CN109724687B - Method for measuring separation of bending wave and torsional wave in bending-torsion combined vibration of structure - Google Patents
Method for measuring separation of bending wave and torsional wave in bending-torsion combined vibration of structure Download PDFInfo
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Abstract
The invention discloses a method for measuring the separation of bending waves and torsional waves in bending-twisting combined vibration of a structure. Bending-torsion combined vibration often occurs when a structure is subjected to steady-state, transient or random eccentric excitation, and it is very difficult to separately measure the frequency response of bending or torsion vibration when the vibration of the structure is tested. According to the method, two measuring points which are connected with a line and pass through the geometric center of the right section and are symmetrical about the geometric center are selected on the right section of a position to be measured of a measured structure, and a bending vibration response signal and a torsional vibration response signal can be respectively obtained by performing simple addition and subtraction post-processing on displacement response signals measured by the two points, so that the separation of the bending wave and the torsional wave is realized, and the structural bending-torsion combined vibration mode analysis is better performed.
Description
Technical Field
The invention belongs to the field of mechanical vibration measurement, and particularly relates to a method for measuring the separation of bending waves and torsional waves in bending-torsion combined vibration with a symmetrical cross section structure.
Background
Modal analysis is a modern method for researching the dynamic characteristics of a structure, and is the application of a system identification method in the field of engineering vibration. The modes are natural vibration characteristics of the mechanical structure, each having a specific natural frequency, damping ratio and mode shape. The vibration mode is an inherent, integral property of the spring structure. By knowing the main modal characteristics of each order of the structure in a certain section of susceptible frequency domain range through a modal analysis method, the actual vibration response of the structure under the action of various vibration sources outside or inside the frequency domain range can be predicted. Therefore, modal analysis is an important method for structure dynamic design and equipment fault diagnosis.
Bending vibration is the most influential factor in structural vibration, and torsional vibration is the most basic vibration form of shafts. For bending vibrations, which are generally the most influential factors in structural vibrations, it is the first task to analyze the modes of bending when studying structural vibrations. Meanwhile, transient impact and transient process in the aspects of machinery, electricity, power or load and the like can cause transient or continuous fluctuation of transmitted torque, so that the rotary shaft system generates torsional vibration. Torsional stress generated by torsional vibration causes each section of the shafting to be subjected to alternating shear stress, so that fatigue accumulation of shafting materials is caused, and larger noise is caused and the abrasion of parts is accelerated, thereby shortening the service life of the shafting. Cracks and cuts are formed and gradually spread, so that the shaft system is broken and crashed, and the subsequent events are usually destructive and malignant accidents, and the loss is very disastrous. When the structure undergoes bending and twisting combined vibration, it is necessary to analyze the bending vibration and the torsional vibration separately, but few methods are available to separate the vibration responses of the two from the current research. The method of the invention obtains displacement vibration signals (the signals can be transient vibration response signals or steady-state vibration signals) of two points of the structure with the response end symmetrical about the axis by using the sensor, and then obtains the separated bending vibration response signals only containing bending vibration components and the torsional vibration response signals only containing torsional vibration by performing addition and subtraction post-processing. The steady-state signal can directly make a transmission ratio to obtain a frequency response curve, and the transient signal in a short time after the transient signal is selected and separated is subjected to fast FFT conversion, so that the separated bending and torsion frequency response curves can be perfectly made. In the prior art methods in China, more about measurement and research of strain, displacement, pure bending and pure torsion are performed, and basically, the method for separately researching bending vibration and torsion vibration when the structure generates bending-torsion combined vibration is not available. The method has the advantages of novelty and practicability.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method for measuring the separation of bending waves and torsional waves in bending-twisting combined vibration with a symmetrical cross section structure.
The method for measuring the separation of the bending wave and the torsional wave in the bending-torsion combined vibration of the structure comprises the following steps:
1) selecting a right section on a measured structure as a response position to be measured; selecting two measuring points on the right section, wherein the connecting line of the two measuring points passes through the geometric center of the right section; and the distances between the two measuring points and the geometric center are equal;
2) measuring displacement response signals of the two measuring points selected in the step 1) by using a displacement sensor;
3) adding the two measured displacement response signals to obtain a displacement signal of pure bending vibration, and subtracting the two measured displacement response signals to obtain a displacement signal of pure torsional vibration (namely an equivalent torsional angle signal);
4) when the structure is subjected to a steady-state excitation load, the measured signals are processed in the step 3), and the separated displacement signals of the pure bending vibration and the pure torsional vibration are directly used for obtaining a frequency response curve of the bending and the torsion of the structure;
when the structure is subjected to transient eccentric excitation or random excitation load, the measured signals are processed in the step 3), and then a frequency response curve of the separated bending and torsion is obtained by using Fast Fourier Transform (FFT).
Preferably, the right section is a symmetrical section. When the normal section of the measured position is a symmetrical section, the frequency response characteristics of bending vibration and torsional vibration can be obtained by separation, and the actual change conditions of torsion and bending can be measured in real time.
Preferably, existing displacement sensors, either contact (e.g., fiber grating sensing) or non-contact (e.g., eddy current displacement sensor, doppler laser displacement sensor, etc.), can be used as the displacement sensor of the present invention.
Preferably, the measuring points are arranged on the surface of the structure to be measured, and the method does not need to punch holes in the structure to be measured or carry out other operations for damaging the structure to be measured.
In the step 3), as can be seen from the bending vibration, when the connecting line of the two optical fibers is perpendicular to the propagation direction of the bending wave, they have the same displacement amplitude, so the displacement signals measured in S1 and S2 are both signals of the bending vibration with the same magnitude. However, the signals measured at S1 and S2 at the time of torsional vibration are displacement signals of equal magnitude and opposite directions. When the beam vibration includes both bending and torsional vibrations, the signal measured at S1 is "bending vibration displacement + torsional vibration displacement", and the signal measured at S2 is "bending vibration displacement-torsional vibration displacement", the signals measured at S1 and S2 are added to obtain a displacement signal of pure bending vibration, and the signals measured at S1 and S2 are subtracted to obtain a displacement signal of pure torsional vibration.
In the step 4), if the structure is subjected to a steady-state excitation load, the measured signal is subjected to the step 4, and then the separated data is subjected to logarithmic processing directly, so that a frequency response curve of bending and torsion of the structure can be drawn quickly. If the structure is subjected to transient eccentric excitation or random excitation load, the measured signal is subjected to the step 4 and then subjected to Fast Fourier Transform (FFT) to obtain a frequency response curve of separated bending and torsion.
Compared with the prior art, the method has the beneficial effects that:
1) the method disclosed by the invention has the advantages of simple step principle and strong operability, and can effectively separate the bending vibration and the torsional vibration in the structure.
2) The existing experimental measurement technology or method can only singly determine one type of sensor, and only one type of sensor can be used, and has particularity.
Drawings
FIG. 1 is a schematic diagram of the separation of bending and torsional combined vibration bending waves and torsional waves of the present invention: (a) bending and twisting separation principle; (b) a bending vibration characteristic mode; (c) a torsional vibration characteristic mode.
FIG. 2 is a schematic diagram of a simple aluminum shaft structure under eccentric steady state excitation;
FIG. 3 case one (a) structural frequency responses before separation using the method of the present invention; (b) after processing by the inventive method (the solid line is the bending vibration frequency response and the dotted line is the torsional vibration frequency response).
FIG. 4 is an experimental set-up diagram of bending-torsion combined vibration bending and torsion separation in case of two transient vibrations.
Fig. 5 case two FFT comparisons of steady state frequency response and transients after separation: (a) bending a steady-state frequency response curve; (b) twisting a steady-state frequency response curve; (c) bending transient FFT frequency response; (d) and twisting the transient FFT frequency response.
Detailed Description
As shown in fig. 1, when the characteristics of the structural bending vibration and the torsional vibration, i.e., the bending vibration (see fig. 1(b)), are utilized, the two points are measured with the same displacement amplitude when the two points are perpendicular to the propagation direction of the bending wave, so that the displacement signals measured at S1 and S2 are the same magnitude of the bending vibration signal. However, in the case of torsional vibration (see fig. 1(c)), the signals measured at S1 and S2 are displacement signals of equal magnitude and opposite directions in the same manner. When the beam vibration includes a combination of bending and torsional vibrations, the signal measured at S1 is "bending vibration displacement + torsional vibration displacement", and the signal measured at S2 is "bending vibration displacement-torsional vibration displacement", and then the bending and torsional vibration response signals of the structure can be separated by simply adding and subtracting the two signals.
Case one:
as shown in fig. 2, the present embodiment is a finite element simulation case, a pure aluminum shaft is selected as a measured structure, one end of the pure aluminum shaft is fixed, the other end of the pure aluminum shaft excites a stationary sinusoidal force in the vertical direction, two symmetrical points are selected near the fixed end as measurement points, so as to verify the correctness of the method of the present invention, and the process is as follows:
1) a model of the circular axis is built inside the finite element (see fig. 2), the material properties of the aluminum are defined, a fixed boundary is applied at one end, the other end is free, and two points symmetrical about the axis are selected as measuring points.
2) At the other end, a stationary sinusoidal force excitation in the vertical direction is applied to the blue point shown in fig. 2, and the measured displacement signals of the two points are derived after calculation.
3) The frequency response is plotted by taking the logarithm of one group of the obtained displacement response signals to obtain a frequency response shown in fig. 3(a), and it can be seen that the frequency response in fig. 3(a) is relatively disordered and bending or torsion cannot be basically distinguished.
4) The obtained displacement signals are added to obtain signal logarithm curves, the signal logarithm curves are drawn to form a solid line bending vibration frequency response curve in the graph (b) in fig. 3, and the signal logarithm curves are subtracted to form a dotted line torsion vibration frequency response curve in the graph (b) in fig. 3.
Fig. 3 is a schematic diagram of the results, and it can be seen from a comparison of fig. 3 that the information in fig. 3(a) is very confusing, and it is impossible to directly analyze the modal characteristics of the structure of the bending-torsional combined vibration. In fig. 3(b), separate bending and torsional frequency responses are successfully separated by the method of the present invention. By performing characteristic frequency analysis (namely free vibration analysis) on the structure and comparing with the result after separation, the method of the invention is verified to separate the vibration frequency response of bending and pure torsion. The invention proves that the invention is simple and has obvious effect.
Example two
As shown in fig. 4, the present embodiment is a transient experiment for studying phononic crystal bending and twisting combined vibration separation by using a fiber grating sensing system, and includes an innovative set of displacement sensing device for self-demodulation single fiber grating, wherein the displacement sensing device includes a broadband light source, a single fiber sensor, an oscilloscope, a charge amplifier, a phononic crystal made of 6061 pure aluminum beam, a fixed support, a piezoelectric film, some optical circulators, and the like.
Acquiring eccentric excitation signals of the steel balls through a piezoelectric film, and amplifying the eccentric excitation signals through a charge amplifier and then connecting the amplified eccentric excitation signals to an oscilloscope for displaying; obtaining the displacement response of a measuring point by using fiber bragg grating sensing; the electric signals are converted into electric signals through a photodiode, the electric signals are displayed on an oscilloscope, and an excitation signal and a displacement signal containing bending vibration and pure torsional vibration are derived from the oscilloscope. The experimental procedure was as follows:
1) processing a pure aluminum beam phononic crystal, as shown in an experimental device of fig. 4, fixing the pure aluminum beam phononic crystal on a support to form a cantilever phononic crystal beam;
2) piezoelectric films (PVDF) are respectively attached to the upper surface and the lower surface of the tail end of the beam and used for recording the collision load process of the steel ball eccentrically impacting the beam, and two measuring points passing through a geometric center straight line on a positive section of a position to be measured are selected at the position, close to a fixed end, of the surface of the beam and are connected with two single fiber sensors;
3) eccentrically impacting a piezoelectric film at the tail end of the beam by using steel balls, recording an impacted load history signal and transient response signals of measuring points 1 and 2 on an oscilloscope, and archiving;
4) and (3) performing addition and subtraction processing on the obtained transient response signals 1 and 2 to respectively obtain a pure bending transient signal and a pure torsion transient signal, and performing fast Fourier transform on the response 10ms before the obtained bending transient signal and torsion transient signal to obtain a bending frequency response curve and a torsion frequency response curve which are separated and finished, as shown in fig. 5.
5) Meanwhile, an excitation signal measured by the piezoelectric film is led into a finite element analysis model for transient analysis, the model corresponds to an experiment, and the obtained response is subjected to post-processing and fast Fourier transform by the method of the invention to obtain a Finite Element (FEM) calculation part in the figure 5 (b).
While fig. 5(a) and (c) are frequency response curves obtained for pure bending excitation and pure torsion excitation of the beam, respectively, fig. 5(b) and (d) are the separated bending and torsion frequency responses obtained by FFT of the signals obtained by the above steps (including finite element calculations and experiments), it can be seen that the method of the present invention perfectly separates the pure bending vibration signal and the pure torsion vibration signal from the bending-torsion combined vibration. The results of the finite element calculations, which are also perfectly separate and correspond well to the experimental results, are obtained in fig. 5(b) and (d) via step 5. The reliability of the method of the invention is demonstrated.
Claims (2)
1. A method for measuring the separation of bending waves and torsional waves in bending-torsion combined vibration of a structure is characterized by comprising the following steps:
1) selecting a right section on a measured structure as a response position to be measured; selecting two measuring points on the right section, wherein the connecting line of the two measuring points passes through the geometric center of the right section, and the distances between the two measuring points and the geometric center are equal; the measuring points are arranged on the surface of the measured structure;
2) measuring displacement response signals of the two measuring points selected in the step 1) by using a displacement sensor; the displacement sensor is a fiber grating sensor, an eddy current displacement sensor or a Doppler laser displacement sensor;
3) adding the two measured displacement response signals to obtain a displacement signal of pure bending vibration, and subtracting the two measured displacement response signals to obtain a displacement signal of pure torsional vibration, namely an equivalent torsional angle signal;
4) when the structure is subjected to a steady-state excitation load, the measured signals are processed in the step 3), and the separated displacement signals of the pure bending vibration and the pure torsional vibration are directly used for obtaining a frequency response curve of the bending and the torsion of the structure;
when the structure is subjected to transient eccentric excitation or random excitation load, the measured signals are processed in the step 3), and then the separated bending and torsion frequency response curves are obtained by using fast Fourier transform.
2. The method of claim 1, wherein the normal section is a symmetrical section.
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