TWI382171B - Method for analyzing vibrations of mechanism system by exponential decay frequencies - Google Patents

Description

Method for analyzing mechanical system vibration by exponential decay

The invention relates to a method for analyzing vibration of a mechanical system by exponential decay, in particular to an exponential decay constant obtained by using an envelope signal, and displaying a damaged bearing state, thereby effectively applying the mechanical damage to the diagnostic analysis method of the exponential decay. The inventor of the diagnostic analysis.

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 the vibration signal becomes larger and more obvious than the noise vibration energy, but since the component damage has become serious at this time, the mechanical system may cause serious failure to stop operation at any time. This phenomenon is the difficulty faced by the general spectrum analyzer in analyzing mechanical vibration signals. When using it, it is impossible to exert a major lack of damage diagnosis and warning effect.

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 is approximated by a stepwise function. The envelope signal of the signal, the vibration signal can be mapped to the trigonometric function base established by the resonant frequency, and then the linear least squares estimation method is used to obtain the mapping coefficient pair. The square of the coefficient pair and the 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 envelope signal is divided by the maximum value of the tapping period to obtain an exponential decay function, and then the exponential decay function is taken as a natural logarithm to obtain a linearity. Function, the slope of the linear function can be used to find the exponential decay constant of the mechanical system, and 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. Damping parameters of the mechanical system.

The acquisition of the envelope signal is the operation of the damping parameter applied to the mechanical system. Now the inventor has developed a method of analyzing the vibration of the mechanical system by exponential decay with the development of technology and the process of research and development. For effective analysis of diagnostic analysis of mechanical damage.

The present invention relates to a method for analyzing vibration of a mechanical system by exponential decay, which is obtained by a vibration signal of a mechanical system to obtain a package of resonance modes. The signal of the envelope signal is obtained by natural logarithm transformation, and the series of tapping signals are represented by a matrix, and then the linear least square analysis is used to obtain the index of the envelope signal. The attenuation constant is applied to the bearing damage analysis result by the above method. It can be shown that the exponential decay constant increases greatly with the modal number in different modes, and the exponential decay constant obtained by the damaged bearing is much larger than the exponential decay constant of the normal bearing. Therefore, the diagnostic analysis method with exponential decay can be effectively applied to diagnostic analysts of mechanical damage.

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 relates to a method for analyzing mechanical system vibration by exponential decay, wherein : The resonance mode number is determined by the vibration spectrum of the mechanical system vibration signal, and the resonance frequency is set as the highest peak frequency in the mode, respectively, as the initial resonance frequency of each resonance mode, and is obtained by applying the envelope signal analysis method. The envelope signal of the vibration signal in each resonance mode is converted into a natural logarithm by the obtained envelope signal, and then expressed in a matrix form, and a series of tapping signals are analyzed, and then the linear least square method is used. The linear least square analysis can obtain the exponential decay constant of the envelope signal. The above method can be applied to the bearing damage analysis result. It can show that the exponential decay constant increases greatly with the modal number in different modes, and the bearing is damaged. The exponential decay constants obtained are much larger than the exponential decay constants of normal bearings; therefore, the diagnostic analysis method of exponential decay Effectively applicable to mechanical damage by the diagnostic analysis.

In accordance with the above-described manner, a preferred embodiment of the series is illustrated and illustrated in a mathematical mode; and the acquisition of the envelope signal can be obtained in various feasible ways, and the envelope signal obtained as follows is obtained. For the other way, it is as follows: 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 _1m ( t ) is the transfer function of the vibration path; [sigma] ₁ is an exponential decay constant; f _l is a resonance frequency of the first die; the vibration signal v (t) will exhibit a frequency characteristic of the resonant frequency as 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 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 If the expression of the above formula is simplified, it can be expressed as Calculate the coefficient of the above formula by linear least squares estimation Accordingly, a first envelope signal corresponding to a first mode of (1) can be obtained of the formula

Corresponding to this envelope signal and the traditional demodulation analysis method has the advantage of simple analysis and calculation, and the envelope signal is only one of the ways. Please refer to the first figure for the vibration spectrum of different mechanical modes after the mechanical vibration of the mechanical system. And if the solution of (7) is substituted into (6), the vibration signal can be restored.

The reduction signal of the equation (9) has the noise removal capability compared to the vibration signal of the equation (6). Please refer to the second figure, the low frequency noise on the far left, compare (a) and (b) Low frequency noise can be found in the vibration spectrum of the restored signal Significantly reduced, can be confirmed. The third figure (a) is the original vibration signal, and (b)~(e) are the envelope signals of the first to fourth modes, respectively, which can clearly show the envelope analysis result of (a), and (f) It is a vibration signal that is reduced after the four modes of (b)~(e) are synthesized, and is also apparently similar to the height of (a) the original vibration. In addition, the resulting envelope spectrum has a better ability to highlight the characteristic frequency, and the fourth and fifth figures can be verified.

In the spectrum of the system vibration signal, the vibration signal utilizes the lack of low-frequency mechanical noise, and the impact of the change on the envelope signal is a shocking frequency and a high-exponential attenuation frequency. On the contrary, the index of the envelope signal is blocked. The frequency of the normal bearing will be reduced, and correspondingly, the bearing damage can be diagnosed and analyzed according to the exponential decay of the envelope signal. A study to analyze the vibration of a mechanical system by exponential decay is as follows: Assume that between two consecutive taps, the vibration signal in equation (1) will be completely attenuated, and the frequency of q _m ( t ) a _lm ( t ) is much lower. At the frequency of u _m ( t ), the magnitude of q _m ( t ) a _lm ( t ) can be approximated as constant in any tapping cycle, so the tapping period Δ t is obtained by equation (8). The first mode the envelope signal can be expressed as

If the envelope signal of the above formula has a k-sampling point during any tapping period, the above formula can be written in a matrix after natural logarithmic transformation. Its simplified form can be expressed as The analysis of a series of tapping signals is solved by linear least square analysis.

Thus, the first mode of the signal envelope exponential decay constant σ _l can be obtained, followed by the practical applications is the average value of 20 is obtained to represent the exponential decay constant of the system. The results of applying the above method to bearing damage analysis are shown in Tables 1 and 2:

Table 1 shows the analysis results at 800 rpm. It shows that the exponential decay constant increases greatly with the modal number in different modes, and the exponential decay constant obtained by the damaged bearing is much larger than the exponential decay constant of the normal bearing.

Table 2 shows the analysis results at 1600 rpm, and also shows the same results as Table 1. Therefore, the diagnostic analysis method of the present invention can be effectively applied to the diagnosis of mechanical damage. Break analysis.

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 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.

The first figure (a): the vibration spectrum of the first mode for decomposing the vibration signal, the first figure (b): the vibration spectrum of the second mode for decomposing the vibration signal, the first picture (c): the vibration of the third mode for decomposing the vibration signal The first spectrum (d) of the spectrum is the vibration spectrum of the fourth mode of the vibration signal. The second picture (a): the spectrum of the original vibration signal (Fig. 2): the first picture (a) to (d) The third model of the vibration signal spectrum of the four modes (a): the original vibration signal, the third picture (b): the first mode of the envelope vibration signal, the third picture (c): the second mode of the envelope vibration signal Figure 3 (d): Envelope vibration signal of the third mode (Fig. 3): Envelope vibration signal of the fourth mode (Fig. 3): 4 (a) to (d) The fourth figure of the reduced vibration signal of the modular synthesis (a): the demodulation spectrum of the first mode of the decomposition vibration signal, the fourth picture (b): the demodulation spectrum of the second mode of the decomposition vibration signal, the fourth picture (c): the decomposition vibration The fourth spectrum of the demodulation spectrum of the third mode of the signal (d): the demodulation spectrum of the fourth mode of the decomposed vibration signal. (fi) (a): the demodulation spectrum of the bandpass 1 kHz to 3 kHz. Figure (b): High-frequency demodulation analysis method for band-passing 3 kHz to 5 kHz demodulation spectrum Figure 5 (c): High-frequency demodulation analysis method for band-passing 6 kHz to 8 kHz demodulation spectrum Figure 5 (d): High-frequency demodulation analysis method for demodulation spectrum of bandpass 8.5kHz~10.5kHz

Claims (4)

A method for analyzing mechanical system vibration by exponential decay, wherein: an envelope signal of each resonant mode is obtained by a mechanical system vibration signal, and the obtained envelope signal is converted by natural logarithm transformation to a matrix The expression represents a series of tapping signals, and then the linear least square analysis solves the exponential decay constant of the envelope signal. The method for analyzing the vibration of a mechanical system by exponential decay as described in the first claim of the patent scope, wherein the resonance mode number can be determined by the vibration spectrum of the mechanical system vibration signal, and the resonance frequency is respectively set as the highest peak frequency in the mode, As the initial resonance frequency of each resonance mode, the envelope signal signal is used to obtain the envelope signal of the vibration signal in each resonance mode. A method for analyzing mechanical system vibration by exponential decay as described in claim 2, wherein the envelope signal analysis method uses a stepwise function to approximate an envelope signal of the vibration 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 can be used to obtain the mapping coefficient coefficient pair, and the squared sum of the obtained coefficient pairs can be obtained. The vibration signal is an envelope signal of each resonant mode. A method for analyzing mechanical system vibration by exponential decay as described in claim 1 of the patent application, wherein one of the above methods for analyzing mechanical system vibration by exponential decay is applied to a diagnostic analyzer for mechanical damage.