TWI382324B - Envelope analysis method for amendment of resonance frequencies with resonance on bases of resonance modes - Google Patents

Description

Method for obtaining accurate resonance frequency by analyzing system resonance mode

The invention relates to a method for obtaining a precise resonance frequency by analyzing a resonance mode of a system, in particular to an envelope signal which uses a vibration spectrum to determine a resonance mode number, obtains a resonance frequency and derives each resonance mode, and then The vibration signal is restored to eliminate the noise of the original vibration signal, and the highest peak frequency is obtained from the restored vibration signal, and the verification is repeated until the resonance frequency values are nearly the same, so that the modal resonances can be accurately estimated. The frequency is the application of the invention.

According to the diagnostic analysis process of the mechanical system components, it can be divided into three stages: data acquisition, signal processing and spectrum analysis. First, the vibration sensor (such as a displacement meter, speed gauge or accelerometer) is used to convert the physical quantity of the vibration into a voltage form, and then the voltage is moderately amplified by the amplifier, and the voltage is input into the computer through the analog-to-digital conversion interface to perform digital signal. Processing, finally taking the vibration spectrum to present the frequency characteristics of the vibration signal, and determining the damage of the mechanical system components via the frequency distribution and pattern of the spectrum.

The damage of the mechanical system components will cause the system to operate with percussion vibration, and since most of the moving components in the mechanical system belong to the rotating components, if such components are damaged, periodic tapping will occur, thus diagnosing the operation of the mechanical components. It is to detect the occurrence of this periodic vibration signal. However, due to the considerable amount of noise in the mechanical system vibration signal, if the component damage is slight, the vibration signal energy generated is small, so it will be hidden by the noise and it is difficult to detect, only when serious damage occurs. The vibration signal energy generated by it becomes larger, and is significantly larger than the noise vibration energy. Quantity, but since the component damage has become severe at this time, the mechanical system may cause serious malfunctions to stop operation at any time. This phenomenon is the difficulty faced by the general spectrum analyzer in analyzing mechanical vibration signals, and it is also a major lack of damage diagnosis and early warning effect in actual application.

Based on the above-mentioned shortcomings, the inventors have previously developed an envelope signal obtained by the system resonance mode, and its application and operation formula, and the application for the invention patent No. 095137475 (in the application) is mainly: An acquisition of an envelope signal by a system resonance mode, wherein a resonance mode number is determined by a vibration spectrum of a mechanical system vibration signal, and a resonance frequency of each resonance mode is obtained, and the vibration signal is approximated by a stepwise function. The envelope signal, the vibration signal can be mapped to the trigonometric function base established by the resonance frequency, and then the linear least squares estimation method is used to obtain the mapping coefficient pair, and the obtained coefficient pair The square root opening number can obtain the envelope signal of the mechanical vibration signal in each resonance mode.

The result obtained above is an envelope signal of a vibration signal, and the exponential decay function is obtained by dividing the envelope signal by the maximum value of the tapping period, and then taking a linear function by taking the exponential decay function as a natural logarithm. The slope of the linear function can be used to find the exponential decay constant of the mechanical system. Then the exponential decay constant is divided by its resonant frequency to obtain the damping parameter of the mechanical system, and the exponential decay constant is divided by its resonant frequency to obtain the mechanical system. Damping parameters.

The acquisition of the envelope signal is the operation of the damping parameter applied to the mechanical system. Now the inventor has developed a process to analyze the resonance mode of the system to remove noise and the process of development and experiment. The method of obtaining the precise resonance frequency and its calculation formula to confirm the set Whether the modal number is correct.

The invention relates to a method for obtaining a precise resonance frequency by analyzing a resonance mode of a system, which determines a resonance mode number from a vibration spectrum, and respectively sets an initial resonance frequency to any one of its modal frequencies, that is, The resonant frequency of each resonant mode, and approximating the envelope signal of the vibration signal by a step function, the vibration signal can be mapped onto the trigonometric function base established by the resonant frequency, and then obtained by the linear least squares estimation method. The pair of mapping coefficients can obtain the envelope signal of the vibration signal in each resonance mode by the squared sum of the obtained coefficient pairs, and the envelope signal is modulated by resonance to restore the vibration signal to reconstruct the modal vibration without noise. Signal, then restore each modal vibration signal to obtain its spectrum separately, and re-select the resonant frequency as the highest peak frequency in its mode; thus, repeat the above steps in sequence until the resonant frequency values approach the same [convergence] , to obtain accurate estimates of the various modal resonance frequencies.

In order to make the technical means of the present invention more complete and clear, please refer to the drawings and drawings, and explain in detail as follows: First, the present invention obtains a precise resonant frequency by analyzing the resonance mode of the system. The method is characterized in that: the resonance mode is determined by the vibration spectrum of the vibration signal of the mechanical system, and the resonance frequency of each resonance mode is obtained, and the initial resonance frequency is respectively set to any peak frequency of the mode thereof, based on Set the resonant frequency, apply the stepwise function to approximate the envelope signal of the vibration signal, then the vibration signal can be mapped to the trigonometric function base established by the resonant frequency, and then linearly minimized The linear least squares estimation method is used to obtain the pair of mapping coefficient coefficients, and the square root of the obtained coefficient pairs is used to obtain the envelope signal of the vibration signal in each resonance mode; The modal envelope signal is brought into the reduction vibration signal to reconstruct the modal vibration signals without noise, and the restored modal vibration signals are respectively used to obtain the spectrum, and the resonance frequency is re-selected as the highest peak in the mode. Frequency; repeat the above steps in sequence until the resonant frequency values approach the same, then the modal resonance frequencies of the accurate estimation can be obtained.

Continued, mathematical mode indicates that the amplitude modulation signal in the machine can be expressed as

Where: L is the number of system vibration modes; md is the number of damages; d _m ( t ) is the pulse indicating damage; q _m ( t ) is the energy factor associated with the tap; a _lm ( t ) is the transfer function of the vibration path; σ _l is an exponential decay constant; f _i is a resonance frequency of the first mode; the vibration signal v (t) of the frequency characteristic of the resonant frequency will appear at the center frequency of the band expand. This phenomenon is the amplitude modulation.

If between two consecutive taps, the vibration signal d _m ( t ) will be completely attenuated, and its exponential decay frequency is smaller than the system resonance frequency. Therefore, in the integral term of the formula (1), q _m ( t ) and a _m ( t ) can be regarded as constants; therefore, the equation (1) can be expressed as And , t' = mod( t , 1 / f _dm ), f _dm is the tap frequency.

Expanding the formula (2) can be rewritten as

Furthermore, in a resonant frequency period, u _m ( t ) q _m ( t ) a _lm ( t ) can be approximated as a constant. Therefore, the vibration signal can be approximated as a step function as

Where i and j are the number of steps and sampling points, respectively versus Then is the step function, q _m ( i ) and a _m ( i ) are the approximate constant values of q _m ( t ) and a _m ( t ) in the i-th step, respectively; To estimate α _l ( i ) and β _l ( i ), the number of sampling points in the i-th step is set to N and N. 2 L , and expressed in a matrix, the following formula among them Calculate the coefficient of equation (5) by linear least squares estimation Accordingly, a first envelope signal corresponding to a first mode of (1) can be obtained of the formula Substituting the following formula, the vibration signal can be restored.

From the restored modal vibration signals, the spectrum is obtained separately, and the resonant frequency is reselected as the highest peak frequency in the modal state; the steps of (6) and (7) are repeated in sequence until the operation is performed. Each of the resonant frequency values approaches the same, thus obtaining an accurately estimated modal resonant frequency.

The following application example is described with reference to the following figure: (a) is a mechanical vibration signal, in which there are three vibration modes, and the first mode has obvious peaks on both sides of 2000 Hz, and the energy is equivalent. The second mode has multiple peaks at 3000~4000Hz, and the energy is also equivalent. Therefore, the two modes cause troubles in determining the resonance frequency. The restored signal spectrum after three times of iteration by the above method is as described. Figure (b), which can be It is proved that this spectrum has a three-mode, and the vibration spectrum of each mode, as shown in the first figure (b), (c), (d), can accurately estimate the resonant frequency of each mode. It is 1785, 3940, 5704 Hz.

The above-mentioned embodiments or the illustrations are not intended to limit the structure or the dimensions of the present invention, and any suitable variations or modifications of the present invention will be apparent to those skilled in the art.

In the above, the original amplitude modulation signal is mapped onto the trigonometric function base established by the system resonance frequency, and the envelope signal is obtained by the linear least square estimation method, corresponding to the envelope signal and the traditional demodulation analysis method. The utility model has the advantages of simple analysis and calculation, and brings the obtained modal envelope signals into the reduction vibration signal to reconstruct the modal vibration signals without noise, and obtains the spectrum from the restored modal vibration signals respectively. And re-select the resonant frequency as the highest peak frequency in its mode; repeat the above steps in sequence until the resonant frequency values approach the same, then the modal resonance frequencies can be accurately estimated.

In summary, the embodiments of the present invention can achieve the expected use efficiency, and the specific structure disclosed therein has not been seen in similar products, nor has it been disclosed before the application, and has completely complied with the provisions of the Patent Law. And the request, the application for the invention of a patent in accordance with the law, please forgive the review, and grant the patent, it is really sensible.

Figure (a): The spectrum of the mechanical vibration signal for the original measurement

Figure (b): Restoring the spectrum of the vibration signal by the envelope signal

Figure (c): Vibration signal spectrum for the first mode

First figure (d): the vibration signal spectrum of the second mode

Figure (e): Vibration signal spectrum for the third mode

Claims (2)

A method for obtaining a precise resonance frequency by analyzing a resonance mode of a system, wherein: a resonance mode number is determined by a vibration spectrum of a mechanical system vibration signal, and a resonance frequency is set as a highest peak frequency in the mode, respectively, as each resonance The initial resonant frequency of the modality is obtained by applying an envelope signal analysis method to obtain an envelope signal of the vibration signal in each resonant mode; the obtained envelope signal is reconstructed by resonance to reconstruct the noise removing signal, and then The reconstruction removes the modal vibration signals of the noise to obtain the spectrum thereof, and can re-select the resonance frequency as the highest peak frequency in the modal state; then repeat the above analysis envelope signal and reconstruct the noise removal signal. Steps such as reselecting the resonant frequency until the resonant frequency values approach the same, then the modal resonance frequencies of the accurate estimation can be obtained. The method for obtaining a precise resonance frequency by analyzing a system resonance mode according to the first aspect of the patent application, wherein the envelope signal analysis method uses a stepwise function to approximate an envelope signal of the vibration signal. Then, the vibration signal can be mapped to the trigonometric function base established by the resonance frequency, and then the linear least squares estimation method is used to obtain the mapping coefficient coefficient pair, and the obtained coefficient pairs are squared and rooted. An envelope signal of the vibration signal in each resonance mode can be obtained.