CN102878989B - Triaxial angular vibration measuring method through adopting satellite-borne linear accelerometers - Google Patents

Triaxial angular vibration measuring method through adopting satellite-borne linear accelerometers Download PDF

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CN102878989B
CN102878989B CN201210355302.1A CN201210355302A CN102878989B CN 102878989 B CN102878989 B CN 102878989B CN 201210355302 A CN201210355302 A CN 201210355302A CN 102878989 B CN102878989 B CN 102878989B
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axis
delta
theta
measurand
mean
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CN102878989A (en
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王海明
赵伟
孙峻
杨芳
赵键
雷军刚
霍红庆
罗世魁
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航天东方红卫星有限公司
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Abstract

A triaxial angular vibration measuring method through adopting satellite-borne linear accelerometers includes the following steps: firstly, selecting a mounting plane representing the angular vibration characteristic of a to-be-measured object on the to-be-measured object; secondly, selecting a rectangle region on the mounting plane and mounting the four linear accelerometers; thirdly, collecting time-domain data of the four linear accelerometers, amplifying and filtering the data on the satellite, and downloading the data to the ground; fourthly, calculating the vibration angular acceleration of the to-be-measured object in the directions of x-axis, y-axis and z-axis; and fifthly, calculating the root-mean-square value of the vibration angular acceleration, the root-mean-square value of the vibration angular velocity and the root-mean-square value of the vibration angular displacement, so as to complete the triaxial angular vibration measurement. Through the adoption of the method provided by the invention, requirements of the sensor for the mounting plane of the satellite as well as the resource occupation of the satellite are reduced, the mounting accuracy of the sensor can be guaranteed more easily, and the realization manner is simpler.

Description

A kind of method utilizing spaceborne linear accelerometer to carry out three shaft angle vibration surveys

Technical field

The present invention relates to a kind of high precision angular oscillation method of AEROSPACE APPLICATION, particularly a kind of method utilizing spaceborne linear accelerometer to carry out three shaft angle vibration surveys.

Background technology

Angular oscillation Measurement & Control realizes the prerequisite of the sensing of satellite high-precision attitude and remote optical sensing load high-resolution imaging and basis.Obvious impact may be brought on the camera modulation transfer function of Optical remote satellite (MTF), image resolution ratio, image geometry distortion and geographic position mensuration etc. when angular oscillation amplitude is excessive.

The common method that may be used for the vibration of direct measured angular at present utilizes gyro, star sensor and angular-rate sensor, the measuring accuracy of current optical fibre gyro can reach 0.05 "/s; star sensor difference estimates the angular velocity of spacecraft, and measuring accuracy can reach 0.01 °/s.The main measurement frequency band of both is low-frequency range at present, generally lower than 10Hz.Although in recent years, laser gyro and optical fibre gyro achieve develops faster, and measuring frequency band can reach 500Hz, and the degree of ripeness of product not enough.

Angular velocity or displacement transducer are the angular-rate sensors of magnetic fluid (magneto_hydro_dynamic, the MHD) kinetic theory based on plasma characteristics, and its research starts from the seventies in last century six.The product of successful Application mainly contains the ARS series of ATA company of the U.S. in the world.Sensor output signal can be treated to angular acceleration, angular velocity or angular displacement data by circuit or software.Wherein ARS-12 type sensor is the sensitiveest inertia angular oscillation sensor, and noise equivalent angle is better than 35nrad (0.007arcsec), bandwidth 1 ~ 1000Hz.Japan have employed angular displacement sensor (ADS) at its ALOS (ALOS) and has carried out angle displacement measurement.Its ADS sensor have employed the wideband angular rate sensor (Angular Rate Sensor, ARS) based on magnetohydrodynamics principle.It uses three ARS-12G angular rate sensors and optional power supply/signal condition and temperature measuring circuit to form Dynapak 12 or Dynapak 14 sensor bag.The variation in angular displacement in 2Hz ~ 500Hz can be measured, it is said that it reaches 0.01arcsec (rms) in the measuring accuracy at 500Hz place.But due to the sensor that ARS is based on angular rate measurement principle, therefore, can only by the angular speed of time domain acquisition at equal intervals discrete data obtain angular displacement as numerical integration in real time.

At home, at present mainly through parameters such as traditional attitude sensor instrumented satellite attitude angular velocities in-orbit, also do not experience the matured product of the wide-band measured angular vibration of flight validation.And attitude sensor limit by its principle, low-frequency range measurement (< 10Hz) can only be carried out, measurement requirement cannot be met.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, provides a kind of method utilizing spaceborne linear accelerometer to carry out three shaft angle vibration surveys.

Technical solution of the present invention is:

Utilize spaceborne linear accelerometer to carry out a method for three shaft angle vibration surveys, step is as follows:

(1) in measurand, select a mounting plane and determine coordinate system, this plane can represent the angular oscillation feature of measurand, the initial point of coordinate system, X-axis and Y-axis are all positioned at this mounting plane, measurand axis of rolling direction is X-axis, pitch axis direction is Y-axis, Z axis becomes right-handed coordinate system with X-axis, Y-axis, and described measurand refers to useful load on satellite or star;

(2) on mounting plane, select rectangular area, install four linear accelerometers respectively at rectangle four drift angles, wherein First Line accelerometer is three axis accelerometer meters; Second and the 3rd linear acceleration count two-axis accelerometer, two axis of the second linear accelerometer point to Y-direction and Z-direction respectively, two axis of the 3rd linear accelerometer point to respectively X to and Z-direction; 4th linear acceleration counts single-axis accelerometer, and it axially points to Z-direction, and the limit of described rectangular area and X-axis, Y-axis are parallel;

(3) gather the time domain data of 4 linear accelerometers, through to amplify and after filtering process on star, under pass to ground;

(4) formula is passed through &theta; . . 1 x = c z - a z La &theta; . . 1 y = b z - a z Lb &theta; . . 1 z = c x - a x La With &theta; . . 2 x = d z - b z La &theta; . . 2 y = d z - c z Lb &theta; . . 2 z = b y - a y La Calculate the angle of throw acceleration of two groups of measurands around X-axis, Y-axis, Z axis three axis with pass through formula more afterwards &theta; . . x = &theta; . . 1 x + &theta; . . 2 x 2 &theta; . . y = &theta; . . 1 y + &theta; . . 2 y 2 &theta; . . z = &theta; . . 1 z + &theta; . . 2 z 2 Its mean value is asked to obtain with

In formula: a x, a y, a zthe X being respectively First Line accelerometer to, Y-direction, Z-direction acceleration, b y, b zbe respectively the Y-direction of the second linear accelerometer, Z-direction acceleration, c x, c zthe X being respectively the 3rd linear accelerometer to, Z-direction acceleration, d zit is the Z-direction acceleration of the 4th linear accelerometer; The rectangle that La, Lb are respectively four linear accelerometers composition is along the length of side of Y-axis and X-axis;

(5) according to obtain in step (4) with calculate angle of throw acceleration root-mean-square value, angular velocity of vibration root-mean-square value and angle of throw displacement root-mean-square value, namely complete the measurement of three shaft angle vibrations.

Basis in described step (5) with calculate angle of throw acceleration root-mean-square value, angular velocity of vibration root-mean-square value and angle of throw displacement root-mean-square value, carry out in accordance with the following steps:

(5.1) formula is passed through B X ( i&Delta;f ) = 2 h N X &OverBar; ( i&Delta;f ) &CenterDot; X ( i&Delta;f ) B Y ( i&Delta;f ) = 2 h N Y &OverBar; ( i&Delta;f ) &CenterDot; Y ( i&Delta;f ) B Z ( i&Delta;f ) = 2 h N Z &OverBar; ( i&Delta;f ) &CenterDot; Z ( i&Delta;f ) I=0,1,2 ..., N/2 calculates the angle of throw acceleration power spectral density of measurand around X-axis, Y-axis, Z axis three axis,

Wherein, i is the sequence number of power spectral density value, and N is sampling sum;

Δ f is frequency interval,

B x(i Δ f), B y(i Δ f) and B z(i Δ f) for measurand is around the angular acceleration power spectral density value of frequency at f=i Δ f place of X-axis, Y-axis, Z axis three axis,

X (i Δ f), Y (i Δ f) and Z (i Δ f) are for measurand is around the FFT function of frequency at f=i Δ f place of X-axis, Y-axis, Z axis three axis;

with be followed successively by the conjugate complex number with X (i Δ f), Y (i Δ f) and Z (i Δ f);

(5.2) according to the angle of throw acceleration power spectral density B of the measurand calculated in step (5.1) around X-axis, Y-axis, Z axis three axis x(i Δ f), B y(i Δ f) and B z(i Δ f), by formula

&theta; . . X _ RMS | [ f 1 , f 2 ] = &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B X ( i&Delta;f ) &theta; . . Y _ RMS | [ f 1 , f 2 ] = 1 2 &pi; &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B Y ( i&Delta;f ) &theta; . . Z _ RMS | [ f 1 , f 2 ] = 1 2 &pi; &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B Z ( i&Delta;f ) i=0,1,2,…,N/2

Calculate the frequency angle of throw acceleration root-mean-square value at f=i Δ f place of measurand around X-axis, Y-axis, Z axis three axis with

Wherein: with being followed successively by measurand around X-axis, Y-axis, Z axis three axial frequency intervals is [f 1, f 2] angle of throw acceleration root-mean-square value;

(5.3) according to the angle of throw acceleration power spectral density B of the measurand calculated in step (5.1) around X-axis, Y-axis, Z axis three axis x(i Δ f), B y(i Δ f) and B z(i Δ f), by formula

&theta; . X _ RMS | [ f 1 , f 2 ] = 1 2 &pi; &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B X 2 ( i&Delta;f ) ( i&Delta;f ) 2 &theta; . Y _ RMS | [ f 1 , f 2 ] = 1 2 &pi; &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B Y 2 ( i&Delta;f ) ( i&Delta;f ) 2 &theta; . Z _ RMS | [ f 1 , f 2 ] = 1 2 &pi; &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B Z 2 ( i&Delta;f ) ( i&Delta;f ) 2 i=0,1,2,…,N/2

Calculate the frequency angular velocity of vibration root-mean-square value at f=i Δ f place of measurand around X-axis, Y-axis, Z axis three axis with

Wherein: with being followed successively by measurand around X-axis, Y-axis, Z axis three axial frequency intervals is [f 1, f 2] angular velocity of vibration root-mean-square value;

(5.4) according to the angle of throw acceleration power spectral density B of the measurand calculated in step (5.1) around X-axis, Y-axis, Z axis three axis x(i Δ f), B y(i Δ f) and B z(i Δ f), by formula

&theta; X _ RMS | [ f 1 , f 2 ] = 1 4 &pi; 2 &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B X 2 ( i&Delta;f ) ( i&Delta;f ) 4 &theta; Y _ RMS | [ f 1 , f 2 ] = 1 4 &pi; 2 &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B Y 2 ( i&Delta;f ) ( i&Delta;f ) 4 &theta; Z _ RMS | [ f 1 , f 2 ] = 1 4 &pi; 2 &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B Z 2 ( i&Delta;f ) ( i&Delta;f ) 4 i=0,1,2,…,N/2

Calculate the frequency angle of throw displacement root-mean-square value at f=i Δ f place of measurand around X-axis, Y-axis, Z axis three axis with

Wherein: with being followed successively by measurand around X-axis, Y-axis, Z axis three axial frequency intervals is [f 1, f 2] angle of throw displacement root-mean-square value.

The present invention's advantage is compared with prior art:

(1) the direct measurement means of angular oscillation such as gyro, star sensor and angular-rate sensor are relatively adopted, linear accelerometer technology is more simple, ripe, and in industrial circle widespread use, only need that a series of data processing is carried out to measurement data and can obtain angular oscillation data;

(2) linear accelerometer that the present invention is used adopts coplanar layout, and all accelerometers are arranged in a plane, and the range accuracy of installation and the depth of parallelism can be ensured by plane machining, requires lower to satellite;

(3) the present invention only needs the acceleration information of four linear accelerometers totally 8 passages, two groups of angular oscillation data can be obtained, angular oscillation data are obtained by the mode of averaging, improve the accuracy that angular oscillation is measured, and data volume is less, take satellite resource when transmitting over the ground less.

(4) the present invention obtains angular acceleration time domain data and adopts the mode of difference can eliminate the impact of neighbourhood noise, angular acceleration frequency domain data is being obtained subsequently through FFT conversion, successively obtain angular velocity of vibration data and angular displacement data by twice integration, spectral leakage is few.

Accompanying drawing explanation

Fig. 1 is the coplanar mounting arrangement figure of accelerometer of the present invention.

Fig. 2 is that the present invention adopts the coplanar installation of accelerometer to carry out the system composition diagram of angular oscillation measurement.

Fig. 3 is the inventive method process flow diagram.

Embodiment

Below in conjunction with accompanying drawing, the present invention will be further described.

The invention provides a kind of method utilizing spaceborne linear accelerometer to carry out three shaft angle vibration surveys, spaceborne linear accelerometer be exactly have space environment adaptive, carry out linear oscillator acceleration analysis, the sensor with certain measuring accuracy.The method of three shaft angle vibration surveys includes the space layout implementation method of accelerometer on satellite or useful load and adopts linear accelerometer to carry out the implementation method of angular oscillation calculating, the present invention utilizes spaceborne linear accelerometer to carry out the method for three shaft angle vibration surveys, define the configuration layouts implementation of sensor on star, solve the inconvenience of sensor complex configuration layouts implementation.Adopt this method, both reduced sensor to the requirement of satellite mounting plane and taking satellite resource, make again sensor installation accuracy be more prone to ensure, implementation is more simple.

As shown in Figure 3, step is as follows:

(1) in measurand, select a mounting plane and determine coordinate system, this plane can represent the angular oscillation feature of measurand, the initial point of coordinate system, X-axis and Y-axis are all positioned at this mounting plane, measurand axis of rolling direction is X-axis, pitch axis direction is Y-axis, Z axis becomes right-handed coordinate system with X-axis, Y-axis, and described measurand refers to useful load on satellite or star;

(2) on mounting plane, select rectangular area, install four linear accelerometers respectively at rectangle four drift angles, as shown in Figure 1, wherein First Line accelerometer is three axis accelerometer meters; Second and the 3rd linear acceleration count two-axis accelerometer, two axis of the second linear accelerometer point to Y-direction and Z-direction respectively, two axis of the 3rd linear accelerometer point to respectively X to and Z-direction; 4th linear acceleration counts single-axis accelerometer, and it axially points to Z-direction, and the limit of described rectangular area and X-axis, Y-axis are parallel;

(3) as shown in Figure 2, gather the time domain data of 4 linear accelerometers, through to amplify and after filtering process on star, under pass to ground;

(4) formula is passed through &theta; . . 1 x = c z - a z La &theta; . . 1 y = b z - a z Lb &theta; . . 1 z = c x - a x La With &theta; . . 2 x = d z - b z La &theta; . . 2 y = d z - c z Lb &theta; . . 2 z = b y - a y La Calculate the angle of throw acceleration of two groups of measurands around X-axis, Y-axis, Z axis three axis with pass through formula more afterwards &theta; . . x = &theta; . . 1 x + &theta; . . 2 x 2 &theta; . . y = &theta; . . 1 y + &theta; . . 2 y 2 &theta; . . z = &theta; . . 1 z + &theta; . . 2 z 2 Its mean value is asked to obtain with

In formula: a x, a y, a zthe X being respectively First Line accelerometer to, Y-direction, Z-direction acceleration, b y, b zbe respectively the Y-direction of the second linear accelerometer, Z-direction acceleration, c x, c zthe X being respectively the 3rd linear accelerometer to, Z-direction acceleration, d zit is the Z-direction acceleration of the 4th linear accelerometer; The rectangle that La, Lb are respectively four linear accelerometers composition is along the length of side of Y-axis and X-axis;

(5) according to obtain in step (4) with calculate angle of throw acceleration root-mean-square value, angular velocity of vibration root-mean-square value and angle of throw displacement root-mean-square value, namely complete the measurement of three shaft angle vibrations.

Specifically carry out in accordance with the following steps:

A () passes through formula B X ( i&Delta;f ) = 2 h N X &OverBar; ( i&Delta;f ) &CenterDot; X ( i&Delta;f ) B Y ( i&Delta;f ) = 2 h N Y &OverBar; ( i&Delta;f ) &CenterDot; Y ( i&Delta;f ) B Z ( i&Delta;f ) = 2 h N Z &OverBar; ( i&Delta;f ) &CenterDot; Z ( i&Delta;f ) I=0,1,2 ..., N/2 calculates the angle of throw acceleration power spectral density of measurand around X-axis, Y-axis, Z axis three axis,

Wherein, i is the sequence number of power spectral density value, and N is sampling sum;

Δ f is frequency interval,

B x(i Δ f), B y(i Δ f) and B z(i Δ f) for measurand is around the angular acceleration power spectral density value of frequency at f=i Δ f place of X-axis, Y-axis, Z axis three axis,

X (i Δ f), Y (i Δ f) and Z (i Δ f) are for measurand is around the FFT function of frequency at f=i Δ f place of X-axis, Y-axis, Z axis three axis;

with be followed successively by the conjugate complex number with X (i Δ f), Y (i Δ f) and Z (i Δ f);

B () is according to the angle of throw acceleration power spectral density B of the measurand calculated in step (a) around X-axis, Y-axis, Z axis three axis x(i Δ f), B y(i Δ f) and B z(i Δ f), by formula

&theta; . . X _ RMS | [ f 1 , f 2 ] = &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B X ( i&Delta;f ) &theta; . . Y _ RMS | [ f 1 , f 2 ] = 1 2 &pi; &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B Y ( i&Delta;f ) &theta; . . Z _ RMS | [ f 1 , f 2 ] = 1 2 &pi; &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B Z ( i&Delta;f ) i=0,1,2,…,N/2

Calculate the frequency angle of throw acceleration root-mean-square value at f=i Δ f place of measurand around X-axis, Y-axis, Z axis three axis with

Wherein: with being followed successively by measurand around X-axis, Y-axis, Z axis three axial frequency intervals is [f 1, f 2] angle of throw acceleration root-mean-square value;

C () is according to the angle of throw acceleration power spectral density B of the measurand calculated in step (a) around X-axis, Y-axis, Z axis three axis x(i Δ f), B y(i Δ f) and B z(i Δ f), by formula

&theta; . X _ RMS | [ f 1 , f 2 ] = 1 2 &pi; &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B X 2 ( i&Delta;f ) ( i&Delta;f ) 2 &theta; . Y _ RMS | [ f 1 , f 2 ] = 1 2 &pi; &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B Y 2 ( i&Delta;f ) ( i&Delta;f ) 2 &theta; . Z _ RMS | [ f 1 , f 2 ] = 1 2 &pi; &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B Z 2 ( i&Delta;f ) ( i&Delta;f ) 2 i=0,1,2,…,N/2

Calculate the frequency angular velocity of vibration root-mean-square value at f=i Δ f place of measurand around X-axis, Y-axis, Z axis three axis with

Wherein: with being followed successively by measurand around X-axis, Y-axis, Z axis three axial frequency intervals is [f 1, f 2] angular velocity of vibration root-mean-square value;

D () is according to the angle of throw acceleration power spectral density B of the measurand calculated in step (a) around X-axis, Y-axis, Z axis three axis x(i Δ f), B y(i Δ f) and B z(i Δ f), by formula

&theta; X _ RMS | [ f 1 , f 2 ] = 1 4 &pi; 2 &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B X 2 ( i&Delta;f ) ( i&Delta;f ) 4 &theta; Y _ RMS | [ f 1 , f 2 ] = 1 4 &pi; 2 &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B Y 2 ( i&Delta;f ) ( i&Delta;f ) 4 &theta; Z _ RMS | [ f 1 , f 2 ] = 1 4 &pi; 2 &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B Z 2 ( i&Delta;f ) ( i&Delta;f ) 4 i=0,1,2,…,N/2

Calculate the frequency angle of throw displacement root-mean-square value at f=i Δ f place of measurand around X-axis, Y-axis, Z axis three axis with

Wherein: with being followed successively by measurand around X-axis, Y-axis, Z axis three axial frequency intervals is [f 1, f 2] angle of throw displacement root-mean-square value.

Claims (1)

1. utilize spaceborne linear accelerometer to carry out a method for three shaft angle vibration surveys, it is characterized in that step is as follows:
(1) in measurand, select a mounting plane and determine coordinate system, this plane can represent the angular oscillation feature of measurand, the initial point of coordinate system, X-axis and Y-axis are all positioned at this mounting plane, measurand axis of rolling direction is X-axis, pitch axis direction is Y-axis, Z axis becomes right-handed coordinate system with X-axis, Y-axis, and described measurand refers to useful load on satellite or star;
(2) on mounting plane, select rectangular area, install four linear accelerometers respectively at rectangle four drift angles, wherein First Line accelerometer is three axis accelerometer meters; Second and the 3rd linear acceleration count two-axis accelerometer, two axis of the second linear accelerometer point to Y-direction and Z-direction respectively, two axis of the 3rd linear accelerometer point to respectively X to and Z-direction; 4th linear acceleration counts single-axis accelerometer, and it axially points to Z-direction, and the limit of described rectangular area and X-axis, Y-axis are parallel;
(3) gather the time domain data of 4 linear accelerometers, through to amplify and after filtering process on star, under pass to ground;
(4) formula is passed through &theta; . . 1 x = c z - a z La &theta; . . 1 y = b z - a z Lb &theta; . . 1 z = c x - a x La With &theta; . . 2 x = d z - b z La &theta; . . 2 y = d z - c z Lb &theta; . . 2 z = b y - a y La Calculate the angle of throw acceleration of two groups of measurands around X-axis, Y-axis, Z axis three axis with pass through formula more afterwards &theta; . . x = &theta; . . 1 x + &theta; . . 2 x 2 &theta; . . y = &theta; . . 1 y + &theta; . . 2 y 2 &theta; . . z = &theta; . . 1 z + &theta; . . 2 z 2 Its mean value is asked to obtain with
In formula: a x, a y, a zthe X being respectively First Line accelerometer to, Y-direction, Z-direction acceleration, b y, b zbe respectively the Y-direction of the second linear accelerometer, Z-direction acceleration, c x, c zthe X being respectively the 3rd linear accelerometer to, Z-direction acceleration, d zit is the Z-direction acceleration of the 4th linear accelerometer; The rectangle that La, Lb are respectively four linear accelerometers composition is along the length of side of Y-axis and X-axis;
(5) according to obtain in step (4) with calculate angle of throw acceleration root-mean-square value, angular velocity of vibration root-mean-square value and angle of throw displacement root-mean-square value, namely complete the measurement of three shaft angle vibrations;
Basis in described step (5) with calculate angle of throw acceleration root-mean-square value, angular velocity of vibration root-mean-square value and angle of throw displacement root-mean-square value, carry out in accordance with the following steps:
(5.1) formula is passed through B X ( i&Delta;f ) = 2 h N X &OverBar; ( i&Delta;f ) &CenterDot; X ( i&Delta;f ) B Y ( i&Delta;f ) = 2 h N Y &OverBar; ( i&Delta;f ) &CenterDot; Y ( i&Delta;f ) B Z ( i&Delta;f ) = 2 h N Z &OverBar; ( i&Delta;f ) &CenterDot; Z ( i&Delta;f ) I=0,1,2 ..., N/2 calculates the angle of throw acceleration power spectral density of measurand around X-axis, Y-axis, Z axis three axis,
Wherein, i is the sequence number of power spectral density value, and N is sampling sum;
Δ f is frequency interval,
B x(i Δ f), B y(i Δ f) and B z(i Δ f) for measurand is around the angular acceleration power spectral density value of frequency at f=i Δ f place of X-axis, Y-axis, Z axis three axis,
X (i Δ f), Y (i Δ f) and Z (i Δ f) are for measurand is around the FFT function of frequency at f=i Δ f place of X-axis, Y-axis, Z axis three axis;
with be followed successively by the conjugate complex number with X (i Δ f), Y (i Δ f) and Z (i Δ f);
(5.2) according to the angle of throw acceleration power spectral density B of the measurand calculated in step (5.1) around X-axis, Y-axis, Z axis three axis x(i Δ f), B y(i Δ f) and B z(i Δ f), by formula
&theta; . . X _ RMS | [ f 1 , f 2 ] = &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B X ( i&Delta;f ) &theta; . . Y _ RMS | [ f 1 , f 2 ] = 1 2 &pi; &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B Y ( i&Delta;f ) &theta; . . Z _ RMS | [ f 1 , f 2 ] = 1 2 &pi; &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B Z ( i&Delta;f ) i=0,1,2,…,N/2
Calculate the frequency angle of throw acceleration root-mean-square value at f=i Δ f place of measurand around X-axis, Y-axis, Z axis three axis with
Wherein: with being followed successively by measurand around X-axis, Y-axis, Z axis three axial frequency intervals is [f 1, f 2] angle of throw acceleration root-mean-square value;
(5.3) according to the angle of throw acceleration power spectral density B of the measurand calculated in step (5.1) around X-axis, Y-axis, Z axis three axis x(i Δ f), B y(i Δ f) and B z(i Δ f), by formula
&theta; . X _ RMS | [ f 1 , f 2 ] = 1 2 &pi; &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B X 2 ( i&Delta;f ) ( i&Delta;f ) 2 &theta; . Y _ RMS | [ f 1 , f 2 ] = 1 2 &pi; &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B Y 2 ( i&Delta;f ) ( i&Delta;f ) 2 &theta; . Z _ RMS | [ f 1 , f 2 ] = 1 2 &pi; &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B Z 2 ( i&Delta;f ) ( i&Delta;f ) 2 i=0,1,2,…,N/2
Calculate the frequency angular velocity of vibration root-mean-square value at f=i Δ f place of measurand around X-axis, Y-axis, Z axis three axis with
Wherein: with being followed successively by measurand around X-axis, Y-axis, Z axis three axial frequency intervals is [f 1, f 2] angular velocity of vibration root-mean-square value;
(5.4) according to the angle of throw acceleration power spectral density B of the measurand calculated in step (5.1) around X-axis, Y-axis, Z axis three axis x(i Δ f), B y(i Δ f) and B z(i Δ f), by formula &theta; X _ RMS | [ f 1 , f 2 ] = 1 4 &pi; 2 &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B X 2 ( i&Delta;f ) ( i&Delta;f ) 4 &theta; Y _ RMS | [ f 1 , f 2 ] = 1 4 &pi; 2 &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B Y 2 ( i&Delta;f ) ( i&Delta;f ) 4 &theta; Z _ RMS | [ f 1 , f 2 ] = 1 4 &pi; 2 &Delta;f &Sigma; i = f 1 / &Delta;f f 2 / &Delta;f B Z 2 ( i&Delta;f ) ( i&Delta;f ) 4 i=0,1,2,…,N/2
Calculate the frequency angle of throw displacement root-mean-square value at f=i Δ f place of measurand around X-axis, Y-axis, Z axis three axis with
Wherein: with being followed successively by measurand around X-axis, Y-axis, Z axis three axial frequency intervals is [f 1, f 2] angle of throw displacement root-mean-square value.
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