CN110987149A - Device and method for measuring micro-vibration of reaction wheel - Google Patents
Device and method for measuring micro-vibration of reaction wheel Download PDFInfo
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- CN110987149A CN110987149A CN201911262978.4A CN201911262978A CN110987149A CN 110987149 A CN110987149 A CN 110987149A CN 201911262978 A CN201911262978 A CN 201911262978A CN 110987149 A CN110987149 A CN 110987149A
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- G01—MEASURING; TESTING
- G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
- G01H9/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves by using radiation-sensitive means, e.g. optical means
Abstract
One technical scheme of the invention is to provide a reaction wheel micro-vibration measuring device. The invention also provides a reaction wheel micro-vibration measuring method. By means of the device and the method for measuring the micro-vibration of the reaction wheel, the real-time and standard measurement of the micro-vibration of the reaction wheel can be realized, and disturbance components in six directions are obtained; by means of the visual detection device and the three-dimensional digital image correlation technology, interference of a system on a measurement target can be avoided, and good measurement precision is achieved; by utilizing the optical element and the adjusting mechanism in the visual detection device, the number of high-speed cameras required in three-dimensional image measurement is reduced, the equipment cost is effectively reduced, and the synchronous acquisition advantage is achieved. The device and the method are not only suitable for micro-vibration measurement of the reaction wheel, but also can be used for full-field modal test of other parts, and have better flexibility.
Description
Technical Field
The invention belongs to the technical field of vibration testing, and relates to a device and a method for measuring micro-vibration of a reaction wheel.
Background
As an important functional component of the satellite, the reaction wheel realizes the attitude control of the whole satellite and the space interference balance by changing the angular momentum of the reaction wheel. When the reaction wheel runs in an orbit, the reaction wheel generates micro-vibration under the influence of factors such as unbalance of a rotor, defects of a bearing and the like, the working environment of equipment is deteriorated, and imaging blurring of the satellite-borne camera is caused. The micro-vibration of the reaction wheel has the characteristics of small amplitude, wide frequency band and the like, and has higher requirements on measuring equipment. The measurement method for micro-vibration is mainly ground test and is divided into contact type and non-contact type.
The contact measurement completes the conversion from vibration signals to electric signals by installing a sensor, and common equipment comprises a Qishile force measurement system and a seismic mass vibration measurement system. The Qishile force measuring system utilizes four triaxial force sensors in the platform to complete the measurement of disturbance force and moment of a reaction wheel, the measurement precision is milli-Newton level, but the equipment price is high. The seismic mass vibration measurement system consists of a large mass block, two high-sensitivity accelerometers and a spring suspension structure, the accelerometers are used for capturing vibration signals, and the vibration magnitude of the reaction wheel is calculated by combining physical parameters of the mass block. Although the seismic mass vibration measurement system is relatively low in cost, the mass center position of the mass block has an error in three-dimensional simulation, so that the final measurement accuracy is reduced.
The non-contact measurement can complete static or dynamic measurement without contacting with a measured object, and system interference is reduced. The measuring means includes image measurement, photoelectric position sensor measurement, laser measurement, etc., such as an air-float type micro-vibration measuring system developed in japan. The system utilizes the CCD laser sensor to realize the radial vibration signal acquisition of the reaction wheel, and the measurement precision under the stable state can reach 10-4N, the disadvantage is that only low frequency disturbance forces in one direction can be measured. With the rapid development of computer and image technologies, optical measurement methods combined with machine vision have been studied in large quantities. The three-dimensional digital image correlation technology is based on the binocular stereo vision principle, and becomes one of powerful means in vibration measurement by the characteristics of full field property, real-time property, high precision and the like.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the existing reaction wheel micro-vibration measuring device has certain interference on a measured target during measurement, and has no full-field property and high equipment cost; the existing optical measurement aiming at the micro-vibration of the reaction wheel has certain limitation on function, only can measure the vibration in a single direction, and the structure of the equipment is relatively complex.
In order to solve the above-mentioned problems, one aspect of the present invention is to provide a reaction wheel micro-vibration measuring device, including:
the reaction wheel is fixed on the measuring plate, the measuring plate is supported by the supporting system, and random speckles are sprayed on the surface of the measuring plate;
the visual detection system comprises a mounting frame, wherein an annular light source, a high-speed camera, a height adjusting mechanism and two angle adjusting mechanisms are fixed on the mounting frame; the height adjusting mechanism is provided with a right-angle prism reflector, the high-speed camera and the annular light source are positioned right above the reaction wheel, and the right-angle prism reflector is positioned between the reaction wheel and the high-speed camera and between the reaction wheel and the annular light source; two plane reflectors are respectively arranged on the two angle adjusting mechanisms and are respectively positioned on the left side and the right side of the right-angle prism reflector; the speckle images on the surface of the measuring plate are mapped on the two plane reflectors, and speckle images formed by the two plane reflectors are refracted to the high-speed camera through the right-angle prism reflector, so that the high-speed camera can collect the speckle images formed by the plane reflectors, and the speckle images of the two plane reflectors are displayed on the left picture and the right picture of the same image;
and the control processing system is used for controlling the reaction wheel to run and triggering the high-speed camera to collect the speckle images in real time, and the control processing system processes the fed-back speckle image sequence to obtain the micro-vibration signals of the reaction wheel.
Preferably, the braced system includes the support frame, and marble platform bottom support has the isolator between marble platform and support frame on the support frame, and the top surface of marble platform is equipped with the switching frock, measure the board and locate on the switching frock.
Preferably, the top of mounting bracket is equipped with camera fixed plate and annular light source mounting panel, high-speed camera reaches annular light source fixes respectively on camera fixed plate and light source mounting panel, annular light source encircles high-speed camera a week.
Preferably, the height adjusting mechanism comprises a mounting plate arranged on the mounting frame, a bottom plate is arranged below the mounting plate, the bottom plate is arranged on a screw in a penetrating manner, one end of the screw penetrates through the bottom plate and then is screwed into the mounting plate, a first star-shaped handle is arranged at the other end of the screw, sliding rods are arranged on two sides of the screw, the sliding rods are fixed between the mounting plate and the bottom plate, a sliding block is arranged on the screw and the sliding rods in a penetrating manner, the screw is rotated after the star-shaped handle is rotated, so that the sliding block is driven to move up; the rear side of the bottom plate is provided with a side plate which is fixedly connected with the mounting plate.
Preferably, angle adjustment mechanism is including locating installation piece on the mounting bracket is equipped with the multirow screw hole on the installation piece, and position control spare is fixed through the screw hole of difference and is reached the purpose of regulation off-plane height on the installation piece, is equipped with the angle modulation spare of taking star handle two on the position control spare, and the picture frame is located on the angle modulation spare, in the picture frame was arranged in to the plane mirror, utilized angle modulation spare to adjust through rotating star handle two the deflection angle of plane mirror.
The invention also provides a reaction wheel micro-vibration measuring method, which is characterized in that the device comprises the following steps:
step 1): the right-angle prism reflector and the plane reflector are adjusted to proper positions by utilizing the height adjusting mechanism and the angle adjusting mechanism, so that the left view and the right view of the high-speed camera can completely present speckle characteristics of the measuring plate, and internal parameters and relative position parameters of the left view and the right view of the high-speed camera are obtained by adopting a Zhang-up friend calibration method;
step 2): installing a reaction wheel, and controlling the reaction wheel to operate according to the measuring working condition and then triggering the high-speed camera to carry out real-time acquisition;
step 3): processing the image sequence collected by the high-speed camera, and selecting four initial reference points (N) on the measuring plate1,N2,N3,N4) The coordinate positions of the four initial reference points on the world coordinate system are shown in the following formula (1):
in the formula (1), a is the distance from a coordinate point to a horizontal y-axis, and b is the distance from the coordinate point to a horizontal x-axis;
corresponding a reference point to an image coordinate system through calibrated internal and external parameters, calculating a zero-mean normalized cross-correlation coefficient ZNCC by using a Newton-Raphson algorithm, and performing two-dimensional matching search on the reference point, wherein the zero-mean normalized cross-correlation coefficient CznccAs shown in the following formula (2):
in the formula (2), f (x)i,yi) For measuring the image coordinates (x) before the plate vibration displacementi,yi) Gray value of g (x)i,yi) For measuring the displaced image coordinates (x) of the plate vibrationi,yi) Gray value of fmAnd gmRespectively is the gray average value of the image before and after the vibration displacement;
step 4): corresponding the two-dimensional image coordinates which are matched and searched to a world coordinate system through calibration parameters, and obtaining three-dimensional coordinates q of four reference points at different moments tn(t)＝[xn(t),yn(t),zn(t)](ii) a Carrying out second-order derivation on the coordinates, and calculating to obtain disturbance force F of the reference point on three coordinate axesqn(t) represented by the following formula (3):
in the formula (3), n is a reference point ordinal number and is 1,2,3 or 4; m is the mass of the measuring plate;
step 5): using reference points (N)1,N2,N3,N4) Three-component disturbance force Fqn(t) calculating to obtain six time-domain components (F) of the micro-vibration of the reaction wheelx,Fy,Fz,Mx,My,Mz) As shown in the following formula (4):
in the formula (4), Fx1、Fx2、Fx3、Fx4Respectively represent reference points (N)1,N2,N3,N4) Disturbance force on the x-axis; fy1、Fy2、Fy3、Fy4Respectively represent reference points (N)1,N2,N3,N4) Disturbance force on the y-axis; fz1、Fz2、Fz3、Fz4Respectively represent reference points (N)1,N2,N3,N4) Disturbance force in the z-axis.
By means of the device and the method for measuring the micro-vibration of the reaction wheel, the real-time and standard measurement of the micro-vibration of the reaction wheel can be realized, and disturbance components in six directions are obtained; by means of the visual detection device and the three-dimensional digital image correlation technology, interference of a system on a measurement target can be avoided, and good measurement precision is achieved; by utilizing the optical element and the adjusting mechanism in the visual detection device, the number of high-speed cameras required in three-dimensional image measurement is reduced, the equipment cost is effectively reduced, and the synchronous acquisition advantage is achieved. The device and the method are not only suitable for micro-vibration measurement of the reaction wheel, but also can be used for full-field modal test of other parts, and have better flexibility.
Drawings
FIG. 1 is a system diagram of a reaction wheel micro-vibration measurement device according to the present invention;
FIG. 2 is a schematic structural diagram of a reaction wheel micro-vibration measuring device according to the present invention;
FIG. 3 is a schematic view of an optical element and an adjusting mechanism of the vision inspection system according to the present invention;
FIG. 4 is a flow chart of a vibration measurement method based on three-dimensional digital image correlation according to the present invention;
FIG. 5 is a schematic view of the measurement plate and the surface reference point of the present invention.
Detailed Description
The invention will be further illustrated with reference to the following specific examples. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Further, it should be understood that various changes or modifications of the present invention may be made by those skilled in the art after reading the teaching of the present invention, and such equivalents may fall within the scope of the present invention as defined in the appended claims.
As shown in figures 1 and 2, the reaction wheel micro-vibration measuring device provided by the invention comprises a supporting system A, a visual detection system B and a control processing system C.
The supporting system A comprises a supporting frame 1, a vibration isolator 2, a marble platform 3, a switching tool 4 and a measuring plate 5. The bottom of the marble platform 3 is supported on the support frame 1, and a vibration isolator 2 is arranged between the marble platform 3 and the support frame 1. The top surface of marble platform 3 is equipped with switching frock 4. The measuring plate 5 is fixed on the marble platform 3 through the switching tool 4 and the reaction wheel D, and random speckles are sprayed on the surface.
The visual inspection system B comprises a mounting frame 6, an annular light source 15, a light source mounting plate 16, a camera fixing plate 17, a high-speed video camera 18, a height adjusting mechanism B1, a right-angle prism reflector 13, an angle adjusting mechanism B2 and a plane reflector 24. The mounting frame 6 is constructed and connected by aluminum profiles by using angle pieces and trapezoidal bolts. The mounting frame 6 is fixed with an annular light source 15, a high-speed camera 18, a height adjusting mechanism B1 and two angle adjusting mechanisms B2. The height adjusting mechanism B1 is provided with a rectangular prism reflector 13, the high-speed camera 18 and the annular light source 15 are positioned right above the reaction wheel D, and the rectangular prism reflector 13 is positioned between the reaction wheel D and the high-speed camera 18 and the annular light source 15. Two angle adjusting mechanisms B2 are respectively provided with a plane reflector 24, and the two plane reflectors 24 are respectively positioned at the left and right sides of the right-angle prism reflector 13. Speckle images on the surface of the measuring plate 5 are mapped on the two plane reflectors 24, and speckle images formed by the two plane reflectors 24 are refracted to the high-speed camera 18 through the right-angle prism reflector 13, so that the high-speed camera 18 collects the speckle images formed by the plane reflectors 24, and the speckle images of the two plane reflectors 24 are displayed on the left picture and the right picture of the same image.
The top of the mounting frame 6 is provided with a camera fixing plate 17 and an annular light source mounting plate 16, the high-speed camera 18 and the annular light source 15 are respectively fixed on the camera fixing plate 17 and the light source mounting plate 16, and the annular light source 15 surrounds the high-speed camera 18 for a circle.
The height adjusting mechanism B1 comprises a mounting plate 14 arranged on the mounting frame 6, a bottom plate 8 is arranged below the mounting plate 14, the bottom plate 8 is arranged on a screw 12 in a penetrating manner, one end of the screw 12 penetrates through the bottom plate 8 and then is screwed into the mounting plate 14, a star-shaped handle I7 is arranged at the other end of the screw 12, slide bars 9 are arranged on two sides of the screw 12, the slide bars 9 are fixed between the mounting plate 14 and the bottom plate 8, a slide block 10 is arranged on the screw 12 and the slide bars 9 in a penetrating manner, the screw 12 is rotated after the star-shaped handle 7 is rotated, so that the slide block 10 is driven to move; the rear side of the bottom plate 8 is provided with a side plate 11, and the side plate 11 is fixedly connected with a mounting plate 14.
Angle adjustment mechanism B2 is including locating installation piece 19 on mounting bracket 6, be equipped with the multirow screw hole on installation piece 19, position control piece 20 is fixed through different screw holes and is reached the purpose of regulation height from the face on installation piece 19, be equipped with angle modulation piece 21 of taking star handle two 22 on the position control piece 20, picture frame 23 is located on festival angle modulation piece 21, in picture frame 23 is arranged in to plane mirror 24, utilize angle modulation piece 21 to adjust the deflection angle of plane mirror 24 through rotating star handle two 22.
The control processing system C comprises a driving power supply 25 and a computer 26, wherein the computer 26 is connected with the driving power supply 25 to control the reaction wheel to run and trigger the high-speed camera 18 to collect data in real time; the computer 26 is provided with software integrated with a vibration measurement method based on three-dimensional digital image correlation, and processes the image sequence to obtain micro-vibration signals of the reaction wheel.
The vibration measurement method based on three-dimensional digital image correlation is shown in fig. 4, and comprises the following steps:
step 1): the right-angle prism reflector 13 and the plane reflector 24 are adjusted to proper positions by using a height adjusting mechanism B1 and an angle adjusting mechanism B2, so that the left view and the right view of the high-speed camera 18 can completely present the speckle characteristics of the measuring plate 5, and the internal parameters and the relative position parameters of the left view and the right view of the high-speed camera 18 are obtained by adopting a Zhang friend calibration method;
step 2): installing a reaction wheel D, and controlling the reaction wheel D to operate according to the measuring working condition and then triggering the high-speed camera 18 to carry out real-time acquisition;
step 3): the image sequence collected by the high-speed camera 18 is processed, and four initial reference points (N) on the measuring plate 5 are selected1,N2,N3,N4) The coordinate positions of the four initial reference points on the world coordinate system are shown in the following formula (1):
in the formula (1), a is the distance from a coordinate point to a horizontal y-axis, and b is the distance from the coordinate point to a horizontal x-axis;
corresponding a reference point to an image coordinate system through calibrated internal and external parameters, calculating a zero-mean normalized cross-correlation coefficient ZNCC by using a Newton-Raphson algorithm, and performing two-dimensional matching search on the reference point, wherein the zero-mean normalized cross-correlation coefficient CznccAs shown in the following formula (2):
in the formula (2), f (x)i,yi) For measuring the image coordinates (x) before the plate 5 is vibrated displacedi,yi) Gray value of g (x)i,yi) For measuring the image coordinates (x) after the plate (5) has been displaced by vibrationi,yi) Gray value of fmAnd gmRespectively is the gray average value of the image before and after the vibration displacement;
step 4): corresponding the two-dimensional image coordinates which are matched and searched to a world coordinate system through calibration parameters, and obtaining three-dimensional coordinates q of four reference points at different moments tn(t)＝[xn(t),yn(t),zn(t)](ii) a Carrying out second-order derivation on the coordinates, and calculating to obtain disturbance force F of the reference point on three coordinate axesqn(t) represented by the following formula (3):
in the formula (3), n is a reference point ordinal number and is 1,2,3 or 4; m is the mass of the measuring plate 5;
step 5): using reference points (N)1,N2,N3,N4) Three-component disturbance force Fqn(t) calculating to obtain six time-domain components (F) of the micro-vibration of the reaction wheelx,Fy,Fz,Mx,My,Mz) As shown in the following formula (4):
in the formula (4), Fx1、Fx2、Fx3、Fx4Respectively represent reference points (N)1,N2,N3,N4) Disturbance force on the x-axis; fy1、Fy2、Fy3、Fy4Respectively represent reference points (N)1,N2,N3,N4) Disturbance force on the y-axis; fz1、Fz2、Fz3、Fz4Respectively represent reference points (N)1,N2,N3,N4) Disturbance force in the z-axis.
Claims (6)
1. A reaction wheel micro-vibration measurement device, comprising:
the reaction wheel (D) is fixed on the measuring plate (5), the measuring plate (5) is supported by the supporting system (A), and random speckles are sprayed on the surface of the measuring plate (5);
the visual detection system (B) comprises a mounting frame (6), wherein an annular light source (15), a high-speed camera (18), a height adjusting mechanism (B1) and two angle adjusting mechanisms (B2) are fixed on the mounting frame (6); the height adjusting mechanism (B1) is provided with a right-angle prism reflector (13), the high-speed camera (18) and the annular light source (15) are positioned right above the reaction wheel (D), and the right-angle prism reflector (13) is positioned between the reaction wheel (D) and the high-speed camera (18) and the annular light source (15); two plane reflectors (24) are respectively arranged on the two angle adjusting mechanisms (B2), and the two plane reflectors (24) are respectively positioned on the left side and the right side of the right-angle prism reflector (13); speckle images on the surface of the measuring plate (5) are mapped on the two plane reflectors (24), speckle images formed by the two plane reflectors (24) are refracted to the high-speed camera (18) through the right-angle prism reflector (13), so that the high-speed camera (18) collects the speckle images formed by the plane reflectors (24), and the speckle images of the two plane reflectors (24) are displayed on the left and right frames of the same image;
and the control processing system (C) is used for controlling the reaction wheel to run and triggering the high-speed camera (18) to acquire the speckle images in real time, and the control processing system (C) processes the speckle image sequence fed back to obtain the micro-vibration signals of the reaction wheel (D).
2. The reaction wheel micro-vibration measuring device of claim 1, wherein the supporting system (a) comprises a supporting frame (1), the bottom of the marble platform (3) is supported on the supporting frame (1), a vibration isolator (2) is arranged between the marble platform (3) and the supporting frame (1), the top surface of the marble platform (3) is provided with a switching tool (4), and the measuring plate (5) is arranged on the switching tool (4).
3. The micro-vibration measuring device for reaction wheel as claimed in claim 1, wherein the top of the mounting frame (6) is provided with a camera fixing plate (17) and an annular light source mounting plate (16), the high-speed camera (18) and the annular light source (15) are respectively fixed on the camera fixing plate (17) and the light source mounting plate (16), and the annular light source (15) surrounds the high-speed camera (18) for a circle.
4. The reaction wheel micro-vibration measurement device of claim 1, the height adjusting mechanism (B1) comprises a mounting plate (14) arranged on the mounting frame (6), a bottom plate (8) is arranged below the mounting plate (14), the bottom plate (8) is arranged on the screw rod (12) in a penetrating way, one end of the screw rod (12) penetrates through the bottom plate (8) and then is screwed into the mounting plate (14), a first star-shaped handle (7) is arranged at the other end of the screw rod (12), slide rods (9) are arranged on two sides of the screw rod (12), the slide rods (9) are fixed between the mounting plate (14) and the bottom plate (8), a slide block (10) is arranged on the screw rod (12) and the slide rods (9) in a penetrating way, the screw rod (12), thereby driving the sliding block (10) to move up and down along the sliding rod (9), and the right-angle prism reflector (13) is arranged on the sliding block (10); a side plate (11) is arranged on the rear side of the bottom plate (8), and the side plate (11) is fixedly connected with the mounting plate (14).
5. The reaction wheel micro-vibration measuring device of claim 1, characterized in that the angle adjusting mechanism (B2) comprises a mounting block (19) disposed on the mounting frame (6), the mounting block (19) is provided with a plurality of rows of threaded holes, a position adjusting member (20) is fixed on the mounting block (19) through different threaded holes for adjusting the height of the off-plane, the position adjusting member (20) is provided with an angle adjusting member (21) having a star-shaped handle two (22), the mirror frame (23) is disposed on the angle adjusting member (21), the plane mirror (24) is disposed in the mirror frame (23), and the deflection angle of the plane mirror (24) is adjusted by rotating the star-shaped handle two (22) through the angle adjusting member (21).
6. A method of reaction wheel micro-vibration measurement using the apparatus of claim 1, comprising the steps of:
step 1): the right-angle prism reflector (13) and the plane reflector (24) are adjusted to proper positions by using a height adjusting mechanism (B1) and an angle adjusting mechanism (B2), so that the left view and the right view of the high-speed camera (18) can completely present the speckle characteristics of the measuring plate (5), and the internal parameters and the relative position parameters of the left view and the right view of the high-speed camera (18) are obtained by adopting a Zhang Zhengyou calibration method;
step 2): installing a reaction wheel (D), and controlling the reaction wheel (D) to operate according to the measuring working condition and then triggering a high-speed camera (18) to carry out real-time acquisition;
step 3): processing the image sequence acquired by the high-speed camera (18), and selecting four initial reference points (N) on the measuring plate (5)1,N2,N3,N4) The coordinate positions of the four initial reference points on the world coordinate system are shown in the following formula (1):
in the formula (1), a is the distance from a coordinate point to a horizontal y-axis, and b is the distance from the coordinate point to a horizontal x-axis;
corresponding a reference point to an image coordinate system through calibrated internal and external parameters, calculating a zero-mean normalized cross-correlation coefficient ZNCC by using a Newton-Raphson algorithm, and performing two-dimensional matching search on the reference point, wherein the zero-mean normalized cross-correlation coefficient CznccAs shown in the following formula (2):
in the formula (2), f (x)i,yi) For measuring the image coordinates (x) before the plate (5) is displaced by vibrationi,yi) Gray value of g (x)i,yi) For measuring the image coordinates (x) after the plate (5) has been displaced by vibrationi,yi) Gray value of fmAnd gmRespectively is the gray average value of the image before and after the vibration displacement;
step 4): corresponding the two-dimensional image coordinates which are matched and searched to a world coordinate system through calibration parameters, and obtaining three-dimensional coordinates q of four reference points at different moments tn(t)＝[xn(t),yn(t),zn(t)](ii) a Carrying out second-order derivation on the coordinates, and calculating to obtain disturbance force F of the reference point on three coordinate axesqn(t) represented by the following formula (3):
in the formula (3), n is a reference point ordinal number and is 1,2,3 or 4; m is the mass of the measuring plate (5);
step 5): using reference points (N)1,N2,N3,N4) Three-component disturbance force Fqn(t) calculating to obtain six time-domain components (F) of the micro-vibration of the reaction wheelx,Fy,Fz,Mx,My,Mz)，As shown in the following formula (4):
in the formula (4), Fx1、Fx2、Fx3、Fx4Respectively represent reference points (N)1,N2,N3,N4) Disturbance force on the x-axis; fy1、Fy2、Fy3、Fy4Respectively represent reference points (N)1,N2,N3,N4) Disturbance force on the y-axis; fz1、Fz2、Fz3、Fz4Respectively represent reference points (N)1,N2,N3,N4) Disturbance force in the z-axis.
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| 刘振玉: "《光电技术》", 31 August 1990, 北京理工大学出版社 * |
| 陈忠: "基于双目立体视觉与数字散斑图像相关的全场振动测量", 《振动与冲击》 * |
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