CN115204016A - Verification method for measurement result of small-size cylinder space vibration mode - Google Patents
Verification method for measurement result of small-size cylinder space vibration mode Download PDFInfo
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- CN115204016A CN115204016A CN202210843155.6A CN202210843155A CN115204016A CN 115204016 A CN115204016 A CN 115204016A CN 202210843155 A CN202210843155 A CN 202210843155A CN 115204016 A CN115204016 A CN 115204016A
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Abstract
The invention relates to a verification method for a space vibration modal measurement result of a small-size cylinder, which particularly realizes verification through a simulation model, and comprises the steps of optimizing the simulation model, namely acquiring an excitation signal and a response signal of the cylinder to be measured, taking the excitation signal as the input of a mathematical model, taking the response signal as the output, setting natural frequency to obtain a model parameter, inputting the model parameter into a physical model, and comparing a frequency response function output by the physical model with an actually measured frequency response function to realize optimization; and then using different excitation signals to perform verification by using the optimized simulation model. According to the method, the physical model of the small-size cylinder space vibration modal measurement is constructed, and the parameters of the physical model are identified in combination with the mathematical model, so that more accurate fitting parameters are obtained, the defect that the damping ratio of the physical model is obtained by experience is overcome, and meanwhile, the simulation model is optimized through the experimental measurement result, and the accuracy of simulation model verification is greatly improved.
Description
Technical Field
The invention relates to the technical field of vibration mode measurement, in particular to a verification method for a small-size cylinder space vibration mode measurement result.
Background
Vibration measurement experiments typically require traditional sensor or accelerometer measurement data as reference values for validating the measurement results or calibrating the system.
However, when the cylinder at the top end part of the micro-device is used, the two measuring points are slightly separated from each other but the two vibration states are far away from each other, so that the accelerometer sensor cannot be used as a standard sensor for vibration measurement; the measured values cannot be verified by conventional methods,
with the progress of science and technology, methods for verifying test results through simulation modeling appear in various fields, but damping ratio in the simulation modeling is generally obtained through experience, and the damping ratio has larger deviation with physical characteristics of a test piece in an actual experiment.
Therefore, it is an urgent problem to be solved by those skilled in the art to provide a reliable verification method for the measurement result of the spatial vibration mode of the small-sized cylinder.
Disclosure of Invention
In view of the above, the present invention provides a method for verifying a measurement result of a spatial vibration mode of a small-sized cylinder,
in order to achieve the purpose, the invention adopts the following technical scheme:
a verification method for a measurement result of a small-size cylinder space vibration mode is characterized by comprising the following steps: verifying through a simulation model, wherein the simulation model comprises a mathematical model and a physical model, and the verifying step comprises the following steps:
s1, collecting an excitation signal and a response signal of vibration data of a cylinder to be detected;
s2, taking the excitation signal as the input of the mathematical model, taking the response signal as the output of the mathematical model, and setting the natural frequency to obtain model parameters;
s3, inputting the model parameters into the physical model, wherein the physical model is used for simulating the vibration of the cylinder to be tested, outputting a simulated frequency response function after inputting the model parameters, comparing the simulated frequency response function with an experimental frequency response function, and optimizing the model parameters according to a comparison result until the simulated frequency response function is matched with the experimental frequency response function to obtain an optimized simulation model;
s4, verifying the measurement result of the spatial vibration mode of the small-size cylinder by using the optimized simulation model;
preferably, the physical model is built in COMSOL software, and the mathematical model is built in SIMULINK;
preferably, the mathematical model comprises three groups of proportional links and two-order oscillation links, each group of proportional links and two-order oscillation links are connected in series, and the three groups of proportional links and the two-order oscillation links are connected in parallel;
preferably, the natural frequency is obtained by performing finite element calculation on the cylinder to be measured through the physical model;
preferably, the model parameters comprise a proportionality coefficient and a damping ratio, the initial value of the damping ratio is defined to be 0-1, and the initial value of the proportionality coefficient is defined to be constantly greater than zero;
preferably, in step S3, the matching comparison result is judged according to a modal confidence criterion, and the modal confidence criterion calculation formula is:
in the formula, phi i And phi j The vibration mode vector is obtained by experiments and simulation.
According to the technical scheme, compared with the prior art, the verification method for the space vibration modal measurement result of the small-size cylinder is disclosed, the physical model for the space vibration modal measurement of the small-size cylinder is constructed, the parameters of the physical model are identified by combining a mathematical model, the fitted parameters are more accurate, the defect that the damping ratio of the physical model is obtained by experience is overcome, meanwhile, the test and the simulation are combined, the simulation model is optimized through the test measurement result, and the verification accuracy of the simulation model is greatly improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a diagram of a mathematical model provided by the present invention;
FIG. 2 is a graph illustrating the initial setting of the damping ratio and scaling factor provided by the present invention;
FIG. 3 is a diagram of a finite element simulation model of a physical model according to the present invention;
FIG. 4 is a drawing showing the position of a specimen irradiated by a vibration meter according to the present invention;
fig. 5 is a flow chart of frequency response function calculation provided by the present invention.
FIG. 6 is a flow chart illustrating parameter identification provided by the present invention;
FIG. 7 is a schematic diagram of the relative position of a vibration meter and a test piece according to the present invention;
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the invention discloses a method for verifying a measurement result of a small-size cylinder in a space vibration mode, which is verified by a simulation model, wherein the simulation model comprises a mathematical model and a physical model, and comprises the following steps:
s1, collecting an excitation signal and a response signal of vibration of a cylinder to be detected;
s2, taking the excitation signal as the input of the mathematical model, taking the response signal as the output of the mathematical model, and setting the natural frequency to obtain model parameters;
s3, inputting the model parameters into the physical model, wherein the physical model is used for simulating the vibration of the cylinder to be tested, outputting a simulated frequency response function after inputting the model parameters, comparing the simulated frequency response function with an experimental frequency response function, and optimizing the model parameters according to a comparison result until the simulated frequency response function is matched with the experimental frequency response function to obtain an optimized simulation model;
s4, verifying the measurement result of the space vibration mode of the small-size cylinder by using the optimized simulation model;
specifically, a physical model is built in COMSOL software, a mathematical model is built in SIMULINK,
for the vibration mode recognition principle, based on the integral structure and working characteristics of the electron gun, the cylinder of the filament main body part of the electron gun can accurately reflect the vibration condition of the whole filament of the electron gun, so the vibration measurement should be focused on the cylinder part of the filament main body of the electron gun,
the modal parameters of the system are obtained by adopting a modal parameter identification method, and the modes of all orders of the system are solved accordingly. The modal parameter identification method is to use actually measured vibration displacement data or frequency response function data and solve modal parameters of the system according to a modal expansion of a frequency response function, then decouple the multi-degree-of-freedom system into a series of single-degree-of-freedom systems in a modal space through coordinate transformation based on a modal analysis method, and transform coordinates in the modal space into actual physical coordinates through coordinate transformation to obtain time domain displacement solutions of the coordinates of the multi-degree-of-freedom system.
Further, a cylindrical test piece is taken as a research object, the cylindrical part of the filament of the electron gun is assumed to be a linear structure, the cylindrical part is discretized into a three-degree-of-freedom linear steady system, and a motion differential equation can be expressed as the following formula:
wherein M, C, K are respectively a mass matrix, a damping matrix and an elastic matrix, F is an external excitation force vector,
the second derivative of x, which is the displacement,
the transfer function can reflect the relation between system input and system output, and is an important basis for identifying system modal parameters in a frequency domain. The transfer function of the system can be obtained by performing Laplace transform on the formula (1):
H(s)＝(s 2 M+sC+K) -1 (2)
s is x after the Laplace transform,
for the linear time invariant system in this study, let the transform factor s = j ω, where s = jw is the corresponding relationship between laplace transform and fourier transform, s is the complex frequency, w frequency is the real number,
the relationship between the transfer function and the modal parameters is obtained as follows:
wherein, ω is r Is the r-th order natural frequency, m, in the vibration mode r Is the quality of the order r mode, ξ r Is the damping ratio of the r-th order r Is the r-th order mode shape.
The frequency response function is the ratio of the output response and the input excitation force of the system structure, and the row and column of the frequency response function matrix contain all modal information of the system. Transforming from the time domain to the frequency domain by a Fast Fourier Transform (FFT) yields the displacement admittance function of the excitation at j and the response at i, which can be expressed as:
if the natural frequencies of the orders of the system are far apart, and the coupling between the modes is weak, when the excitation frequency is close to a certain natural frequency, the order mode is dominant, and the frequency response function at this time can be approximately expressed as:
wherein s is r 、
Is a system pole and satisfies the relation:
system pole information, i.e. frequency and damping information, # ir 、
Is the corresponding feature vector. Meanwhile, the scoreboard:
in the formula, A ijr 、
To leave a r 、
Is the corresponding modal quality.
From the above, any frequency response function contains all the information of the natural frequency and damping of each order modal parameter, and to determine each order modal vector, one row and one column of the displacement admittance function matrix must be measured, i.e. a set of excitation signals and response signals of the system are measured.
Based on the theoretical analysis of the vibration modes, a mathematical model is built in SIMULINK and comprises three groups of proportional links and two-order oscillation links, each group of proportional links and the two-order oscillation links are connected in series, and the three groups of proportional links and the two-order oscillation links are connected in parallel, as shown in figure 1; wherein K is a proportional link, the intermediate link is an oscillation link, and in the formula, dpr is a damping ratio, pi is pi, fn is a natural frequency, and K is a proportional coefficient.
Firstly, the invention adopts a laser vibration meter to collect vibration data of a cylinder to be measured to obtain a group of corresponding excitation signals and response signals,
then, setting the natural frequency of the mathematical model, setting the initial values of the damping ratio and the proportionality coefficient as shown in fig. 2 (parameter setting), defining the range of the damping ratio as 0-1, the proportionality coefficient as being constantly greater than zero, using the collected excitation signal as the input of the mathematical model, using the collected response signal as the output of the mathematical model, and performing parameter identification by using a nonlinear least square method and a Trust-Region-reflecting algorithm, in one embodiment, setting the natural frequency as the theoretical natural frequency of the output of a physical model of the test piece established in COMSOL software, wherein the whole material of the test piece can be stainless steel, the density is 7850, and the young modulus is 200GPa. The whole is based on a physical field control grid, a model after grid division is shown in figure 3, the inherent frequency of a test piece is calculated by a COMSOL simulation model finite element, and the three-order inherent frequencies can be obtained as follows: 66.895Hz,418.5Hz,1168.35Hz;
the Parameter identification adopts a Parameter identification function module in a tool box, namely a Parameter Estimation Toolbox module, to carry out Parameter identification on unknown parameters in the mathematical model, wherein the unknown parameters in the mathematical model comprise a proportionality coefficient and a damping ratio,
inputting the damping ratio obtained by recognition into a COMSOL physical model, setting an input signal the same as that of a vibration test, outputting a simulated vibration mode,
for the vibration test part, since the accelerometer sensor can not be used as a standard sensor for vibration measurement, 3 vibration meters are used for collecting vibration data of the cylinder to be measured, the position of the test piece irradiated by the vibration meters is shown in figure 4,
when the laser doppler vibrometer is used for measuring vibration of a cylindrical test piece, modal parameter identification by directly using measurement data is not accurate. Because the actual vibration displacement is not equal to the data measured by the laser vibrometer, a calculation step needs to be added in the data processing, and the measured data is converted into the actual displacement data of the cylindrical test piece. The calculation method is already applied for: 202010590578.2, entitled: a laser measuring method for the vibration displacement of the tip of the filament of electronic gun in scanning electronic microscope is disclosed.
Then, the response vibration measurement data of the to-be-tested piece is calculated according to the algorithm to obtain an actual displacement signal, then a frequency response function containing vibration modal information of the to-be-tested piece is calculated, and the calculation flow is shown in fig. 5:
in order to reflect the similarity of the signal value itself as a function of the time evolution of the independent variable, the autocorrelation function for the signal x (t) can be expressed as:
in the formula, τ is a time delay amount of an autocorrelation function, autocorrelation analysis is performed on a signal, namely, a signal x (t + τ) obtained after the signal x (t) is delayed by time τ is subjected to convolution calculation on x (t) and x (t + τ), and an obtained result is the autocorrelation function of x (t).
The signal y (t) is shifted by a time tau to obtain y (t + tau), and then the correlation between x (t) and y (t + tau) is calculated. The cross-correlation function can be written as:
the self-power spectrum describes the frequency structure of the signal, and reflects the distribution of vibration energy on each frequency. The definition of the self-power spectral density function is the Fourier transform of the autocorrelation, as follows:
similarly, the cross-power spectral density function is defined as the Fourier transform of the cross-correlation function, as follows:
then, the cross-power spectral density function is divided by the self-power spectral density function to obtain a frequency response function.
Comparing the frequency response function with the frequency response function measured by the vibration experiment, optimizing the model parameters until matching, which is an optimization process, wherein the flow of identifying the parameters is shown in fig. 6, in the process, the matching comparison result is judged by adopting a modal confidence criterion, and the modal confidence criterion calculation formula is as follows:
in the formula, phi i And phi j For the mode shape vectors obtained by the test and simulation,
when the MAC is 1, it represents a match, and when the MAC is 0, it represents a mismatch.
The Parameter Estimation Toolbox module identifies vibration data measured by an experiment to obtain three-order vibration modal parameters, and continuously optimizes the modal parameters until the modal parameters are highly fitted with the experiment result.
In one embodiment, different excitation signals are used, a frequency response function obtained through a vibration test is compared and matched with a frequency response function obtained through simulation, secondary verification of the simulation model is achieved, and if the frequency response functions are not matched, parameters of the simulation model are optimized continuously.
In the test verification process, different excitation signals are input to the vibration test part, in one embodiment, the signal generator is set to generate a sine wave frequency sweep signal with the frequency range of 100 Hz-2000 Hz, the test piece connected with the vibration exciter is excited, the vibration meter 3 measures the excitation signals, and the vibration meter 1 and the vibration meter 2 measure vibration data in a plane, as shown in FIG. 7. Calculating the obtained vibration test frequency response function;
meanwhile, the different excitation signals are set in the simulation model, a simulation frequency response function is output,
and finally, comparing and analyzing the obtained simulation frequency response function with a frequency response function obtained by a vibration experiment test, and verifying an experiment measurement result.
In the comparison analysis, the error of the natural frequency and the peak value of the frequency response function is mainly analyzed, and the additional quality causing the error is searched. Such as: when the natural frequency drifts, the existence of additional mass can be considered, and the large peak error can be considered to introduce additional damping due to poor contact vibration conduction.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (6)
1. A verification method for a measurement result of a small-size cylinder space vibration mode is characterized by comprising the following steps: verifying through a simulation model, wherein the simulation model comprises a mathematical model and a physical model, and the verifying step comprises the following steps:
s1, collecting an excitation signal and a response signal of vibration of a cylinder to be detected;
s2, taking the excitation signal as the input of the mathematical model, taking the response signal as the output of the mathematical model, and setting the natural frequency to obtain model parameters;
s3, inputting the model parameters into the physical model, wherein the physical model is used for simulating the vibration of the cylinder to be tested, outputting a simulated frequency response function after inputting the model parameters, comparing the simulated frequency response function with an experimental frequency response function, and optimizing the model parameters according to a comparison result until the simulated frequency response function is matched with the experimental frequency response function to obtain an optimized simulation model;
and S4, verifying the measurement result of the space vibration mode of the small-size cylinder by using the optimized simulation model.
2. The method for verifying the measurement result of the spatial vibration mode of the small-sized cylinder as claimed in claim 1, wherein the physical model is built in COMSOL software, and the mathematical model is built in SIMULINK.
3. The method according to claim 1, wherein the mathematical model comprises three sets of proportional links and two-order oscillatory links, each set of the proportional links and the second-order oscillatory link is connected in series, and the three sets of the proportional links and the second-order oscillatory link are connected in parallel.
4. A verification method of spatial vibration mode measurement of a small-sized cylinder as claimed in claim 1, wherein said natural frequency is obtained by performing finite element calculation on said cylinder to be measured through said physical model.
5. The method for verifying the measurement result of the spatial vibration mode of the small-size cylinder according to claim 1, wherein the method comprises the following steps: the model parameters comprise a proportionality coefficient and a damping ratio, the initial value of the damping ratio is limited to be 0-1, and the initial value of the proportionality coefficient is limited to be constantly larger than zero.
6. The method for verifying the spatial vibration modal measurement result of the small-sized cylinder according to claim 1, wherein in step S3, the matching comparison result is judged according to a modal confidence criterion, and the modal confidence criterion calculation formula is as follows:
in the formula, phi i And phi j The vibration mode vector is obtained by experiments and simulation.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115982625A (en) * | 2023-01-06 | 2023-04-18 | 哈尔滨工业大学（深圳） | Long-term working mode analysis method and detection method based on prior information |
| CN117470752A (en) * | 2023-12-28 | 2024-01-30 | 广东省有色工业建筑质量检测站有限公司 | Method for detecting prestress grouting content in steel pipe truss body |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115982625A (en) * | 2023-01-06 | 2023-04-18 | 哈尔滨工业大学（深圳） | Long-term working mode analysis method and detection method based on prior information |
| CN115982625B (en) * | 2023-01-06 | 2023-10-03 | 哈尔滨工业大学（深圳） | Priori information-based long-term working mode analysis method and detection method |
| CN117470752A (en) * | 2023-12-28 | 2024-01-30 | 广东省有色工业建筑质量检测站有限公司 | Method for detecting prestress grouting content in steel pipe truss body |
| CN117470752B (en) * | 2023-12-28 | 2024-05-07 | 广东省有色工业建筑质量检测站有限公司 | Method for detecting prestress grouting content in steel pipe truss body |
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