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CN108844733B - Gear state monitoring index extraction method based on KL divergence and root mean square value - Google Patents

Gear state monitoring index extraction method based on KL divergence and root mean square value Download PDF

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CN108844733B
CN108844733B CN201810346271.0A CN201810346271A CN108844733B CN 108844733 B CN108844733 B CN 108844733B CN 201810346271 A CN201810346271 A CN 201810346271A CN 108844733 B CN108844733 B CN 108844733B
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divergence
gear
amplitude
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王琇峰
李若松
郭美娜
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Suzhou Veizu Equipment Diagnosis Technology Co ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/02—Gearings; Transmission mechanisms
    • G01M13/021—Gearings
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
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Abstract

A gear state monitoring index extraction method based on KL divergence and root mean square value is characterized in that key phase information is used for removing influence of rotation speed fluctuation through angle domain resampling, and a time domain synchronous averaging method is adopted for obtaining a stable modulation signal; then filtering out 1-time meshing frequency and 3-time side frequency by cutoff filtering, determining accurate meshing frequency and side frequency by using amplitude search, increasing the amplitude of the meshing frequency to enable the amplitude to exceed the sum of the amplitudes of the side frequency, solving signal envelope by using Hilbert transform to obtain envelope signals, taking 30 groups of signals, drawing a KL divergence trend graph and a normalized RMS value trend graph, and evaluating the running state of the gear by combining the KL divergence trend and the normalized RMS value trend.

Description

Gear state monitoring index extraction method based on KL divergence and root mean square value
Technical Field
The invention belongs to the technical field of gear state monitoring index extraction, and particularly relates to a gear state monitoring index extraction method based on KL divergence and root mean square values.
Background
The gear transmission system is a universal connecting device and a power transmission device in mechanical equipment and is applied to various fields. The gear has an extremely complex machining process and high assembly precision, and often works in a high-speed or heavy-load working environment, so that the failure rate of the gear is high, which is one of important reasons for causing failure or incapability of working of mechanical equipment. Therefore, the gear state monitoring is realized by extracting accurate and effective gear running state indexes, and the gear state monitoring method has important engineering significance.
The gear has defects or faults, or the faults such as shaft bending and the like can cause the abnormal vibration of the gear, the vibration signal mainly shows a modulation behavior, the modulated carrier frequency is the meshing frequency and the frequency multiplication thereof, the modulation signal is the rotating frequency of a fault shaft and the higher harmonic thereof, the fault degree is different, and the modulation degree is different. How to effectively depict the side frequency information and use the side frequency information for monitoring the gear state is a key point and a difficult point of research. The gear fault characteristics are weak, and the signal-to-noise ratio is low. In multi-stage transmission, the low-speed shaft has low rotating speed, the side frequency of the gear is often seriously influenced by noise, the gear state index fluctuation is large when the conventional diagnosis methods are practiced on industrial fields, and the characteristics of early faults such as gear pitting, cracks and the like are not reflected in time. The defects of easy misjudgment and delayed fault alarm exist. Mcfadd proposes a classical time domain synchronous averaging method, can eliminate noise components mixed in signals and natural frequency components of a gear box irrelevant to gear rotation, and improves the signal-to-noise ratio of smooth modulation signals. The KL divergence (Kullback-Leibler divergence) is a relative entropy used for describing the distance between two random distributions, and can effectively measure the difference degree between a signal to be measured and a normal signal. Root Mean Square (RMS) is used to describe the magnitude of the signal energy used to distinguish between gear failure and normal conditions. At present, a gear state monitoring index extraction method combining a time domain synchronous averaging method, KL divergence and a root mean square value does not exist.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a gear state monitoring index extraction method based on KL divergence and a root mean square value, which accurately extracts state information of a specific gear through a vibration acceleration signal and a key phase signal and realizes the state monitoring of the gear according to the trend of the index.
In order to achieve the purpose, the invention adopts the technical scheme that:
a gear state monitoring index extraction method based on KL divergence and root mean square value comprises the following steps:
step 1: sampling an original vibration signal of a gear box by using an acceleration sensor, and sampling an input shaft key phase signal by using a photoelectric sensor;
step 2: carrying out angle domain resampling on the original vibration signal according to the key phase signal in the step 1, and carrying out time domain synchronous averaging on the original vibration signal, wherein the amplitude response function is H1(f) Obtaining a low-noise vibration signal;
and step 3: designing cut-off filter frequency response function H aiming at gear parameter and rotating speed information2(f) And the low-noise vibration signal obtained in the step 2 passes through a cut-off filter frequency response function H2(f) Extracting the meshing frequency and the side frequency thereof to obtain a steady modulation signal;
and 4, step 4: finding out the accurate meshing frequency and the accurate 1-3 times of side frequency in the stable modulation signal obtained in the step 3 through amplitude search, and increasing the amplitude of the meshing frequency to enable the amplitude to be larger than the sum of the 1-3 times of side frequency to obtain a characteristic signal;
and 5: solving the characteristic signal obtained in the step 4 by using Hilbert transform to obtain an envelope signal;
step 6: taking the number N of groups as 30, repeating the steps 2-5 on 30 groups of early-stage acquired data to obtain envelope signals of 30 groups of data, taking the envelope signals as a reference, calculating KL divergence between newly acquired data and each group of reference data to obtain 30 values, taking the minimum value of the KL divergence as a state monitoring index of the acquisition time, and drawing a KL divergence trend graph;
taking the number N of groups as 30, repeating the steps 2-5 on 30 groups of early-collected data, calculating the average value of RMS values of 30 groups of data, taking the average value as a reference, calculating the ratio of newly-collected data to the reference value as a state monitoring index of the collection time, and drawing a normalized RMS value trend graph;
and 7: the gear operating conditions are evaluated in conjunction with the KL divergence trend and the normalized RMS value trend of step 6.
The amplitude response function H of the time domain synchronous average in the step 21(f) The expression is as follows:
Figure BDA0001632048900000031
wherein f is0Representing the rotation frequency of the shaft on which the gear is positioned, and N represents the division of the signal into N sections.
The frequency response function H of the cut-off filter in the step 32(f) The expression is as follows:
Figure BDA0001632048900000032
wherein f isnRepresenting the frequency of engagement.
Selecting the amplitude search meshing frequency in the step 4n-0.1f0,fn+0.1f0]Selecting [ f ] as the side frequency of the inner maximum amplitude as the accurate meshing frequencyn-mf0-0.1f0,fn-mf0+0.1f0]The inner maximum amplitude is taken as an accurate side frequency, wherein the value range of m is { -3, -2, -1,1,2,3 }.
The invention has the beneficial effects that:
removing the influence of rotation speed fluctuation by utilizing key phase information through angle domain resampling, and acquiring a stable modulation signal by adopting a time domain synchronous averaging method; then filtering out 1 time of meshing frequency and 3 times of side frequency by cutoff filtering, determining accurate meshing frequency and side frequency by using amplitude search, increasing the amplitude of the meshing frequency to exceed the sum of the amplitudes of the side frequencies, solving signal envelope by using Hilbert transform, calculating RMS value of a measuring signal and Kullback-Leibler divergence between the measuring signal and a normal signal, and effectively monitoring the state of the gearbox.
According to the invention, the state information of the specific gear is accurately extracted through the vibration acceleration signal and the key phase signal, and the state monitoring of the gear is realized according to the trend of indexes.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a schematic view of an embodiment gearbox drive.
FIG. 3 is a time domain diagram and a frequency domain diagram of an original vibration signal according to an embodiment.
FIG. 4 is a time domain diagram and a frequency spectrum diagram of a low noise vibration signal according to an embodiment.
FIG. 5 is a time domain plot and a frequency domain plot of an early data feature signal according to an embodiment.
FIG. 6 is a time domain plot and a frequency domain plot of a late data signature signal according to an embodiment.
FIG. 7 is a time domain diagram of early data and late data envelopes of an embodiment.
FIG. 8 is a KL divergence trend chart of the full life cycle of the gear according to the embodiment.
FIG. 9 is a graph of normalized RMS value trend for the full life cycle of an embodiment gear.
Detailed Description
The invention is further described in detail by the data of the fatigue total life of the primary axle by combining the attached drawings and the embodiment.
As shown in fig. 1, a method for extracting a gear state monitoring index based on KL divergence and root mean square value includes the following steps:
step 1: sampling the original vibration signal of a normal gearbox through a vibration acceleration sensorNo. 3, normal gear box key phase signal is sampled through photoelectric sensor, and sampling frequency is 5767Hz, and this axle gear box is tertiary transmission, and the structure is as shown in figure 2, and its structural parameter is as follows: the speed n of input shaft is 1352rpm, the first stage is spur gear pair engagement, the number of teeth of driving wheel is z 123, driven wheel number of teeth z 248; the second stage is straight gear pair engagement, the number of teeth of the driving wheel is z324, driven wheel number of teeth z445, percent; the third stage is a straight gear pair engagement with a driving gear tooth number z 522, driven wheel tooth number z 676; extracting monitoring indexes of the second-stage meshing driving wheel, wherein 1 time of meshing frequency is 259Hz, and 1-3 times of side frequency are 226.7Hz, 237.5Hz, 248.2Hz, 269.8Hz, 280.6Hz and 291.4Hz respectively;
step 2: performing angle domain resampling on the original vibration signal according to the key phase signal in the step 1, performing time domain synchronous average processing, and taking 10 average segments to obtain a low-noise vibration signal; the time domain and frequency domain waveforms of a certain original vibration signal are shown in fig. 3, and the time domain and frequency domain waveforms of a low-noise vibration signal are shown in fig. 4;
and step 3: designing cut-off filter frequency response function H aiming at gear parameter and rotating speed information2(f) And the low-noise vibration signal obtained in the step 2 passes through a cut-off filter frequency response function H2(f) Extracting the meshing frequency and the side frequency thereof to obtain a steady modulation signal, wherein the waveform of the early data time domain and the frequency domain of the gearbox is shown in figure 5, and the waveform of the late data time domain and the frequency domain is shown in figure 6;
and 4, step 4: finding the accurate positions of the 1-time meshing frequency and the 1-3 times of side frequency of the gear in the stable modulation signal obtained in the step 3 through amplitude searching, and increasing the amplitude of the meshing frequency to be larger than the sum of the 1-3 times of the side frequency amplitude to obtain a characteristic signal;
and 5: performing hilbert transform on the characteristic signal to solve the characteristic signal envelope obtained in step 4 to obtain an envelope signal, wherein time domain waveforms of the early data envelope signal and the late data envelope signal are shown in fig. 7;
step 6: taking the group number N as 30, repeating the steps 2-5 on 30 groups of early-stage acquired data to obtain envelope signals of 30 groups of data, taking the envelope signals as a reference, calculating the KL divergence of the newly acquired data and each group of reference data to obtain 30 values, taking the minimum value of the KL divergence as a state monitoring index at the acquisition time, and drawing a KL divergence trend graph as shown in FIG. 8;
taking the number of groups N as 30, repeating the steps 2-5 for 30 groups of early-stage collected data, calculating the average value of the RMS values of 30 groups of data, taking the average value as a reference, calculating the ratio of newly collected data to the reference value as a state monitoring index of the collection time, and drawing a normalized RMS value trend graph as shown in FIG. 9;
and 7: and (6) judging the gear state by combining the KL divergence trend and the normalized RMS value trend in the step (6), after 367 groups of data are collected, increasing the KL divergence trend and the normalized RMS value trend, and judging that the gear operation state is reduced and a fault occurs.
The method can effectively identify the gear state, has good stability and is not easy to generate misjudgment.

Claims (4)

1. A gear state monitoring index extraction method based on KL divergence and root mean square value is characterized by comprising the following steps:
step 1: sampling an original vibration signal of a gear box by using an acceleration sensor, and sampling an input shaft key phase signal by using a photoelectric sensor;
step 2: carrying out angle domain resampling on the original vibration signal according to the key phase signal in the step 1, and carrying out time domain synchronous averaging on the original vibration signal, wherein the amplitude response function is H1(f) Wherein f represents frequency, obtaining a low-noise vibration signal;
and step 3: designing cut-off filter frequency response function H aiming at gear parameter and rotating speed information2(f) Wherein f represents frequency, and the low-noise vibration signal obtained in the step 2 is subjected to a frequency response function H by a cut-off filter2(f) Extracting the meshing frequency and the side frequency thereof to obtain a steady modulation signal;
and 4, step 4: finding out the accurate meshing frequency and the accurate 1-3 times of side frequency in the stable modulation signal obtained in the step 3 through amplitude search, and increasing the amplitude of the meshing frequency to enable the amplitude to be larger than the sum of the 1-3 times of side frequency to obtain a characteristic signal;
and 5: solving the characteristic signal envelope obtained in the step 4 by using Hilbert transform to obtain an envelope signal;
step 6: taking the number N of groups as 30, repeating the steps 2-5 on 30 groups of early-stage acquired data to obtain envelope signals of 30 groups of data, taking the envelope signals as a reference, calculating KL divergence between newly acquired data and each group of reference data to obtain 30 values, taking the minimum value of the KL divergence as a state monitoring index of the acquisition time, and drawing a KL divergence trend graph;
taking the number N of groups as 30, repeating the steps 2-5 on 30 groups of early-collected data, calculating the average value of RMS values of 30 groups of data, taking the average value as a reference, calculating the ratio of newly-collected data to the reference value as a state monitoring index of the collection time, and drawing a normalized RMS value trend graph;
and 7: the gear operating conditions are evaluated in conjunction with the KL divergence trend and the normalized RMS value trend of step 6.
2. The method according to claim 1, wherein the method for extracting the gear state monitoring index based on the KL divergence and the RMS value is characterized in that: the amplitude response function H of the time domain synchronous average in the step 21(f) The expression is as follows:
Figure FDA0002358179880000021
wherein f is0Representing the rotation frequency of the shaft on which the gear is positioned, and N represents the division of the signal into N sections.
3. The method according to claim 1, wherein the method for extracting the gear state monitoring index based on the KL divergence and the RMS value is characterized in that: the frequency response function H of the cut-off filter in the step 32(f) The expression is as follows:
Figure FDA0002358179880000022
wherein f is0Representing the rotation frequency of the shaft on which the gear is located, fnRepresenting the frequency of engagement.
4. The method according to claim 1, wherein the method for extracting the gear state monitoring index based on the KL divergence and the RMS value is characterized in that: selecting the amplitude search meshing frequency in the step 4n-0.1f0,fn+0.1f0]Selecting [ f ] as the side frequency of the inner maximum amplitude as the accurate meshing frequencyn-mf0-0.1f0,fn-mf0+0.1f0]The inner maximum amplitude is taken as an accurate side frequency, wherein the value range of m is { -3, -2, -1,1,2,3}, and f0Representing the rotation frequency of the shaft on which the gear is located, fnRepresenting the frequency of engagement.
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CN110044610B (en) * 2019-05-17 2021-09-07 苏州德姆斯信息技术有限公司 Gear fault diagnosis method
CN112098065B (en) * 2020-09-21 2022-08-23 成都卓微科技有限公司 Method for diagnosing equipment running state, storage medium and terminal
CN112857798B (en) * 2021-02-23 2023-03-10 太原理工大学 Multi-shafting mechanical transmission system quality evaluation method and device based on spectrum analysis
CN113465916B (en) * 2021-06-24 2022-06-07 西安交通大学 Gear tooth state evaluation method, device, equipment and medium of planetary gear train
CN113865860A (en) * 2021-08-25 2021-12-31 浙江运达风电股份有限公司 Gear tooth breakage fault diagnosis method based on frequency conversion sideband RMS trend analysis
CN114936444A (en) * 2022-02-25 2022-08-23 核电运行研究(上海)有限公司 Method for estimating residual service life of equipment based on different degradation trends
CN115031959A (en) * 2022-05-26 2022-09-09 上海电气风电集团股份有限公司 Gear fault diagnosis method and system and computer readable storage medium

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