阅读说明：本技术 用于滚动轴承故障诊断的同步压缩变换阶比分析法 (Synchronous compression transformation order ratio analysis method for fault diagnosis of rolling bearing ) 是由 魏志恒 王文斌 戴源廷 赵俣钧 李玉路 周永志 于 2019-07-29 设计创作，主要内容包括：本发明公开了一种用于滚动轴承故障诊断的同步压缩变换阶比分析法,先利用SST对轴承的变转速振动信号进行分析得到其时频分布,然后提取转频的瞬时频率脊线并对其进行高阶多项式拟合,得到拟合瞬时频率曲线,根据拟合瞬时频率曲线求取鉴相时标,再对原始振动信号进行等角度重采样,获得角域信号,接着对角域信号进行Hilbert包络解调,求其包络阶次谱,通过分析包络阶次谱来判断滚动轴承是否存在故障及其故障类型,给出诊断结果,提出维修建议,从而是保证地铁车辆的正常运行。本发明的同步压缩变换阶比分析法能够将包含在振动信号中的瞬时转频信息精确地提取出来,实现阶比跟踪,无需特定硬件装置,大大简化安装过程,降低故障监测成本。(The invention discloses a synchronous compression transformation order ratio analysis method for fault diagnosis of a rolling bearing, which comprises the steps of firstly analyzing variable-speed vibration signals of the bearing by utilizing SST to obtain time-frequency distribution of the variable-speed vibration signals, then extracting frequency-converted instantaneous frequency ridge lines and carrying out high-order polynomial fitting on the frequency-converted instantaneous frequency ridge lines to obtain a fitted instantaneous frequency curve, solving a phase discrimination time scale according to the fitted instantaneous frequency curve, then carrying out equal-angle resampling on original vibration signals to obtain angle domain signals, then carrying out Hilbert envelope demodulation on the angle domain signals to obtain an envelope order spectrum of the angle domain signals, judging whether the rolling bearing has faults and fault types of the rolling bearing by analyzing the envelope order spectrum, giving diagnosis results and providing maintenance suggestions, thereby ensuring normal operation of subway vehicles. The synchronous compression transformation order ratio analysis method can accurately extract instantaneous frequency conversion information contained in the vibration signal, realizes order ratio tracking, does not need a specific hardware device, greatly simplifies the installation process and reduces the fault monitoring cost.)

1. A synchronous compression transformation order ratio analysis method for fault diagnosis of a rolling bearing is characterized by comprising the following steps:

step 1, carrying out low-pass filtering and down-sampling treatment on the collected vibration signals of the variable rotating speed of the bearing;

step 2, SST time frequency analysis processing is carried out on the processed vibration signal to obtain the time frequency spectrum thereof, the instantaneous frequency in the vibration signal is estimated, and the instantaneous frequency ridge line f of the frequency conversion is extracted_cs(k) Namely the instantaneous frequency of the rotating speed, wherein k is the serial number of a sampling point;

step 3, extracting the ridge line f of the instantaneous frequency_cs(k) Performing high-order polynomial fitting to obtain a fitted instantaneous frequency curve f_i(t)；

Step 4, utilizing the obtained fitting instantaneous frequency curve f_i(T) carrying out interpolation filtering, and calculating to obtain a phase discrimination time scale sequence T_n；

Step 5, according to the phase discrimination time scale sequence T_nCarrying out equal-angle resampling on the original vibration signal to obtain a quasi-steady-state angular domain signal sequence x (T)_n)；

Step 6, diagonal domain signal sequence x (T)_n) Further carrying out Hilbert envelope demodulation, and solving an envelope order spectrum through FFT (fast Fourier transform), so as to realize order ratio analysis on the vibration signal;

and 7, judging whether the rolling bearing has faults and fault types thereof by analyzing the envelope order spectrum, giving a diagnosis result, proposing a maintenance suggestion, and completing the fault diagnosis of the bearing in the subway speed change process.

2. The synchronous compression transform order ratio analysis method of claim 1, wherein in step 1, the cut-off frequency of the low-pass filtering cannot be lower than the maximum value of the conversion frequency.

3. The synchronous compression transformation order ratio analysis method as claimed in claim 1, wherein in step 2, the peak search is used on the time frequency spectrum to obtain the instantaneous frequency ridge line f of the frequency conversion_cs(k)。

4. The synchronous compression transformation order ratio analysis method as claimed in claim 1, wherein in step 3, the instantaneous frequency ridge line f is measured_cs(k) When fitting is carried out, high-order polynomial fitting and spline fitting are adopted in a small range.

5. The synchronous compressive transformation order ratio analysis method of claim 1, wherein in the step 3, a second-order polynomial fitting is adopted, and the fitting equation is as follows:

f_i(t)＝at²+bt+c (1)

assuming ε is the error of the fitting equation, the sum of the squares of ε is:

if so:andfitting coefficients a, b and c can be obtained.

6. The synchronous compressive transformation order ratio analysis of claim 1Method, characterized in that in step 4, a phase discrimination time scale sequence T is calculated_nThe formula used is as follows:

in the formula, N is 1,2,3, N is a sampling time sequence number, and N is a sampling sequence length; delta theta pi/O_max，O_maxIs the maximum theoretical order;

integrating equation (3) yields:

get T₀And (5) further calculating to obtain a phase discrimination time scale sequence T required by equal-angle resampling_n。

7. The synchronous compression transformation order ratio analysis method as claimed in claim 1, wherein in step 5, a phase-detecting time scale sequence T is used_nAccording to the interpolation principle, original data are subjected to equal-angle resampling, and unsteady-state time domain signals are converted into quasi-steady-state angular domain signal sequences x (T)_n)：

In the formula,. DELTA.t_sIs a time domain sampling interval; m Δ t_sIs at T_nA value in the vicinity; h is_sAnd (t) is an interpolation filter.

Technical Field

The invention relates to the technical field of metro vehicles, in particular to a synchronous compression transformation order ratio analysis method for fault diagnosis of a rolling bearing.

Background

The bearing is used as an important part of the subway axle box and plays an important role in the stable operation of the subway. The vibration signal of the rolling bearing during variable-speed operation contains more abundant characteristic information than constant-speed. In recent years, order ratio analysis is increasingly used in variable-speed mechanical fault diagnosis, and the basic principle is to convert an unstable time domain signal into a quasi-stable angular domain signal through equiangular resampling.

At present, the scale analysis technology at home and abroad is divided into three types: hardware-based step ratio tracking using phase detection means, computational step ratio tracking (COT) and estimation of rotating mechanical step ratio tracking based on instantaneous frequency.

Hardware step ratio tracking requires constant angle incremental sampling of vibration signals by phase detection equipment, but since these equipment are not only complex in result and inconvenient to install, but also expensive, certain production cost is increased. The step ratio tracking is calculated by independently acquiring rotating speed signals by using a tachometer, obtaining a phase discrimination time scale through a corresponding interpolation algorithm and realizing equal-angle interval sampling on the basis of software, but for some equipment, the tachometer is inconvenient to install, and when the rotating speed of rotating equipment changes too fast, the obtained rotating speed change information is inaccurate, so that although the step ratio tracking is more convenient than hardware type step ratio tracking, a specific device is not required, and the limitation of the tachometer can not be got rid of. The method for tracking the order ratio of the rotating machinery based on instantaneous frequency estimation comprises the following key steps of extracting instantaneous frequency, wherein the commonly used methods for estimating the instantaneous frequency comprise the following steps: short-time Fourier transform (STFT), Wigner Distribution (WD), Wavelet Transform (WT), and the like. The time-frequency resolution of the STFT is not high, and is susceptible to noise interference, which may affect the extraction of the instantaneous frequency. WD has difficulty extracting instantaneous frequency curves due to the presence of cross terms. WT cannot improve the aggregation of time and frequency, and is easily interfered, and the extracted instantaneous frequency curve has low precision.

Disclosure of Invention

In order to solve the above problems, an object of the present invention is to provide a synchronous compression transformation order ratio analysis method for diagnosing a fault of a rolling bearing, which can effectively extract a frequency conversion in a vibration signal of the bearing, realize order ratio analysis based on instantaneous frequency estimation, and provide a reliable theoretical basis for diagnosing a fault of a metro vehicle during a speed change process.

The invention provides a synchronous compression transformation order ratio analysis method for fault diagnosis of a rolling bearing, which comprises the following steps:

step 1, carrying out low-pass filtering and down-sampling treatment on the collected vibration signals of the variable rotating speed of the bearing;

step 2, SST time frequency analysis processing is carried out on the processed vibration signal to obtain the time frequency spectrum thereof, the instantaneous frequency in the vibration signal is estimated, and the instantaneous frequency ridge line f of the frequency conversion is extracted_cs(k) Namely the instantaneous frequency of the rotating speed, wherein k is the serial number of a sampling point;

step 3, extracting the ridge line f of the instantaneous frequency_cs(k) Performing high-order polynomial fitting to obtain a fitted instantaneous frequency curve f_i(t)；

Step 4, utilizing the obtained fitting instantaneous frequency curve f_i(T) carrying out interpolation filtering, and calculating to obtain a phase discrimination time scale sequence T_n；

Step 5, according to the phase discrimination time scale sequence T_nCarrying out equal-angle resampling on the original vibration signal to obtain a quasi-steady-state angular domain signal sequence x (T)_n)；

Step 6, diagonal domain signal sequence x (T)_n) Further carrying out Hilbert envelope demodulation, and solving an envelope order spectrum through FFT (fast Fourier transform), so as to realize order ratio analysis on the vibration signal;

and 7, judging whether the rolling bearing has faults and fault types thereof by analyzing the envelope order spectrum, giving a diagnosis result, proposing a maintenance suggestion, and completing the fault diagnosis of the bearing in the subway speed change process.

As a further improvement of the present invention, in step 1, the cut-off frequency of the low-pass filtering cannot be lower than the maximum value of the conversion frequency.

As a further improvement of the invention, in the step 2, the peak search is used on the time frequency spectrum to obtain the ridge line f of the instantaneous frequency of the frequency conversion_cs(k)。

As a further improvement of the invention, in the step 3, the ridge line f of the instantaneous frequency_cs(k) When fitting is carried out, high-order polynomial fitting and spline fitting are adopted in a small range.

As a further improvement of the present invention, in step 3, a second-order polynomial fitting is adopted, and a fitting equation is:

f_i(t)＝at²+bt+c (1)

assuming ε is the error of the fitting equation, the sum of the squares of ε is:

if so:andfitting coefficients a, b and c can be obtained.

As a further improvement of the invention, in the step 4, the phase discrimination time scale sequence T is calculated_nThe formula used is as follows:

in the formula, N is 1,2,3, N is a sampling time sequence number, and N is a sampling sequence length; delta theta pi/O_max， O_maxIs the maximum theoretical order;

integrating equation (3) yields:

get T₀When the value is equal to 0, goOne-step calculation is carried out to obtain a phase discrimination time scale sequence T required by equal-angle resampling_n。

As a further improvement of the invention, in the step 5, a phase discrimination time scale sequence T is utilized_nAccording to the interpolation principle, original data are subjected to equal-angle resampling, and unsteady-state time domain signals are converted into quasi-steady-state angular domain signal sequences x (T)_n)：

In the formula,. DELTA.t_sIs a time domain sampling interval; m Δ t_sIs at T_nA value in the vicinity; h is_sAnd (t) is an interpolation filter.

The invention has the beneficial effects that:

the SST order ratio analysis method has good capability centralization, can concentrate the energy in time-frequency distribution on a main frequency curve when performing time-frequency analysis, can accurately extract instantaneous frequency conversion information contained in a vibration signal, and realizes order ratio tracking;

the SST order ratio analysis method of the invention does not need a specific hardware device, breaks the limitation of hardware, greatly simplifies the installation process, reduces the fault monitoring cost, can realize order ratio analysis of the variable-speed vibration signal of the bearing only by analyzing the vibration signal, and completes the fault diagnosis of the bearing.

Drawings

Fig. 1 is a schematic flow chart of a synchronous compression transformation order ratio analysis method for fault diagnosis of a rolling bearing according to an embodiment of the present invention;

FIG. 2 is a schematic diagram of a waveform of a constructed simulated acceleration signal and its frequency spectrum;

FIG. 3 is a schematic diagram of an ideal instantaneous frequency ridge compared to an instantaneous frequency ridge extracted using SST;

FIG. 4 is a schematic diagram comparing a fitted instantaneous frequency curve to an ideal instantaneous frequency curve fitted to the instantaneous frequency ridge extracted from SST of FIG. 3;

FIG. 5 is a graphical representation of the results of SST order ratio analysis of the fitted instantaneous frequency curve of FIG. 4;

FIG. 6 is a schematic diagram of an SQI rotor test bed used in the experiment;

FIG. 7 is a schematic view of the arrangement of the measuring points of the SQI rotor test bed;

FIG. 8 is a schematic diagram of a fault vibration signal of an ER-12K inner ring of a bearing collected when an SQI rotor test bed is started;

FIG. 9 is a schematic diagram illustrating the STFT and SST comparing the instantaneous frequency extraction of the filtered and down-sampled inner ring fault vibration signal;

FIG. 10 is a fitted instantaneous frequency curve obtained by second order polynomial fitting of the instantaneous frequency ridge extracted from SST of FIG. 9;

FIG. 11 is a schematic diagram of the angular domain signal obtained after SST order ratio analysis of the fitted instantaneous frequency curve of FIG. 10;

fig. 12 is a diagram illustrating an envelope of the angular domain signal and an envelope order spectrum thereof obtained by performing Hilbert envelope demodulation on the angular domain signal of fig. 11;

FIG. 13 is a schematic diagram of a fault vibration signal of an ER-12K outer ring of a bearing collected when an SQI rotor test bed is started;

FIG. 14 is a schematic diagram showing the comparison between the instantaneous frequency ridge line extracted by SST of the outer ring fault vibration signal and the actually calculated rotation speed;

FIG. 15 is a fitted instantaneous frequency curve obtained by second order polynomial fitting of the instantaneous frequency ridge extracted from SST of FIG. 14;

FIG. 16 is a schematic diagram of the angular domain signal obtained after SST order ratio analysis of the fitted instantaneous frequency curve of FIG. 15;

fig. 17 is a diagram illustrating an envelope of the angular domain signal and an envelope order spectrum thereof obtained by performing Hilbert envelope demodulation on the angular domain signal of fig. 16.

Detailed Description

The present invention will be described in further detail below with reference to specific embodiments and with reference to the attached drawings.

The synchronous compression transformation order ratio analysis method for fault diagnosis of the rolling bearing comprises the steps of firstly analyzing variable-rotating-speed vibration signals of the bearing by utilizing SST to obtain time-frequency distribution of the variable-rotating-speed vibration signals, then extracting instantaneous frequency ridges of frequency conversion, carrying out high-order polynomial fitting on the instantaneous frequency ridges to obtain a fitted instantaneous frequency curve, obtaining a phase discrimination time scale according to the fitted instantaneous frequency curve, carrying out equal-angle resampling on original vibration signals to obtain angle domain signals, further carrying out Hilbert envelope demodulation on the angle domain signals to obtain an envelope order spectrum of the angle domain signals, judging whether the rolling bearing has faults and fault types of the rolling bearing by analyzing the envelope order spectrum, giving diagnosis results, and giving maintenance suggestions, so that normal operation of subway vehicles is guaranteed.

As shown in fig. 1, the synchronous compression transformation (SST) order ratio analysis method of the present invention specifically includes the following steps:

step 1, low-pass filtering and down-sampling processing are carried out on the collected vibration signals of the variable rotating speed of the bearing.

Due to the interference of high-frequency noise, the rotating speed information is not easy to extract, so that the signal is firstly subjected to low-pass filtering and down-sampling processing. After low-pass filtering processing, high-frequency components in the vibration signals are removed, energy is mainly concentrated in the low-frequency components, the down-sampling also has a noise reduction effect, the analyzed data volume is reduced, and time is saved for extracting the instantaneous frequency ridge line.

Further, in order to ensure the integrity of the speed curve in this interval, the low-pass filter cut-off frequency cannot be lower than the maximum value of the rotational frequency.

Step 2, SST time frequency analysis processing is carried out on the processed vibration signal to obtain a time frequency spectrum thereof, peak value searching is utilized on the time frequency spectrum to estimate the instantaneous frequency in the vibration signal, and the instantaneous frequency ridge line f of frequency conversion is extracted_cs(k) I.e. the instantaneous frequency of the rotation speed, where k is the sample point number.

The order ratio analysis method is based on a synchronous compression transform (SST) method, is based on wavelet transform, utilizes a synchronous compression operator to improve the resolution of a time-frequency ridge line on a time-frequency spectrum, and realizes extraction and reconstruction of instantaneous frequency. With ψ (b) as the mother wavelet function, the continuous wavelet transform of signal x (t) is:

wherein a is a scale factor, b is a translation factor,is the conjugate of ψ (t).

Assuming that the input signal is a single-frequency signal, x (t) ═ a · cos (ab), its fourier transform is x (f), and the fourier transform defining its wavelet function is Ψ (ξ), the wavelet transform and its reduction are:

the derivation of the wavelet transform in the translation direction can result in:

the instantaneous frequency information for the (a, b) position in the wavelet domain is therefore:

on the scale a, W (a, b), regardless of the value, the oscillation characteristic on b points to the initial frequency Ω, so:

according to the defined synchronous compression transform, the wavelet inverse transform:

coefficient of phase difference

Omega containing instantaneous frequency information for (a, b) locations in the wavelet domain_x(a, b) are integrated along the direction of the scale a, and are classified into the frequency domain, wherein omega is omega_xAt the position of (a, b), the synchronous compression transform is defined as:

wherein A (b) { a, W_x(a,b)≠0}。

By the formula, the amplitude of the signal is classified to the position of the time frequency domain, and finally, the time frequency spectrum with high resolution can be obtained.

Step 3, extracting the ridge line f of the instantaneous frequency_cs(k) Performing high-order polynomial fitting to obtain a fitted instantaneous frequency curve f_i(t)。

Further, a method of high-order polynomial fitting and spline fitting may be performed in a small range to achieve more accurate approximation.

A second order polynomial fit is used here. Fitting by using a second-order polynomial, wherein the fitting equation is as follows:

f_i(t)＝at²+bt+c (1)

assuming ε is the error of the fitting equation, the sum of the squares of ε is:

if so:andfitting coefficients a, b and c can be obtained.

Step 4, utilizing the obtained fitting instantaneous frequency curve f_i(T) carrying out interpolation filtering, and calculating to obtain a phase discrimination time scale sequence T_n。

In the calculation of phase discrimination time scale sequence T_nThe formula used is as follows:

in the formula, N is 1,2,3, N is a sampling time sequence number, and N is a sampling sequence length; delta theta pi/O_max， O_maxIs the maximum theoretical order;

integrating equation (3) yields:

taking T in general₀And (5) further calculating to obtain a phase discrimination time scale sequence T required by equal-angle resampling_n。

Step 5, utilizing the phase discrimination time mark sequence T_nAccording to the interpolation principle, original data are subjected to equal-angle resampling, and unsteady-state time domain signals are converted into quasi-steady-state angular domain signal sequences x (T)_n)：

In the formula,. DELTA.t_sIs a time domain sampling interval; m Δ t_sIs at T_nA value in the vicinity; h is_sAnd (t) is an interpolation filter.

Step 6, diagonal domain signal sequence x (T)_n) And further carrying out Hilbert envelope demodulation, and solving an envelope order spectrum through FFT (fast Fourier transform), thereby realizing order ratio analysis on the vibration signal.

And 7, judging whether the rolling bearing has faults and fault types thereof by analyzing the envelope order spectrum, giving a diagnosis result, proposing a maintenance suggestion, and completing the fault diagnosis of the bearing in the subway speed change process.

The simulation verification of the SST order ratio analysis method proposed by the present invention will be described in detail below.

Since the subway vehicle is accelerated to a certain set speed at a constant acceleration after being out of the station, the constant speed operation is maintained, and the acceleration process is usually linear change, an acceleration signal with the linear change of the speed is constructed during simulation verification, and the following formula is shown below:

during simulation: the sampling frequency 2000HZ and the number of sampling points 2000 are set, and white gaussian noise with SNR-8 (signal to noise ratio) is added. As can be seen from the equation (6), there are three components in x (t), and assuming that the first component is the rotation speed variation component, the instantaneous frequency is f₀200t, the instantaneous frequencies of the second and third components are f₁＝2.5f₀、 f₂＝3.5f₀. The order of the three components is 1, 2.5 and 3.5 respectively according to the relation between the order and the frequency conversion.

Fig. 2 is a waveform of a constructed simulated acceleration signal and a frequency spectrum thereof. As can be seen from fig. 2, the amplitude of the signal waveform gradually increases while becoming denser; the frequency in the frequency spectrum has a gradual change phenomenon, and fault characteristic information is difficult to find.

Fig. 3 is a graph showing the comparison of an ideal instantaneous frequency ridge with an instantaneous frequency ridge extracted using SST. As can be seen from fig. 3, at the beginning, due to the fact that x (t) is relatively small in amplitude and is buried by noise, the time-frequency distribution of the instantaneous frequency obtained by SST is not clear, but can reflect the linear variation trend of the frequency. With the increase of the amplitude, the time-frequency ridge line obtained by the SST is clearer and has strong concentration. The instantaneous frequency ridge of the SST extraction speed substantially coincides with the ideal instantaneous frequency ridge.

And fitting the instantaneous frequency ridge extracted by the SST in the graph 3 to obtain a fitted instantaneous frequency curve. FIG. 4 is a graph showing a comparison of a fitted instantaneous frequency curve with an ideal instantaneous frequency curve. As can be seen from fig. 4, the fitted instantaneous frequency curve almost coincides with the ideal instantaneous frequency curve, which shows that the SST can accurately extract the frequency conversion information in the vibration signal.

And performing interpolation filtering on the fitted instantaneous frequency curve in the graph 4 to obtain a phase discrimination time scale sequence, and performing equal-angle resampling on the original vibration signal according to the phase discrimination time scale sequence. The maximum order O needs to be set before equal-angle sampling_maxMaximum order follows Nyqu at 20ist theorem of sampling.

The order of the order analysis corresponds to the frequency, and for a rotating machine, the order refers to the relationship between all frequencies in the vibration signal and the ratio of the frequency to the rotating frequency, and the order of 1 indicates that the frequency is consistent with the rotating speed frequency.

Wherein f is frequency (HZ), l is order, and R is rotational speed (rpm).

Figure 5 is a graph showing the results of SST order ratio analysis performed on the fitted instantaneous frequency curve of figure 4. As can be seen from fig. 5, the angular domain signals after equal angle sampling have relatively uniform distribution on the time axis, and the frequency does not change with time. The order 1.002 in the envelope order spectrum of fig. 5 appears very close to the ideal order 1 and can therefore be considered as frequency-converted information, while the orders 2.516 and 3.518 correspond exactly to the second and third component components in the simulated signal. The SST order ratio analysis method provided by the invention can accurately and effectively convert the unsteady variable-speed signal into the steady angular domain signal and obtain the characteristic order, thereby realizing order ratio analysis.

Experimental verification of the SST scale ratio analysis proposed by the present invention will be detailed below.

As shown in FIG. 6, the SQI rotor test bench is used as an experimental platform during the experiment. As shown in fig. 7, the measuring points of the SQI rotor test stand are arranged as follows: the measuring point 1 is a tachometer, the measuring point 2 is a motor extending end bearing, the measuring point 3 is a bearing near the motor end, and the measuring point 4 is a bearing far away from the motor end. During the experiment, the position of the pre-buried fault bearing is located at the end close to a motor (a measuring point 3 in the drawing), and the model of the bearing is ER-12K. The failure characteristic frequency coefficients of the bearing are shown in table 1, for example: the inner ring fault characteristic frequency is 4.95 × revolution frequency. When the SQI rotor test bed is started, the collected fault vibration signal of the bearing inner ring is shown in figure 8. The characteristic order after the order ratio analysis is 4.95. The speed variation range of the rotor test bed is set to be 0-24.5 Hz, the sampling frequency is 6000Hz, and in order to obtain a good acceleration process, the length of the collected signal is 30000.

TABLE 1 ER-12K bearing failure coefficient

Because of the interference of high-frequency noise, the rotating speed information is not easy to extract, and therefore the inner ring fault vibration signal is firstly subjected to pass filtering and down-sampling treatment. It is verified that the extracted instantaneous frequency is the best when the cut-off frequency of the low-pass filtering is 40Hz and the down-sampling interval is 20 s. Fig. 9 is a comparison diagram of the filtered down-sampled instantaneous frequency extraction of the signal for STFT and SST. As can be seen from the time-frequency distribution diagram of fig. 9, compared with STFT, SST has good concentration, and the transient frequency ridge extracted by SST can better reflect the change details of the transient frequency.

Second order polynomial fitting is performed on the instantaneous frequency ridge extracted by SST, and the obtained fitted instantaneous frequency curve is shown in fig. 10. In fig. 10, the solid line is an actual rotating speed curve, the dotted line is a fitted instantaneous frequency curve, and after comparison, the fitted instantaneous frequency curve can basically reflect the variation trend of the rotating speed, and the fitting effect is good.

And solving a phase discrimination time scale through the fitted instantaneous frequency curve obtained in the step 10, and performing equal-angle resampling on the inner ring fault vibration signal in the step 8 by using an interpolation method. Fig. 11 is an angular domain signal obtained by performing SST order ratio analysis on the fitted instantaneous frequency curve of fig. 10, wherein the abscissa is the number of revolutions, and the ordinate is the amplitude, and the angular domain waveform is observed to find an obvious periodic impact phenomenon. FIG. 12 shows that Hilbert envelope demodulation is performed on the angular domain signal of FIG. 11 to obtain the envelope of the angular domain signal and the envelope order spectrum thereof, and it is found that the orders 1.017, 2.024 and 2.996 in the envelope order spectrum are quite obvious, and the signals are analyzed as the frequency conversion l_r1-3 times of frequency. In addition, orders 4.979, 9.969, 14.95 are also more prominent than inner ring fault signature order l_iAnd the second and third harmonic order thereof are very closeWhile l is also found_r-l_iAnd l_r+l_iThe orders are very close, and obvious bearing inner ring fault characteristics can be determined.

And collecting bearing outer ring fault vibration signals with the same length to continue experimental verification, wherein the collected bearing outer ring fault vibration signals are shown in fig. 13 when the SQI rotor test bed is started. As can be seen from fig. 13, the signal waveform diagram has a relatively obvious impact, but the impact does not appear periodically, so the SST processing is performed on the vibration signal in the acceleration process to extract the rotation speed change information.

Fig. 14 is a schematic diagram showing the comparison between the instantaneous frequency ridge line extracted by SST of the outer ring fault vibration signal and the actually calculated rotating speed. As shown in fig. 14, some fluctuation of the instantaneous frequency ridge of SST extraction was found due to noise interference, and the change of the frequency with time was smoother, but the trend of the frequency change could be reflected.

Fitting the instantaneous frequency ridge extracted from the SST in FIG. 14 to obtain a fitted instantaneous frequency curve as shown in FIG. 15, wherein the solid line is the actual rotating speed variation curve, the dotted line is the fitted instantaneous frequency curve, and the fitting instantaneous frequency curve is basically overlapped with the actual rotating speed variation curve after comparison, so that the fitting effect is proved to be good.

The phase discrimination time scale is obtained by fitting the instantaneous frequency curve obtained in fig. 15, and the outer ring fault vibration signal in fig. 13 is subjected to equal-angle resampling by using an interpolation method. Fig. 16 is an angular domain signal obtained by performing SST order ratio analysis on the fitted instantaneous frequency curve of fig. 15, wherein the abscissa is the number of revolutions, and the ordinate is the amplitude, and it can be seen from observing the angular domain waveform that there is an obvious periodic impact in the angular domain signal, and the angular domain signal substantially conforms to the outer ring fault vibration signal characteristics collected at a constant rotational speed in a general analysis.

Fig. 17 shows that the angular domain signal of fig. 16 is subjected to Hilbert envelope demodulation to obtain an envelope of the angular domain signal and an envelope order spectrum thereof, and an order of 3.036 and 2-5 harmonic orders thereof are found to be substantially consistent with an outer ring fault order of 3.05, so that the angular domain signal can be determined as a bearing outer ring fault feature.

As shown by simulation verification and experimental verification, the SST order ratio analysis method can effectively and accurately extract instantaneous frequency conversion information contained in the vibration signals, and converts unsteady vibration signals into quasi-steady angular domain signals by using the extracted rotating speed change ridge line, so that order ratio analysis is realized, and rolling bearing faults are successfully diagnosed.

The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.