CN107063443B - Three-dimensional space motion trajectory vibration synthesis method - Google Patents
Three-dimensional space motion trajectory vibration synthesis method Download PDFInfo
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- CN107063443B CN107063443B CN201710246594.8A CN201710246594A CN107063443B CN 107063443 B CN107063443 B CN 107063443B CN 201710246594 A CN201710246594 A CN 201710246594A CN 107063443 B CN107063443 B CN 107063443B
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Abstract
The invention discloses a three-dimensional space motion track vibration synthesis method, which belongs to the field of vibration calibration and comprises the steps of description of space attitude and track shape of an ideal space motion track, calculation of X, Y, Z axial amplitude and phase of a target, generation of a vibration controller, a three-axial vibration table, X, Y, Z axial sinusoidal vibration and synthesis of a three-dimensional space motion track. X, Y, Z axial sinusoidal vibration with arbitrary amplitude and phase synthesizes three-dimensional space motion tracks of three types, namely space straight line, space circular and space ellipse. And respectively describing the space attitude and the track shape of the space elliptical motion track through the orthogonal matrix and the major and minor axes. And (3) calculating X, Y, Z axial amplitude and phase of the target according to the attitude and the shape of the space ellipse, correcting a driving signal through an iterative control algorithm, and controlling the triaxial vibration table to synthesize a required space motion track. The invention can freely adjust the posture and the shape of the three-dimensional space motion trail through X, Y, Z axial amplitude and phase.
Description
Technical Field
The invention belongs to the field of vibration calibration, and particularly relates to a three-dimensional space motion trajectory synthesis method suitable for sinusoidal vibration.
Background
The vibration sensor is widely applied to various fields of aerospace, power machinery, transportation, military mechanical weapons, energy industry, civil construction, electronic industry, environmental protection and the like. Calibration techniques for vibration sensors are a necessary approach to ensure measurement validity and reliability. With the development of high-sensitivity, wide-frequency-range, and other vibration sensors and the increasing demand for high-precision vibration measurement in industry, calibration techniques for vibration sensors are becoming increasingly important.
A traditional single-axial vibration table generates sinusoidal vibration to synthesize a single-directional linear track, a two-axial vibration system generates sinusoidal vibration with any relative amplitude and phase to synthesize an elliptical track in a plane, wherein the linear track (with the same phase and any amplitude) and the circular track (with orthogonal phase and equal amplitude) can be regarded as special cases of the elliptical track. The unidirectional linear track and the plane elliptical track can not provide space vibration excitation for the sensor, and the space response characteristic of the sensor can be obtained only by reinstallation, so that the time consumption is long, and a certain installation error is introduced. The triaxial vibration table can generate a motion track of a three-dimensional space, and provides vibration excitation closer to an actual environment. With the increasing application of multi-component accelerometers, seismometers and the like, urgent needs are brought to multi-component vibration calibration technology. Therefore, a three-dimensional space motion track vibration synthesis method is needed to be provided, the establishment of a three-axial vibration calibration method is supported, the development of vibration measurement in China to a measurement system closer to an actual measurement environment is promoted, the requirement of various application fields on high-performance vibration measurement is met, and the upgrade and progress of advanced manufacturing industry in China are supported.
Disclosure of Invention
The invention aims to provide a method for synthesizing a three-dimensional space motion trail for multi-component vibration calibration. In view of the defects of the existing uniaxial motion track and the in-plane motion track, the invention realizes the aim of synthesizing the three-dimensional motion track by vibration based on a triaxial vibration table.
In order to achieve the purpose, the invention adopts the technical scheme that:
a three-dimensional space motion track vibration synthesis method for vibration calibration comprises the following steps: description of a spatial attitude and trajectory shape 1 of an ideal spatial motion trajectory, calculation of an X-axis amplitude and phase 2 of a target, calculation of a Y-axis amplitude and phase 3 of the target, calculation of a Z-axis amplitude and phase 4 of the target, a vibration controller 5, a triaxial vibration table 6, generation of an X-axis sinusoidal vibration 7, generation of a Y-axis sinusoidal vibration 8, generation of a Z-axis sinusoidal vibration 9, and synthesis of a three-dimensional spatial motion trajectory 10.
Three-dimensional space motion tracks of three types, namely X-axis sinusoidal vibration 7, Y-axis sinusoidal vibration 8 and Z-axis sinusoidal vibration 9 which are orthogonal to each other, and X, Y, Z axial sinusoidal vibrations with any amplitude and phase are synthesized into space straight lines 15, space circles and space ellipses 14. Where the spatial straight line 15 and the spatial circle are considered as two special cases of the spatial ellipse 14.
Describing the space attitude of the space elliptical motion track through an orthogonal matrix, wherein the first two column vectors of the orthogonal matrix are respectively parallel to the long axis and the short axis of an ellipse, and the third column vector is perpendicular to the plane of the ellipse; the track shape of the spatial motion track is described by the lengths of the major axis and the minor axis.
And calculating the X-axis amplitude and phase 2, the Y-axis amplitude and phase 3 and the Z-axis amplitude and phase 4 of the target according to the attitude and the shape of the space ellipse. The vibration controller 5 repeatedly and iteratively corrects the driving frequency spectrum 19 to enable the feedback response frequency spectrum 20 to reach an ideal reference frequency spectrum 21, and controls the triaxial vibration table 6 to generate X-axis sinusoidal vibration 7, Y-axis sinusoidal vibration 8 and Z-axis sinusoidal vibration 9 with specific amplitude and phase.
Compared with the prior art, the invention has the following beneficial effects:
the vibration synthesis method gives the type, shape and spatial attitude of a three-dimensional space motion track synthesized by X, Y, Z axial sinusoidal vibration with any amplitude and phase.
The vibration synthesis method can adjust the space attitude and the track shape of the three-dimensional space motion track through the amplitude and the phase of X, Y, Z axial sinusoidal vibration.
On the basis of the traditional sinusoidal vibration control iterative algorithm, the vibration synthesis method only needs to increase the amplitude and phase calculation links, can be executed based on the traditional multi-axial vibration control system, and is simple.
Drawings
FIG. 1 is a schematic diagram of a three-dimensional spatial motion trajectory synthesis method;
FIG. 2 is a schematic view of X, Y, Z axial sinusoidal oscillations;
FIG. 3 is a schematic diagram of a spatial elliptical motion trajectory;
FIG. 4 is a schematic diagram of a spatial linear motion trajectory;
FIG. 5 is a schematic diagram of an orthogonal unit vector;
FIG. 6 is a schematic diagram of an iterative control algorithm;
reference numbers in the figures:
1-space attitude and track shape of ideal space motion track; 2-X-axis amplitude and phase of the target; 3-Y-axis amplitude and phase of the target; 4-Z-axis amplitude and phase of the target; 5-a vibration controller; 6-triaxial vibration table; 7-X axial sinusoidal vibration; 8-Y axial sinusoidal vibration; 9-Z axial sinusoidal vibration; 10-spatial motion trajectory; 11-X axial sinusoidal vibration; 12-Y axial sinusoidal vibration; 13-Z axial sinusoidal vibration; 14-a spatial ellipse; 15-a spatial straight line; 16-estimating a system frequency response function; 17-system impedance matrix; 18-an iterative algorithm; 19-drive the spectrum; 20-response spectrum; 21-reference spectrum; 22-error spectrum.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings and specific embodiments.
Fig. 1 is a schematic diagram of a three-dimensional spatial motion trajectory synthesis method. The three-dimensional space motion trajectory synthesis method comprises the following steps: calculating to obtain an X axial amplitude and phase 2, a Y axial amplitude and phase 3 and a Z axial amplitude and phase 4 of the target according to the space attitude of the ideal space motion track and the track shape 1; an iterative algorithm is executed on the vibration controller 5, and control signals are generated according to target amplitude and phase and feedback amplitude and phase of X, Y, Z axial vibration to drive the triaxial vibration table 6 to generate X axial sinusoidal vibration 7, Y axial sinusoidal vibration 8 and Z axial sinusoidal vibration 9; x, Y, Z the sinusoidal vibration in the axial direction will effect a synthesis of the three-dimensional spatial motion profile 10.
Fig. 2, fig. 3 and fig. 4 are schematic diagrams of X, Y, Z axial sinusoidal vibration, a spatial elliptical motion trajectory and a spatial linear motion trajectory respectively. The X-axis sinusoidal vibration 11, the Y-axis sinusoidal vibration 12 and the Z-axis sinusoidal vibration 13 with the same frequency synthesize three-dimensional space motion tracks 10 of three types, namely a space ellipse 14, a space circle and a space straight line 15. Wherein the spatial straight line 15 and the spatial circle correspond to the two cases when the minor axis of the ellipse is zero and the major and minor axes are equal in length. Therefore, the sinusoidal vibration with the same frequency and arbitrary amplitude and phase is synthesized into a three-dimensional elliptical motion track, and the spatial attitude and track shape of the ellipse depend on the amplitude and phase of the vibration of the X, Y, Z axis.
FIG. 5 is a schematic diagram of an orthogonal unit vector. The spatial attitude of the spatial ellipse is described using a set of mutually orthogonal unit vectors [ u, v, w ]:
u＝[u1u2u3]T,v＝[v1v2v3]T,w＝u×v (1) wherein: u is parallel to the major axis of the ellipse, v is parallel to the minor axis of the ellipse, w is perpendicular to the plane of the spatial ellipse, u1、u2、u3Is a coordinate component of the unit vector u, v1、v2、v3Is the coordinate component of the unit vector v. By using λ1And λ2To describe the track shape of the space ellipse when lambda2When it is 0, it corresponds to a spatial straight line locus, when λ1＝λ2Corresponding to a spatial circular trajectory. Then calculating the X-axis amplitude of the target
And phase
Amplitude in the Y-axis direction
And phase
Z-axis amplitude
And phase
Respectively as follows:
fig. 6 is a schematic diagram of an iterative control algorithm. The principle of the iterative algorithm executed on the vibration controller 5 is as follows: exciting the system in advance to obtain a system frequency response function estimation 16, inverting the system frequency response function to obtain a system impedance matrix 17, controlling the target to make the measured response spectrum reach an ideal reference spectrum 21, calculating an error spectrum 22 according to the reference spectrum 21 and the response spectrum 20, and correcting a driving spectrum 19 according to an iterative algorithm 18 of an equation (5):
Dn+1(f)＝Dn(f)+αZ(f)(R(f)-Cn(f)) (5)
in the formula, Dn(f) Driving the spectrum for the nth iteration; dn+1(f) The method comprises the steps of obtaining a driving spectrum for the n +1 th iteration, obtaining a system impedance matrix, obtaining α an iteration gain, wherein the iteration gain is usually selected to be 0 < α < 1 so as to improve the control stability, and repeatedly and iteratively correcting the driving spectrum 19 to enable a response spectrum 20 output by the system to approach a set reference spectrum 21.
The above detailed description is specific to an enabling practical embodiment of the present invention and is not intended to limit the invention in any way. It should be noted that those skilled in the art can make various improvements, modifications or effective implementations without departing from the technical principles of the invention, and the improvements, modifications or effective implementations are all included in the scope of the invention.
Claims (2)
1. A three-dimensional space motion track vibration synthesis method is characterized in that: the method comprises the steps of describing the space attitude and track shape (1) of an ideal space motion track, calculating the X-axis amplitude and phase (2) of a target, calculating the Y-axis amplitude and phase (3) of the target, calculating the Z-axis amplitude and phase (4) of the target, generating a vibration controller (5), a three-axis vibration table (6), generating X-axis sinusoidal vibration (7), generating Y-axis sinusoidal vibration (8), generating Z-axis sinusoidal vibration (9) and synthesizing a three-dimensional space motion track (10);
three-dimensional space motion tracks of three types, namely X-axis sinusoidal vibration (7), Y-axis sinusoidal vibration (8) and Z-axis sinusoidal vibration (9) which are orthogonal to each other, are generated through a three-axis vibration table, and X, Y, Z axial sinusoidal vibrations with any amplitude and phase are synthesized into a space straight line (15), a space circular shape and a space ellipse (14); wherein the spatial straight line (15) and the spatial circle are considered as two special cases of the spatial ellipse (14);
the three-dimensional space motion trajectory synthesis method comprises the following steps: calculating an X-axis amplitude and phase (2), a Y-axis amplitude and phase (3) and a Z-axis amplitude and phase (4) of a target according to the space attitude and the track shape (1) of the ideal space motion track; an iterative algorithm is executed on the vibration controller (5), and a control signal is generated according to the target amplitude and phase and the feedback amplitude and phase of X, Y, Z axial vibration to drive the triaxial vibration table (6) to generate X axial sinusoidal vibration (7), Y axial sinusoidal vibration (8) and Z axial sinusoidal vibration (9); x, Y, Z the axial sinusoidal vibration will realize the synthesis of three-dimensional space motion track (10);
three types of three-dimensional space motion tracks (10) of a space ellipse (14), a space circle and a space straight line (15) are synthesized by X-axis sinusoidal vibration (11), Y-axis sinusoidal vibration (12) and Z-axis sinusoidal vibration (13) with the same frequency; wherein the space straight line (15) and the space circle correspond to two conditions that the minor axis of the ellipse is zero and the lengths of the major axis and the minor axis are equal; therefore, the sinusoidal vibration with the same frequency and any amplitude and phase is synthesized into a three-dimensional elliptical motion track, and the spatial attitude and the track shape of the ellipse depend on the amplitude and the phase of the vibration of the X, Y, Z axis;
the spatial attitude of the spatial ellipse is described using a set of mutually orthogonal unit vectors [ u, v, w ]:
u＝[u1u2u3]T,v＝[v1v2v3]T,w＝u×v (1)
wherein: u is parallel to the major axis of the ellipse, v is parallel to the minor axis of the ellipse, w is perpendicular to the plane of the spatial ellipse, u1、u2、u3Is a coordinate component of the unit vector u, v1、v2、v3Is the coordinate component of the unit vector v; by using λ1And λ2To describe the track shape of the space ellipse when lambda2When it is 0, it corresponds to a spatial straight line locus, when λ1＝λ2Corresponding to a spatial circular track; then calculating the X-axis amplitude of the target
And phase
Amplitude in the Y-axis direction
And phase
Z-axis amplitude
And phase
Respectively as follows:
the principle of executing an iterative algorithm on the vibration controller (5) is as follows: exciting the system in advance to obtain a system frequency response function estimation (16), inverting the system frequency response function to obtain a system impedance matrix (17), controlling the target to make the measured response spectrum reach an ideal reference spectrum (21), calculating an error spectrum (22) according to the reference spectrum (21) and the response spectrum (20), and correcting the driving spectrum (19) according to an iterative algorithm (18) of formula (5):
Dn+1(f)＝Dn(f)+αZ(f)(R(f)-Cn(f)) (5)
in the formula, Dn(f) Driving the spectrum for the nth iteration; dn+1(f) For the n +1 th iteration drive spectrum, Z (f) is the system impedance matrix, α is the iteration gain, usually the iteration gain 0 < α < 1 is selected to improve controlStability; repeatedly and iteratively correcting the drive frequency spectrum (19) to enable the response frequency spectrum (20) output by the system to continuously approach a set reference frequency spectrum (21);
describing the space attitude of the space elliptical motion track through an orthogonal matrix, wherein the first two column vectors of the orthogonal matrix are respectively parallel to the long axis and the short axis of an ellipse, and the third column vector is perpendicular to the plane of the ellipse; the track shape of the spatial motion track is described by the lengths of the major axis and the minor axis.
2. The method for synthesizing the vibration of the motion trail in the three-dimensional space according to claim 1, wherein the method comprises the following steps: calculating the X-axis amplitude and phase (2), the Y-axis amplitude and phase (3) and the Z-axis amplitude and phase (4) of the target according to the attitude and the shape of the space ellipse; the vibration controller (5) repeatedly and iteratively corrects the driving frequency spectrum (19) to enable the feedback response frequency spectrum (20) to reach an ideal reference frequency spectrum (21), and controls the triaxial vibration table (6) to generate X-axis sinusoidal vibration (7), Y-axis sinusoidal vibration (8) and Z-axis sinusoidal vibration (9) with specific amplitude and phase.
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