CN104197955A

CN104197955A - Fully automatic three-axis air bearing platform micro-disturbance torque measurement system and method

Info

Publication number: CN104197955A
Application number: CN201410398151.7A
Authority: CN
Inventors: 李太平; 徐俊; 倪华晨; 洪岩; 程世祥
Original assignee: Shanghai Institute of Satellite Equipment
Current assignee: Shanghai Institute of Satellite Equipment
Priority date: 2014-08-13
Filing date: 2014-08-13
Publication date: 2014-12-10
Anticipated expiration: 2034-08-13
Also published as: CN104197955B

Abstract

The invention discloses a full-automatic triaxial air bearing table micro-interference torque measurement system and method, which comprises an air floating ball and a ball socket, wherein a gyroscope is arranged on the air floating ball and used for measuring angular velocities omega in three directions_mThree balancing mass blocks m are arranged on the air floating ball₁、m₂、m₃And the rotational inertia matrix of a system consisting of the air floating ball, the gyroscope, the mass block and the air injection system under the coordinate of the air floating ball is a 3 multiplied by 3 matrix I_aThe air injection system enables the air floating ball to generate an initial angular velocity, and the angular velocity omega of the air floating ball in the rotation process of the air floating ball is measured through the gyroscope_mAnd according to I_aAnd calculating disturbance moments in three directions. The system and the method provided by the invention can effectively solve the problem of interference between the air ball bearing and the ball socket by utilizing nutation formed by the symmetrical structure during full rotation, and can realize the measurement of the interference torque of the air ball bearing in a small-angle range.

Description

Fully automatic three-axis air bearing platform micro-disturbance torque measurement system and method

技术领域technical field

本发明涉及测量微量级的干扰力矩，更具体的涉及一种三轴气浮台等需要精确测量各个方向干扰力矩，同时单轴测量时存在机械干涉、难以测量的情况。The present invention relates to the measurement of micro-level disturbance torque, and more specifically relates to a three-axis air bearing table and the like that need to accurately measure disturbance torque in all directions, and at the same time, there is mechanical interference in single-axis measurement, which makes it difficult to measure.

背景技术Background technique

三轴气浮台作为研制高精度航天器、验证姿控系统和补偿算法的有效地面测试设备，需要精确地测量其各个方向的干扰力矩。现在工程实践一般根据测量纵向的干扰力矩，但是由于干扰力矩T_d的量级很小，陀螺等测角速率类的仪器的测角速率的精度有限，通过该种方法测量干扰力矩时，需要经过较长时间的积分，才能测量出由于T_d所造成的ω的变化，进而反映到T_d上，但是由于积分时间很长，气浮球需要转过很大的角度，所以，该种方法在水平两个方向上并不适用，否则气浮球将撞击到球窝上。目前工程上尚无有效地手段解决此类问题，一般默认三个方向的干扰力矩一致，缺乏试验数据支持。As an effective ground test equipment for the development of high-precision spacecraft and the verification of attitude control systems and compensation algorithms, the three-axis air bearing table needs to accurately measure the disturbance torque in all directions. Current engineering practice is generally based on Measure the longitudinal disturbance torque, but because the magnitude of the disturbance torque T _d is very small, the accuracy of the angular rate measurement of instruments such as gyroscopes is limited. When measuring the disturbance torque by this method, it takes a long time to integrate , to measure the change of ω caused by T _d , and then reflect it on T _d , but because the integration time is very long, the air float ball needs to turn through a large angle, so this method can be used in both horizontal directions Do not apply, otherwise the air float ball will hit the ball socket. At present, there is no effective means to solve such problems in engineering. Generally, the disturbance torques in the three directions are the same by default, and there is a lack of experimental data support.

发明内容Contents of the invention

本发明针对上述的现有技术中的不足，提供一种全自动三轴气浮台微干扰力矩测量系统及方法，用于测量三轴气浮台气浮球轴承三个转动自由度方向上的干扰力矩的大小。该系统及方法，利用全转动时，对称结构所形成的章动，可以有效地解决气浮球轴承与球窝之间的干涉问题，可以实现在小角度的范围内测量气浮球轴承的干扰力矩。The present invention aims at the deficiencies in the above-mentioned prior art, and provides a fully automatic three-axis air flotation platform micro-disturbance torque measurement system and method for measuring three-axis air flotation platform air flotation ball bearings in three rotational degrees of freedom directions. The magnitude of the disturbance torque. The system and method can effectively solve the interference problem between the air-floating ball bearing and the ball socket by using the nutation formed by the symmetrical structure during full rotation, and can measure the interference of the air-floating ball bearing in a small angle range moment.

为达到上述目的，本发明所采用的技术方案如下：In order to achieve the above object, the technical scheme adopted in the present invention is as follows:

一种全自动三轴气浮台微干扰力矩测量系统，包括气浮球和球窝，在所述气浮球上安装一个陀螺，用于测量三个方向的角速度ω_m，气浮球上安装三个配平质量块m₁、m₂、m₃和喷气系统，所述气浮球、陀螺、质量块以及喷气系统所构成的系统在气浮球坐标下的转动惯量矩阵为一个3×3的矩阵I_a，所述喷气系统使得气浮球产生一个初始角速度，通过所述陀螺测量气浮球在转动过程中的气浮球的角速度ω_m，并根据I_a计算出三个方向的干扰力矩。A fully automatic three-axis air bearing micro-disturbance torque measurement system, including an air floating ball and a ball socket, a gyroscope is installed on the air floating ball to measure the angular velocity ω _m in three directions, and the air floating ball is installed Three trim masses m ₁ , m ₂ , m ₃ and the jet system, the moment of inertia matrix of the system formed by the air float ball, gyroscope, mass block and jet system in the coordinates of the air float ball is a 3×3 Matrix I _a , the jet system makes the air float ball produce an initial angular velocity, the angular velocity ω _m of the air float ball during the rotation process is measured by the gyroscope, and the disturbance torque in three directions is calculated according to I _a .

一种全自动三轴气浮台微干扰力矩测量方法，通过如权利要求1所述的系统来完成，采用三轴同时转动，避免球窝边缘和球边缘的触碰，具体步骤如下：A fully automatic three-axis air bearing table micro-disturbance torque measurement method is completed by the system as claimed in claim 1, using three-axis simultaneous rotation to avoid contact between the edge of the ball socket and the edge of the ball. The specific steps are as follows:

1)球窝通过特定的连接端面固定于地面；1) The ball socket is fixed to the ground through a specific connection end face;

2)在气浮球上安装陀螺；2) Install the gyro on the air float;

3)通过调整气浮球上端面上的质量块m₁、m₂和m₃的位置和配重，使得整个系统的转动惯量矩阵在x、y、z三个方向满足I_xy＝0、I_yz＝0、I_zx＝0、I_yy＝I_zz；3) By adjusting the positions and counterweights of mass blocks m ₁ , m ₂ and m ₃ on the upper end surface of the air float, the moment of inertia matrix of the entire system satisfies I _xy =0, I xy in the three directions of x, y and z _yz = 0, I _zx = 0, I _yy = I _zz ;

4)按照如下公式估算气浮球的初始角速度ω_s0＝[ω_x0 ω_y0 ω_z0]^T：4) Estimate the initial angular velocity ω _s0 =[ω _x0 ω _y0 ω _z0 ] ^T of the air float according to the following formula:

(1)给定合适的ω_z0，并假设ω_x0＝ω_y0＝αω_z0，其中α为一个未知的常数；(1) Given a suitable ω _z0 , and assuming ω _x0 =ω _y0 =αω _z0 , where α is an unknown constant;

(2)气浮球水平向允许的转角的幅值为β，按照初始三个姿态角均为0，则按照下式确定α：(2) The amplitude of the allowable horizontal rotation angle of the air float is β, and according to the initial three attitude angles are all 0, then determine α according to the following formula:

$arctan arctan α α + + arctan arctan \frac{\sqrt{22} {I I}_{zz zz} α α}{{I I}_{xx xx}} < < β β;;$

如果初始时刻气浮球存在一定的偏角，使得整个系统的角动量的方向指向天顶，则确定α时的公式为： If there is a certain deflection angle of the air buoy at the initial moment, so that the direction of the angular momentum of the entire system points to the zenith, then the formula for determining α is:

5)通过喷气系统使得整个气浮台有一个上述4)中的初始角速率；5) Make the entire air bearing table have an initial angular velocity in the above 4) through the jet system;

6)通过陀螺测量台体角速率在整个过程的变化，按照下式计算三轴姿态角ω：6) Measure the change of the platform body angular rate in the whole process through the gyro, and calculate the three-axis attitude angle ω according to the following formula:

$[\begin{matrix} \overset{\cdot &Center Dot;}{φ φ} \\ \overset{\cdot &Center Dot;}{θ θ} \\ \overset{\cdot \cdot}{ψ ψ} \end{matrix}] = = \frac{11}{cos cos θ θ} [\begin{matrix} 11 & 00 & - - sin sin θ θ sin sin φ φ \\ 00 & cos cos θ θ cos cos φ φ & - - cos cos θ θ sin sin φ φ \\ 00 & sin sin φ φ & cos cos φ φ \end{matrix}] [\begin{matrix} {ω ω}_{x x} \\ {ω ω}_{y the y} \\ {ω ω}_{z z} \end{matrix}];;$

7)按照下式计算干扰力矩在本体系下的分量：7) Calculate the component of the disturbance moment in this system according to the following formula:

${T T}_{b b} = = I I \overset{\cdot &Center Dot;}{ω ω} + + ω ω \times \times {I I}_{a a} ω ω;;$

8)按照下式计算干扰力矩在惯性系下的分量8) Calculate the component of the disturbance moment in the inertial system according to the following formula

$T_{i} = [\begin{matrix} \cos θ \cos ψ & \cos θ \sin ψ & - \sin θ \\ - \cos φ \sin ψ + \sin φ \sin θ \cos ψ & \cos φ \cos ψ + \sin \sin θ \sin ψ & \sin φ \cos θ \\ \sin φ \sin ψ + \cos φ \sin θ \cos ψ & - \sin φ \sin ψ + \cos \sin θ \sin ψ & \cos φ \cos θ \end{matrix}] T_{b},$ 式 $T_{i} = [\begin{matrix} \cos θ \cos ψ & \cos θ \sin ψ & - \sin θ \\ - \cos φ \sin ψ + \sin φ \sin θ \cos ψ & \cos φ \cos ψ + \sin \sin θ \sin ψ & \sin φ \cos θ \\ \sin φ \sin ψ + \cos φ \sin θ \cos ψ & - \sin φ \sin ψ + \cos \sin θ \sin ψ & \cos φ \cos θ \end{matrix}] T_{b},$ Mode

中，ψ-θ-φ依次为按照z-y-x顺利转动的三轴姿态角。Among them, ψ-θ-φ are the three-axis attitude angles that rotate smoothly according to z-y-x.

所述质量块的数量可以适当增加，只需要满足最终I_xy＝0、I_yz＝0、I_zx＝0、I_yy＝I_zz即可。The number of the mass blocks can be appropriately increased, as long as the final I _xy =0, I _yz =0, I _zx =0, I _yy =I _zz is satisfied.

本发明所公开的系统及方法，利用全转动时，对称结构所形成的章动，可以有效地解决气浮球轴承与球窝之间的干涉问题，可以实现在小角度的范围内测量气浮球轴承的干扰力矩。The system and method disclosed in the present invention can effectively solve the interference problem between the air-floating ball bearing and the ball socket by using the nutation formed by the symmetrical structure during full rotation, and can realize the measurement of air-floating within a small angle range. Disturbance torque of ball bearings.

附图说明Description of drawings

图1是本发明气浮球安装就位示意图；Fig. 1 is the installation in place schematic diagram of air float ball of the present invention;

图2是气浮球安装就位剖面示意图。Fig. 2 is a schematic cross-sectional view of the air float ball installed in place.

其中：1-陀螺，2-气浮球上端面，3-气浮球，4-球窝，5-连接端面，6-质量块m₁，7-质量块m₂，8-质量块m₃，9-气浮球边缘，10-球和球窝之间的缝隙，11-球窝边缘，12-进气孔。Among them: 1-gyroscope, 2-upper end surface of air floating ball, 3-air floating ball, 4-ball socket, 5-connecting end surface, 6-mass block m ₁ , 7-mass block m ₂ , 8-mass block m ₃ , 9-the edge of the air float, 10-the gap between the ball and the ball socket, 11-the edge of the ball socket, 12-the air inlet.

具体实施方式Detailed ways

下面对本发明的实施例作详细说明，本实施例以本发明技术方案为前提进行实施，给出了详细的实施方式和具体的操作过程，但本发明的保护范围不限于下述的实施例。Embodiments of the present invention are described in detail below, and the present embodiment is implemented on the premise of the technical solution of the present invention, and detailed implementation and specific operation process are provided, but the protection scope of the present invention is not limited to the following embodiments.

如图1～图2所示，本发明所提供的全自动三轴气浮台微干扰力矩测量系统，包括气浮球3和球窝4，在气浮球3上安装一个陀螺1，用于测量三个方向的角速度ω_m，气浮球3上安装三个配平质量块m₁6、m₂7、m₃8和喷气系统(图中未示意出)，气浮球3、陀螺1、三个质量块以及喷气系统所构成的系统在气浮球坐标下的转动惯量矩阵为一个3×3的矩阵I_a，喷气系统使得气浮球产生一个初始角速度，通过陀螺1测量气浮球在转动过程中的气浮球的角速度ω_m，并根据I_a计算出三个方向的干扰力矩。As shown in Figures 1 to 2, the fully automatic three-axis air bearing micro-disturbance torque measurement system provided by the present invention includes an air floating ball 3 and a ball socket 4, and a gyroscope 1 is installed on the air floating ball 3 for Measure the angular velocity ω _m in three directions, install three trim masses m ₁ 6, m ₂ 7, m ₃ 8 and an air injection system (not shown in the figure) on the air float 3, the air float 3, the gyro 1, The moment of inertia matrix of the system composed of three mass blocks and the air-jet system under the coordinates of the air-floating ball is a 3×3 matrix I _a , the air-jet system makes the air-floating ball produce an initial angular velocity, and the air-floating ball is measured by the gyro 1 at The angular velocity ω _m of the air floating ball during the rotation process, and calculate the disturbance torque in three directions according to I _a .

进气孔12内吹入高压气体，高压气体在球3和球窝4之间缝隙10中形成一定的气膜，一般的干扰力矩测量方法在测量水平方向时会使得球边缘9碰到球窝边缘11而导致无法测量。本发明所提供的全自动三轴气浮台微干扰力矩测量方法，采用三轴同时转动，避免了球窝边缘和球边缘的触碰。具体包括步骤如下：High-pressure gas is blown into the air inlet 12, and the high-pressure gas forms a certain air film in the gap 10 between the ball 3 and the ball socket 4. The general disturbance torque measurement method will make the ball edge 9 touch the ball socket when measuring the horizontal direction. Edge 11 makes it impossible to measure. The method for measuring the micro-disturbance torque of the fully automatic three-axis air bearing table provided by the present invention adopts the simultaneous rotation of three axes, avoiding the contact between the edge of the ball socket and the edge of the ball. The specific steps are as follows:

1)球窝通过特定的连接端面5固定于地面；1) The ball socket is fixed to the ground through a specific connection end face 5;

2)在气浮球上安装陀螺1；2) Install the gyro 1 on the air float;

3)通过调整气浮球上端面2上的质量块m₁6、m₂7和m₃8的位置和配重，使得整个系统的转动惯量矩阵按照图1所示的x、y、z三个方向满足I_xy＝0、I_yz＝0、I_zx＝0、I_yy＝I_zz。此处质量块的数量可以适当增加，只需要满足最终I_xy＝0、I_yz＝0、I_zx＝0、I_yy＝I_zz即可；3) By adjusting the positions and counterweights of the mass blocks m ₁ 6, m ₂ 7 and m ₃ 8 on the upper end surface 2 of the air float, the moment of inertia matrix of the entire system follows the three dimensions of x, y, and z shown in Figure 1 The directions satisfy I _xy =0, I _yz =0, I _zx =0, I _yy =I _zz . Here, the number of mass blocks can be appropriately increased, as long as the final I _xy =0, I _yz =0, I _zx =0, I _yy =I _zz are satisfied;

(1)、给定合适的ω_z0，并假设ω_x0＝ω_y0＝αω_z0，其中α为一个未知的常数；(1), given a suitable ω _z0 , and assuming ω _x0 =ω _y0 =αω _z0 , where α is an unknown constant;

(2)、气浮球水平向允许的转角的幅值为β，则按照下式确定α：(2) The amplitude of the allowable horizontal rotation angle of the air float ball is β, then determine α according to the following formula:

$arctan arctan α α + + arctan arctan \frac{\sqrt{22} {I I}_{zz zz} α α}{{I I}_{xx xxx}} < < β β;;$

5)通过喷气系统(图中未画出)使得整个气浮台有一个4中的初始角速率；5) Make the entire air bearing table have an initial angular rate of 4 through the air injection system (not shown in the figure);

$[\begin{matrix} \overset{\cdot &Center Dot;}{φ φ} \\ \overset{\cdot &Center Dot;}{θ θ} \\ \overset{\cdot &Center Dot;}{ψ ψ} \end{matrix}] = = \frac{11}{cos cos θ θ} [\begin{matrix} 11 & 00 & - - sin sin θ θ sin sin φ φ \\ 00 & cos cos θ θ cos cos φ φ & - - cos cos θ θ sin sin φ φ \\ 00 & sin sin φ φ & cos cos φ φ \end{matrix}] [\begin{matrix} {ω ω}_{x x} \\ {ω ω}_{y the y} \\ {ω ω}_{z z} \end{matrix}];;$

中：式中，ψ-θ-φ依次为按照z-y-x顺利转动的三轴姿态角。Where: In the formula, ψ-θ-φ are the three-axis attitude angles that rotate smoothly according to z-y-x.

上述第4)步第(2)条中，计算公式是按照初始三个姿态角均为0，如果初始时刻气浮球存在一定的偏角，使得整个系统的角动量的方向指向天顶，则确定α时的公式应改写为： $\arctan \frac{\sqrt{2} I_{zz} α}{I_{xx}} < β .$ In the above step 4) and item (2), the calculation formula is based on the fact that the initial three attitude angles are all 0, if there is a certain deflection angle of the air float at the initial moment, so that the direction of the angular momentum of the entire system points to the zenith, then The formula for determining α should be rewritten as: $\arctan \frac{\sqrt{2} I_{zz} α}{I_{xxx}} < β .$

尽管本发明的内容已经通过上述优选实施例作了详细介绍，但应当认识到上述的描述不应被认为是对本发明的限制。在本领域技术人员阅读了上述内容后，对于本发明的多种修改和替代都将是显而易见的。因此，本发明的保护范围应由所附的权利要求来限定。Although the content of the present invention has been described in detail through the above preferred embodiments, it should be understood that the above description should not be considered as limiting the present invention. Various modifications and alterations to the present invention will become apparent to those skilled in the art upon reading the above disclosure. Therefore, the protection scope of the present invention should be defined by the appended claims.

Claims

1. A full-automatic three-axis air bearing platform micro-disturbance torque measurement system, comprising an air floating ball and a ball socket, is characterized in that a gyroscope is installed on the air floating ball for measuring the angular velocity ω _m in three directions , three trim masses m ₁ , m ₂ , m ₃ and the jet system are installed on the air float, the moment of inertia matrix of the system composed of the air float, gyroscope, mass and jet system under the coordinates of the air float It is a 3×3 matrix I _a , the air injection system makes the air float ball produce an initial angular velocity, the angular velocity ω _m of the air float ball during the rotation process is measured by the gyroscope, and calculated according to I _a Disturbing moments in three directions.

2. A full-automatic three-axis air bearing table micro-disturbance torque measurement method, is characterized in that, completes by the system as claimed in claim 1, adopts three axes to rotate simultaneously, avoids the touch of ball-socket edge and ball edge, Specific steps are as follows:

1) The ball socket is fixed to the ground through a specific connection end face;

2) Install the gyro on the air float;

3) By adjusting the positions and counterweights of mass blocks m ₁ , m ₂ and m ₃ on the upper end surface of the air float, the moment of inertia matrix of the entire system satisfies I _xy =0, I xy in the three directions of x, y and z _yz = 0, I _zx = 0, I _yy = I _zz ;

4) Estimate the initial angular velocity ω _s0 =[ω _x0 ω _y0 ω _z0 ] ^T of the air float according to the following formula:

(1) Given a suitable ω _z0 , and assuming ω _x0 =ω _y0 =αω _z0 , where α is an unknown constant;

(2) The amplitude of the allowable horizontal rotation angle of the air float is β, and according to the initial three attitude angles are all 0, then determine α according to the following formula:

arctan arctan α α + + arctan arctan \frac{\sqrt{22} {I I}_{zz zz} α α}{{I I}_{xx xx}} < < β β;;

If there is a certain deflection angle of the air buoy at the initial moment, so that the direction of the angular momentum of the entire system points to the zenith, then the formula for determining α is:

5) Make the entire air bearing table have an initial angular velocity in the above 4) through the jet system;

6) Measure the change of the platform body angular rate in the whole process through the gyro, and calculate the three-axis attitude angle ω according to the following formula:

[\begin{matrix} \overset{\cdot &Center Dot;}{φ φ} \\ \overset{\cdot &Center Dot;}{θ θ} \\ \overset{\cdot &Center Dot;}{ψ ψ} \end{matrix}] = = \frac{11}{cos cos θ θ} [\begin{matrix} 11 & 00 & - - sin sin θ θ sin sin φ φ \\ 00 & cos cos θ θ cos cos φ φ & - - cos cos θ θ sin sin φ φ \\ 00 & sin sin φ φ & cos cos φ φ \end{matrix}] [\begin{matrix} {ω ω}_{x x} \\ {ω ω}_{y the y} \\ {ω ω}_{z z} \end{matrix}];;

7) Calculate the component of the disturbance moment in this system according to the following formula:

{T T}_{b b} = = I I \overset{\cdot &Center Dot;}{ω ω} + + ω ω \times \times {I I}_{a a} ω ω;;

8) Calculate the component of the disturbance moment in the inertial system according to the following formula

T_{i} = [\begin{matrix} \cos θ \cos ψ & \cos θ \sin ψ & - \sin θ \\ - \cos φ \sin ψ + \sin φ \sin θ \cos ψ & \cos φ \cos ψ + \sin \sin θ \sin ψ & \sin φ \cos θ \\ \sin φ \sin ψ + \cos φ \sin θ \cos ψ & - \sin φ \sin ψ + \cos \sin θ \sin ψ & \cos φ \cos θ \end{matrix}] T_{b},

Mode

Middle: ψ-θ-φ are the three-axis attitude angles that rotate smoothly according to z-y-x.

3. The full-automatic three-axis air bearing platform micro-disturbance torque measurement method according to claim 1, is characterized in that, the quantity of described mass block can be increased appropriately, only needs to satisfy final _Ixy =0, _Iyz =0, I _zx =0 and I _yy =I _zz are sufficient.