, described gas ejecting system makes air supporting ball produce an initial angle speed, the angular velocity omega of the air supporting ball by described gyro to measure air supporting ball in rotation process _m, and according to I _acalculate the disturbance torque of three directions.

A kind of full-automatic micro-disturbance torque measuring method of three-axis air-bearing table, completes by the system as claimed in claim 1, adopts three axles to rotate simultaneously, avoids the touching at He Qiu edge, ball-and-socket edge, and concrete steps are as follows:

1) ball-and-socket is fixed on ground by specific connecting end surface;

2) on air supporting ball, gyro is installed;

3) by adjusting the mass m on air supporting ball upper surface ₁, m ₂and m ₃position and counterweight, make the moment of inertia matrix of whole system meet I in three directions of x, y, z _xy=0, I _yz=0, I _zx=0, I _yy=I _zz;

4) according to the initial angular velocity omegae of following formula estimation air supporting ball _s0=[ω _x0ω _y0ω _z0] ^t:

(1) given suitable ω _z0, and suppose ω _x0=ω _y0=α ω _z0, wherein α is a unknown constant;

(2) air supporting ball level is β to the amplitude of the corner allowing, and is 0 according to initial three attitude angle, determines according to the following formula α:

$\arctan \mathrm{\&alpha;}+\arctan \frac{\sqrt{2}{I}_{\mathrm{zz}}\mathrm{\&alpha;}}{I_{\mathrm{xx}}}<\mathrm{\&beta;};$

If there is certain drift angle in initial time air supporting ball, make the direction of the angular momentum of whole system point to zenith, the formula while determining α is:

5) make whole air floating table have one above-mentioned 4 by gas ejecting system) in initial angle speed;

6) variation in whole process by gyro to measure stage body angular speed, calculate according to the following formula three-axis attitude angle ω:

$\left[\begin{array}{c}\stackrel{\&CenterDot;}{\mathrm{\&phi;}}\\ \stackrel{\&CenterDot;}{\mathrm{\&theta;}}\\ \stackrel{\&CenterDot;}{\mathrm{\&psi;}}\end{array}\right]=\frac{1}{\cos \mathrm{\&theta;}}\left[\begin{array}{ccc}1& 0& -\sin \mathrm{\&theta;}\sin \mathrm{\&phi;}\\ 0& \cos \mathrm{\&theta;}\cos \mathrm{\&phi;}& -\cos \mathrm{\&theta;}\sin \mathrm{\&phi;}\\ 0& \sin \mathrm{\&phi;}& \cos \mathrm{\&phi;}\end{array}\right]\left[\begin{array}{c}{\mathrm{\&omega;}}_x\\ {\mathrm{\&omega;}}_y\\ {\mathrm{\&omega;}}_z\end{array}\right];$

7) calculate according to the following formula the component of disturbance torque under body series:

$T_b=I\stackrel{\&CenterDot;}{\mathrm{\&omega;}}+\mathrm{\&omega;}\&times;I_a\mathrm{\&omega;};$

8) calculate according to the following formula the component of disturbance torque under inertial system

$T_i=\left[\begin{array}{ccc}\cos \mathrm{\&theta;}\cos \mathrm{\&psi;}& \cos \mathrm{\&theta;}\sin \mathrm{\&psi;}& -\sin \mathrm{\&theta;}\\ -\cos \mathrm{\&phi;}\sin \mathrm{\&psi;}+\sin \mathrm{\&phi;}\sin \mathrm{\&theta;}\cos \mathrm{\&psi;}& \cos \mathrm{\&phi;}\cos \mathrm{\&psi;}+\sin \sin \mathrm{\&theta;}\sin \mathrm{\&psi;}& \sin \mathrm{\&phi;}\cos \mathrm{\&theta;}\\ \sin \mathrm{\&phi;}\sin \mathrm{\&psi;}+\cos \mathrm{\&phi;}\sin \mathrm{\&theta;}\cos \mathrm{\&psi;}& -\sin \mathrm{\&phi;}\sin \mathrm{\&psi;}+\cos \sin \mathrm{\&theta;}\sin \mathrm{\&psi;}& \cos \mathrm{\&phi;}\cos \mathrm{\&theta;}\end{array}\right]T_b,$ Formula

In, ψ-θ-φ is followed successively by the three-axis attitude angle of rotating smoothly according to z-y-x.

The quantity of described mass can suitably increase, and only need to meet final I _xy=0, I _yz=0, I _zx=0, I _yy=I _zz.

System and method disclosed in this invention, while utilizing full rotation, the nutating that symmetrical structure forms, can solve the interference problem between air-floating ball bearing and ball-and-socket effectively, can realize the disturbance torque of measuring air-floating ball bearing in low-angle scope.

Brief description of the drawings

Fig. 1 is air supporting ball installation in position schematic diagram of the present invention;

Fig. 2 is air supporting ball installation in position diagrammatic cross-section.

Wherein: 1-gyro, 2-air supporting ball upper surface, 3-air supporting ball, 4-ball-and-socket, 5-connecting end surface, 6-mass m ₁, 7-mass m ₂, 8-mass m ₃, 9-air supporting ball edge, the gap between 10-ball and ball-and-socket, 11-ball-and-socket edge, 12-air admission hole.

Embodiment

Below embodiments of the invention are elaborated, the present embodiment is implemented as prerequisite taking technical solution of the present invention, provided detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

As shown in Fig. 1～Fig. 2, the micro-disturbance torque measuring system of full-automatic three-axis air-bearing table provided by the present invention, comprises air supporting ball 3 and ball-and-socket 4, and a gyro 1 is installed on air supporting ball 3, for measuring the angular velocity omega of three directions _m, three trim mass m are installed on air supporting ball 3 ₁6, m ₂7, m ₃8 and gas ejecting system (not shown in the figures meaning out), the moment of inertia matrix of the system that air supporting ball 3, gyro 1, three masses and gas ejecting system form under air supporting spherical coordinates is the matrix I of 3 × 3 _a, gas ejecting system makes air supporting ball produce an initial angle speed, measures the angular velocity omega of the air supporting ball of air supporting ball in rotation process by gyro 1 _m, and according to I _acalculate the disturbance torque of three directions.

In air admission hole 12, be blown into gases at high pressure, gases at high pressure form certain air film in gap 10 between ball 3 and ball-and-socket 4, and general disturbance torque measuring method can make ball edge 9 encounter ball-and-socket edge 11 and cause measuring in the time measuring horizontal direction.The micro-disturbance torque measuring method of full-automatic three-axis air-bearing table provided by the present invention adopts three axles to rotate simultaneously, has avoided the touching at He Qiu edge, ball-and-socket edge.Specifically comprise that step is as follows:

1) ball-and-socket is fixed on ground by specific connecting end surface 5;

2) gyro 1 is installed on air supporting ball;

3) by adjusting the mass m on air supporting ball upper surface 2 ₁6, m ₂7 and m ₃8 position and counterweight, make the moment of inertia matrix of whole system meet I according to three directions of the x, y, z shown in Fig. 1 _xy=0, I _yz=0, I _zx=0, I _yy=I _zz.The quantity of mass can suitably increase herein, only need to meet final I _xy=0, I _yz=0, I _zx=0, I _yy=I _zz;

4) according to the initial angular velocity omegae of following formula estimation air supporting ball _s0=[ω _x0ω _y0ω _z0] ^t:

(1), given suitable ω _z0, and suppose ω _x0=ω _y0=α ω _z0, wherein α is a unknown constant;

(2), air supporting ball level is β to the amplitude of corner allowing, and determines according to the following formula α:

$\arctan \mathrm{\&alpha;}+\arctan \frac{\sqrt{2}{I}_{\mathrm{zz}}\mathrm{\&alpha;}}{I_{\mathrm{xx}}}<\mathrm{\&beta;};$

5) make whole air floating table have the initial angle speed in one 4 by gas ejecting system (not shown in FIG.);

6) variation in whole process by gyro to measure stage body angular speed, calculate according to the following formula three-axis attitude angle ω:

$\left[\begin{array}{c}\stackrel{\&CenterDot;}{\mathrm{\&phi;}}\\ \stackrel{\&CenterDot;}{\mathrm{\&theta;}}\\ \stackrel{\&CenterDot;}{\mathrm{\&psi;}}\end{array}\right]=\frac{1}{\cos \mathrm{\&theta;}}\left[\begin{array}{ccc}1& 0& -\sin \mathrm{\&theta;}\sin \mathrm{\&phi;}\\ 0& \cos \mathrm{\&theta;}\cos \mathrm{\&phi;}& -\cos \mathrm{\&theta;}\sin \mathrm{\&phi;}\\ 0& \sin \mathrm{\&phi;}& \cos \mathrm{\&phi;}\end{array}\right]\left[\begin{array}{c}{\mathrm{\&omega;}}_x\\ {\mathrm{\&omega;}}_y\\ {\mathrm{\&omega;}}_z\end{array}\right];$

7) calculate according to the following formula the component of disturbance torque under body series:

$T_b=I\stackrel{\&CenterDot;}{\mathrm{\&omega;}}+\mathrm{\&omega;}\&times;I_a\mathrm{\&omega;};$

8) calculate according to the following formula the component of disturbance torque under inertial system

$T_i=\left[\begin{array}{ccc}\cos \mathrm{\&theta;}\cos \mathrm{\&psi;}& \cos \mathrm{\&theta;}\sin \mathrm{\&psi;}& -\sin \mathrm{\&theta;}\\ -\cos \mathrm{\&phi;}\sin \mathrm{\&psi;}+\sin \mathrm{\&phi;}\sin \mathrm{\&theta;}\cos \mathrm{\&psi;}& \cos \mathrm{\&phi;}\cos \mathrm{\&psi;}+\sin \sin \mathrm{\&theta;}\sin \mathrm{\&psi;}& \sin \mathrm{\&phi;}\cos \mathrm{\&theta;}\\ \sin \mathrm{\&phi;}\sin \mathrm{\&psi;}+\cos \mathrm{\&phi;}\sin \mathrm{\&theta;}\cos \mathrm{\&psi;}& -\sin \mathrm{\&phi;}\sin \mathrm{\&psi;}+\cos \sin \mathrm{\&theta;}\sin \mathrm{\&psi;}& \cos \mathrm{\&phi;}\cos \mathrm{\&theta;}\end{array}\right]T_b,$ Formula

In: in formula, ψ-θ-φ is followed successively by the three-axis attitude angle of rotating smoothly according to z-y-x.

The above-mentioned the 4th) in (2) article of step, computing formula is to be 0 according to initial three attitude angle, if there is certain drift angle in initial time air supporting ball, make the direction of the angular momentum of whole system point to zenith, the formula while determining α should be rewritten as: $\arctan \frac{\sqrt{2}{I}_{\mathrm{zz}}\mathrm{\&alpha;}}{I_{\mathrm{xx}}}<\mathrm{\&beta;}.$

Although content of the present invention has been done detailed introduction by above preferred embodiment, will be appreciated that above-mentioned description should not be considered to limitation of the present invention.Read after foregoing those skilled in the art, for multiple amendment of the present invention and substitute will be all apparent.Therefore, protection scope of the present invention should be limited to the appended claims.

Claims (3)

1. the micro-disturbance torque measuring system of full-automatic three-axis air-bearing table, comprises air supporting ball and ball-and-socket, it is characterized in that, a gyro is installed on described air supporting ball, for measuring the angular velocity omega of three directions _m, three trim mass m are installed on air supporting ball ₁, m ₂, m ₃and gas ejecting system, the moment of inertia matrix of the system that described air supporting ball, gyro, mass and gas ejecting system form under air supporting spherical coordinates is the matrix I of 3 × 3 _a, described gas ejecting system makes air supporting ball produce an initial angle speed, the angular velocity omega of the air supporting ball by described gyro to measure air supporting ball in rotation process _m, and according to I _acalculate the disturbance torque of three directions.

2. the micro-disturbance torque measuring method of full-automatic three-axis air-bearing table, is characterized in that, completes by the system as claimed in claim 1, adopts three axles to rotate simultaneously, avoids the touching at He Qiu edge, ball-and-socket edge, and concrete steps are as follows:

1) ball-and-socket is fixed on ground by specific connecting end surface;

2) on air supporting ball, gyro is installed;

3) by adjusting the mass m on air supporting ball upper surface ₁, m ₂and m ₃position and counterweight, make the moment of inertia matrix of whole system meet I in three directions of x, y, z _xy=0, I _yz=0, I _zx=0, I _yy=I _zz;

4) according to the initial angular velocity omegae of following formula estimation air supporting ball _s0=[ω _x0ω _y0ω _z0] ^t:

(1) given suitable ω _z0, and suppose ω _x0=ω _y0=α ω _z0, wherein α is a unknown constant;

(2) air supporting ball level is β to the amplitude of the corner allowing, and is 0 according to initial three attitude angle, determines according to the following formula α:

$\arctan \mathrm{\&alpha;}+\arctan \frac{\sqrt{2}{I}_{\mathrm{zz}}\mathrm{\&alpha;}}{I_{\mathrm{xx}}}<\mathrm{\&beta;};$

If there is certain drift angle in initial time air supporting ball, make the direction of the angular momentum of whole system point to zenith, the formula while determining α is:

5) make whole air floating table have one above-mentioned 4 by gas ejecting system) in initial angle speed;

6) variation in whole process by gyro to measure stage body angular speed, calculate according to the following formula three-axis attitude angle ω:

$\left[\begin{array}{c}\stackrel{\&CenterDot;}{\mathrm{\&phi;}}\\ \stackrel{\&CenterDot;}{\mathrm{\&theta;}}\\ \stackrel{\&CenterDot;}{\mathrm{\&psi;}}\end{array}\right]=\frac{1}{\cos \mathrm{\&theta;}}\left[\begin{array}{ccc}1& 0& -\sin \mathrm{\&theta;}\sin \mathrm{\&phi;}\\ 0& \cos \mathrm{\&theta;}\cos \mathrm{\&phi;}& -\cos \mathrm{\&theta;}\sin \mathrm{\&phi;}\\ 0& \sin \mathrm{\&phi;}& \cos \mathrm{\&phi;}\end{array}\right]\left[\begin{array}{c}{\mathrm{\&omega;}}_x\\ {\mathrm{\&omega;}}_y\\ {\mathrm{\&omega;}}_z\end{array}\right];$

7) calculate according to the following formula the component of disturbance torque under body series:

$T_b=I\stackrel{\&CenterDot;}{\mathrm{\&omega;}}+\mathrm{\&omega;}\&times;I_a\mathrm{\&omega;};$

8) calculate according to the following formula the component of disturbance torque under inertial system

$T_i=\left[\begin{array}{ccc}\cos \mathrm{\&theta;}\cos \mathrm{\&psi;}& \cos \mathrm{\&theta;}\sin \mathrm{\&psi;}& -\sin \mathrm{\&theta;}\\ -\cos \mathrm{\&phi;}\sin \mathrm{\&psi;}+\sin \mathrm{\&phi;}\sin \mathrm{\&theta;}\cos \mathrm{\&psi;}& \cos \mathrm{\&phi;}\cos \mathrm{\&psi;}+\sin \sin \mathrm{\&theta;}\sin \mathrm{\&psi;}& \sin \mathrm{\&phi;}\cos \mathrm{\&theta;}\\ \sin \mathrm{\&phi;}\sin \mathrm{\&psi;}+\cos \mathrm{\&phi;}\sin \mathrm{\&theta;}\cos \mathrm{\&psi;}& -\sin \mathrm{\&phi;}\sin \mathrm{\&psi;}+\cos \sin \mathrm{\&theta;}\sin \mathrm{\&psi;}& \cos \mathrm{\&phi;}\cos \mathrm{\&theta;}\end{array}\right]T_b,$ Formula

In: ψ-θ-φ is followed successively by the three-axis attitude angle of rotating smoothly according to z-y-x.

3. the micro-disturbance torque measuring method of full-automatic three-axis air-bearing table according to claim 1, is characterized in that, the quantity of described mass can suitably increase, and only need to meet final I _xy=0, I _yz=0, I _zx=0, I _yy=I _zz.