CN103234750A - Constant-depth-tooth bevel gear fault diagnosis method based on modified cepstrum - Google Patents

Abstract

The invention discloses a constant-depth-tooth bevel gear fault diagnosis method based on modified cepstrum and belongs to the technical field of fault diagnosis. The method includes: firstly, measuring a constant-depth-tooth bevel gear box by an acceleration sensor to acquire gear acceleration vibration signals to be analyzed; secondly, introducing the acquired signals to MATLAB (matrix laboratory) to obtain original signals, and subjecting the original signals to Fourier transform and logarithmic transformation to obtain a log power spectrum; thirdly, calculating maximum entropy of the log power spectrum by maximum entropy estimation algorithm; fourthly, drawing a maximum entropy spectrogram (namely a modified cepstrum diagram) of the log power spectrum by MATLAB, and accurately extracting gear fault feature information according to amplitude distribution in the modified cepstrum diagram. The method is an effective fault feature information extraction method, is applicable to fault diagnosis for constant-depth-tooth bevel gears, and is available for quickly and accurately extracting fault feature frequency to finally allow for fault diagnosis on the gears. The method is novel for the fault diagnosis and feature extraction for constant-depth-tooth bevel gears, and is effectively referable for composite fault diagnosis techniques for gears and other rotating machines.

Description

Constant-height tooth bevel gear fault diagnosis method based on improved cepstrum

Technical Field

The invention belongs to the technical field of fault diagnosis, relates to a gear fault diagnosis method, and particularly relates to a constant-height bevel gear fault diagnosis method based on an improved cepstrum method.

Background

Gears, one of the most common transmission means in mechanical devices, transmit motion and power through the continuous meshing of teeth. The constant-height bevel gear is one of two large gear systems of a spiral bevel gear, has the characteristics of stable transmission, high bearing capacity, hard tooth surface scraping technology and the like, is particularly suitable for the fields of high-power and large-torque heavy-load transmission, and is a core transmission component in important fields of heavy high-grade numerical control machines, automobile transmission systems, aerospace equipment and the like. The gear usually works under complex working conditions of heavy load, impact, variable load and the like, phenomena of pitting, gluing, abrasion, even tooth breakage and the like are often generated, and finally the gear is in failure. Whether the running state of the machine is normal or not usually directly affects the performance of the whole machine, if the fault cannot be found and eliminated in time, the whole mechanical equipment is possibly broken down or interrupted, and huge potential safety hazards and huge economic losses can be brought. Therefore, the research on the fault diagnosis technology of the equal-height bevel gear has very important practical significance for ensuring the safety of mechanical equipment, avoiding accidents and huge economic loss and improving the service performance of the equipment by finding and eliminating the fault as soon as possible.

A plurality of scholars and experts at home and abroad carry out wider and intensive research on the gear fault diagnosis technology, obtain better results and provide a plurality of technical schemes and diagnosis methods. For the fault diagnosis of the constant-height bevel gear, available diagnosis information is many and comprises temperature, vibration, noise and the like, but the vibration signal can most directly reflect the state of the gear, and the implementation method is simple and quick, so the characteristic information of the vibration signal is often used as the state of the gear to reflect. However, the vibration signal is generally a nonlinear, non-stationary complex signal, and often contains a large amount of background noise, making the diagnostic task difficult. Accurate diagnosis results can be obtained only by effectively extracting fault characteristic information from the vibration signals. The invention provides a gear fault diagnosis method based on an improved cepstrum method, which can quickly and accurately extract the fault frequency in the faults of the bevel gear with the equal-height teeth. The method provided by the invention can achieve the purposes of gear state monitoring and fault diagnosis, provides a new method for fault diagnosis of the gear, and provides an effective reference for other rotary machinery composite fault diagnosis technologies.

Disclosure of Invention

The invention aims to provide a fault diagnosis method for an equal-height bevel gear based on an improved cepstrum method, which is used for accurately and quickly extracting gear fault characteristics by analyzing and processing vibration signals of the equal-height bevel gear. The invention provides a new method for fault diagnosis and feature extraction of the constant-height bevel gear and provides effective reference for other rotary machine composite fault diagnosis technologies.

The invention is realized by adopting the following technical means:

1. measuring the high-tooth bevel gear box by using an acceleration sensor, and acquiring a gear acceleration vibration signal as a signal to be analyzed;

2. introducing the collected signals to be analyzed into Matlab software to obtain original signals x (t), performing Fourier transform on the original signals to obtain power spectrums G (f) of the original signals, performing logarithmic transform on the power spectrums G (f) to obtain logarithmic power spectrums LG (f), wherein,

G(f)＝|F(x(t))|²

3. calculating the maximum entropy spectrum of the log power spectrum LG (f) by using a maximum entropy spectrum estimation method to obtain an improved cepstrum, and recording the log power spectrum LG (f) as a sequence Y, namely calculating the maximum entropy spectrum of the sequence Y;

3.1. in the signal autoregressive model, the present value of a signal sequence can be considered as a one-step prediction of a linear combination of its past values, i.e.:

$y_k=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{a}_j^{\left(m\right)}{y}_{k-j}+e_k,k=m+1,m+2,...,N$

wherein m is an order number,

predicting error filter coefficients for order m, e_kIs zero mean white noise;

3.2. with y_k-i(i =1,2, 3.... times, m) is multiplied by both sides of the formula 3.1 and the mathematical expectation of both sides is taken, resulting in a mathematical expectation matrix expression:

$\left[\begin{array}{cccccc}R\left(0\right)& R\left(1\right)& \·& \·& \·& R(m-1)\\ R\left(1\right)& R\left(0\right)& \·& \·& \·& R(m-2)\\ \·& \·& & & & \·\\ \·& \·& & & & \·\\ \·& \·& & & & \·\\ R(m-1)& R(m-2)& \·& \·& \·& R\left(0\right)\end{array}\right]\left[\begin{array}{c}{a}_1^{\left(m\right)}\\ a_2^{\left(m\right)}\\ \·\\ \·\\ \·\\ a_m^{\left(m\right)}\end{array}\right]=\left[\begin{array}{c}R\left(1\right)\\ R\left(2\right)\\ \·\\ \·\\ \·\\ R\left(m\right)\end{array}\right]$

wherein,

for a data sequence y_i(i =1, 2...., N).

M order prediction error power P_mCan be expressed as: p_m=E{e_k·y_kWherein E {. is a mathematical expectation.

With y_kMultiplying both sides of the formula in 3.1 and taking the mathematical expectation of both sides yields:

$P_m=R\left(0\right)-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{a}_j^{\left(m\right)}R\left(j\right)$

the formula in simultaneous 3.2 yields:

$\left[\begin{array}{cccccc}R\left(0\right)& R\left(1\right)& \&CenterDot;& \&CenterDot;& \&CenterDot;& R\left(m\right)\\ R\left(1\right)& R\left(0\right)& \&CenterDot;& \&CenterDot;& \&CenterDot;& R(m-1)\\ \&CenterDot;& \&CenterDot;& & & & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & & & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & & & \&CenterDot;\\ R\left(m\right)& R(m-1)& \&CenterDot;& \&CenterDot;& \&CenterDot;& R\left(0\right)\end{array}\right]\left[\begin{array}{c}1\\ -a_1^{\left(m\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ -a_m^{\left(m\right)}\end{array}\right]=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="0"\; label="P\; m"\; filenames="2013101318055100003DEST\_PATH\_IMAGE001.png,2013101318055100003DEST\_PATH\_IMAGE002.png"\; state="\{\{state\}\}">P</figure-callout>}}_m\\ 0\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ 0\end{array}\right]$

3.4. solving the matrix equation in 3.3 yields a recursive formula as follows:

$a_0^{\left(m\right)}=1$

$a_j^{\left(m\right)}=a_j^{(m-1)}-a_m^{\left(m\right)}\&CenterDot;a_{m-j}^{(m-1)},j=\mathrm{1,2},...,m-1$

$a_m^{\left(m\right)}=[\underset{k=1}{\overset{m-1}{\mathrm{\&Sigma;}}}{a}_k^{(m-1)}\&CenterDot;R(m-k)-R\left(m\right)]/P_{m-1}$

$P_m=P_{m-1}\&CenterDot;(1-{\left|a_m^{\left(m\right)}\right|}^2)$

wherein, the initial value is: ${\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="2013101318055100003DEST\_PATH\_IMAGE001.png,2013101318055100003DEST\_PATH\_IMAGE002.png"\; state="\{\{state\}\}">P</figure-callout>}}_0=R\left(0\right)=\frac{1}{N}\underset{j=1}{\overset{\mathrm{<figure-callout\; id="2"\; label="N\; y\; j"\; filenames="995892DEST\_PATH\_IMAGE001.png"\; state="\{\{state\}\}">N</figure-callout>}}{\mathrm{\&Sigma;}}}{y}_j^{}{}_2^{}$

3.5. obtaining m-order prediction error power P by applying successive recursion operation of recursion formula in 3.4_mAnd prediction error filter coefficients of each orderThe maximum entropy of the sequence Y, i.e. the maximum entropy of the log power spectrum LG (f), is calculated by the following formula,

$S\left(\mathrm{\&tau;}\right)=\frac{P_m\&CenterDot;\mathrm{\&Delta;t}}{{|1-\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{a}_i^{\left(m\right)}\&CenterDot;e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="995892DEST\_PATH\_IMAGE001.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;\&tau;i\&Delta;t}}|}^2}$

wherein, Δ t is a sampling time interval;

4. and (3) drawing a maximum entropy spectrogram of the log power spectrum LG (f), namely an improved cepstrum, by adopting Matlab software, and accurately extracting fault characteristic information according to the distribution of the amplitude in the improved cepstrum.

The method is characterized in that a fault diagnosis method for the bevel gear with the equal-height teeth is provided based on a cepstrum and a maximum entropy spectrum estimation theory, and fault characteristics of the bevel gear with the equal-height teeth can be rapidly and accurately extracted through the method, so that the purpose of fault diagnosis of the gear is achieved. The inventive content comprises four parts. In the first part, an acceleration sensor is mainly used for measuring the high-tooth bevel gear box, and a gear acceleration vibration signal is collected to be used as a signal to be analyzed; in the second part, the collected signals are led into Matlab software to obtain original signals x (t), and Fourier transform and logarithmic transform are carried out on the original signals to obtain logarithmic power spectrums; in the third part, the maximum entropy of the log power spectrum is mainly calculated according to a maximum entropy spectrum estimation algorithm; in the fourth part, a maximum entropy spectrogram (namely an improved cepstrum) of a logarithmic power spectrum is drawn by adopting Matlab software, and fault characteristic information is accurately extracted according to the distribution of the amplitude values in the improved cepstrum.

Drawings

FIG. 1 is a flow chart of a gear fault diagnosis method based on an improved cepstrum method

FIG. 2 is a schematic diagram of a signal acquisition system according to the present invention

FIG. 3 illustrates a time domain waveform of a fault signal according to an embodiment of the present invention

FIG. 4 is a spectrum diagram of a fault signal according to an embodiment of the present invention

FIG. 5 improved cepstrum of a fault signal according to an embodiment of the present invention

Detailed Description

The invention will be further clarified by the following description taken in conjunction with the accompanying drawings, which illustrate the method and embodiments of the invention.

The flow chart of the method for diagnosing the faults of the constant-height bevel gear based on the improved cepstrum is shown in figure 1, and the method comprises the following specific implementation steps:

the first step is as follows: measuring the high-tooth bevel gear box by using an acceleration sensor, and acquiring a gear acceleration vibration signal as a signal to be analyzed;

1) arrangement of signal acquisition system and related parameters

Fig. 2 is a schematic diagram of the arrangement structure of the signal acquisition system, which is composed of a gear experiment table, a data acquisition instrument, a notebook computer and the like. As shown in fig. 2, the laboratory bench system mainly comprises three parts, the first part is a three-phase asynchronous motor for providing power for the system; the second part is a power transmission part and is a pair of bevel gear pairs with equal-height teeth, wherein the number of teeth Z1=26 of the gear 1 and the number of teeth Z2=43 of the gear 2; the last part is to provide the load in the system. The gear pair is driven by a motor, a gear 1 is installed on a shaft I (input shaft), a gear 2 is installed on a shaft II (output shaft), and an acceleration sensor is arranged at a bearing cover of the input shaft and used for collecting vibration acceleration signals of the bevel gear with the equal-height teeth. The rotating speed of the middle shaft I (input shaft) in the test is 2240r/min, and the rotating speed, the rotating frequency and the meshing frequency of each shaft can be calculated by various parameters of the gears and a meshing frequency calculation formula as shown in table 1.

TABLE 1 Gear pairing parameters

2) Acquisition of vibration acceleration signals

Before testing, a fault is first simulated on the gear 2, and the simulated fault type is pitting. In the testing process, an ICP type acceleration sensor arranged at the bearing cover of the input shaft is used for collecting a gear pair vibration acceleration signal after a fault occurs and the signal is used as an original signal for fault feature extraction and analysis. And the experimental sampling frequency is 10240Hz, and the gear fault vibration acceleration signals are acquired, wherein the amplitudes of partial vibration signals are shown in the table 2. Fig. 3 is a time domain waveform of a collected fault signal.

TABLE 2 partial experimental data collected

The second step is that: the method comprises the steps of introducing collected signals to be analyzed into Matlab software to obtain original signals x (t), carrying out Fourier transform on the original signals to obtain power spectrums G (f) of the original signals, carrying out logarithmic transformation on the power spectrums G (f) to obtain logarithmic power spectrums LG (f), wherein the power spectrums of gear fault signals are shown in figure 4.

The third step: calculating the maximum entropy of the log power spectrum LG (f) according to a maximum entropy spectrum estimation algorithm;

1) solving the m-order prediction error power P according to the following recursion formula_mAnd prediction error filter coefficients of each order

$a_0^{\left(m\right)}=1$

$a_j^{\left(m\right)}=a_j^{(m-1)}-a_m^{\left(m\right)}\&CenterDot;a_{m-j}^{(m-1)},j=\mathrm{1,2},...,m-1$

$a_m^{\left(m\right)}=[\underset{k=1}{\overset{m-1}{\mathrm{\&Sigma;}}}{a}_k^{(m-1)}\&CenterDot;R(m-k)-R\left(m\right)]/P_{m-1}$

$P_m=P_{m-1}\&CenterDot;(1-{\left|a_m^{\left(m\right)}\right|}^2)$

Wherein, the initial value is: ${\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="2013101318055100003DEST\_PATH\_IMAGE001.png,2013101318055100003DEST\_PATH\_IMAGE002.png"\; state="\{\{state\}\}">P</figure-callout>}}_0=R\left(0\right)=\frac{1}{N}\underset{j=1}{\overset{\mathrm{<figure-callout\; id="2"\; label="N\; y\; j"\; filenames="995892DEST\_PATH\_IMAGE001.png"\; state="\{\{state\}\}">N</figure-callout>}}{\mathrm{\&Sigma;}}}{y}_j^{}{}_2^{}$

2) estimating a calculation formula according to the maximum entropy spectrumAnd calculating to obtain the maximum entropy of the log power spectrum LG (f).

The fourth step: and (3) drawing a maximum entropy spectrogram (namely an improved cepstrum) of a logarithmic power spectrum by adopting Matlab software, and accurately extracting fault characteristic information of the bevel gear with the equal-height teeth according to the distribution of the amplitude in the improved cepstrum.

Fig. 5 is a diagram of a fault signal improvement cepstrum. As can be seen from FIG. 6, the reciprocal frequency τ =0.04297s and the reciprocal harmonic thereof have obvious amplitude, the reciprocal frequency is converted into a frequency value of about 23.27Hz (1/0.04297s), which is close to the frequency of 22.57Hz of the shaft II of the gear experiment table, which indicates that the gear on the shaft II has a fault, so that the signal has modulation, which is consistent with the gear fault mechanism, and the fault characteristic of the bevel gear with the same height is extracted, so that the fault diagnosis of the gear is realized. Therefore, the method can be applied to the fault diagnosis of the bevel gear with the equal-height teeth and can accurately extract the fault frequency.

The analysis of the above examples concluded that: the method can be applied to fault diagnosis of the bevel gear with the equal-height teeth, can quickly and accurately extract fault characteristic information, and finally realizes fault diagnosis of the gear. The method not only provides a new method for fault diagnosis and feature extraction of the constant-height bevel gear, but also provides effective reference for the fault diagnosis technology of the gear and other rotary machinery composite fault diagnosis technologies.

Claims (2)

1. A fault diagnosis method for a constant-height bevel gear based on an improved cepstrum method is characterized by comprising the following steps:

1) measuring the high-tooth bevel gear box by using an acceleration sensor, and acquiring a gear acceleration vibration signal as a signal to be analyzed;

2) introducing the collected signals to be analyzed into Matlab software to obtain original signals x (t), performing Fourier transform on the original signals to obtain power spectrums G (f) of the original signals, performing logarithmic transform on the power spectrums G (f) to obtain logarithmic power spectrums LG (f), wherein,

G(f)＝|F(x(t))|²；

3) calculating the maximum entropy spectrum of the log power spectrum LG (f) by using a maximum entropy spectrum estimation method to obtain an improved cepstrum, and recording the log power spectrum LG (f) as a sequence Y, namely calculating the maximum entropy spectrum of the sequence Y;

4) and (3) drawing a maximum entropy spectrogram of the log power spectrum LG (f), namely an improved cepstrum, by adopting Matlab software, and extracting fault characteristic information according to the distribution of the amplitude in the improved cepstrum.

2. The method for diagnosing faults of constant-height bevel gears based on the modified cepstrum, as claimed in claim 1, wherein the step of calculating the maximum entropy spectrum of the sequence Y of log power spectra LG (f) comprises:

3.1) in the signal autoregressive model, the present value of a signal sequence can be considered as a one-step prediction of a linear combination of its past values, i.e.:

$y_k=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{a}_j^{\left(m\right)}{y}_{k-j}+e_k,k=m+1,m+2,...,N$

wherein m is an order number,

predicting error filter coefficients for order m, e_kIs zero mean white noise;

3.2) with y_k-i(i ═ 1,2,3,.. times, m) by both sides of formula 3.1 and taking the mathematical expectation of both sides, we get the mathematical expectation matrix expression:

$\left[\begin{array}{cccccc}R\left(0\right)& R\left(1\right)& \&CenterDot;& \&CenterDot;& \&CenterDot;& R(m-1)\\ R\left(1\right)& R\left(0\right)& \&CenterDot;& \&CenterDot;& \&CenterDot;& R(m-2)\\ \&CenterDot;& \&CenterDot;& & & & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & & & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & & & \&CenterDot;\\ R(m-1)& R(m-2)& \&CenterDot;& \&CenterDot;& \&CenterDot;& R\left(0\right)\end{array}\right]\left[\begin{array}{c}{a}_1^{\left(m\right)}\\ a_2^{\left(m\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ a_m^{\left(m\right)}\end{array}\right]=\left[\begin{array}{c}R\left(1\right)\\ R\left(2\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ R\left(m\right)\end{array}\right]$

wherein,

for a data sequence y_iAn autocorrelation function of (i ═ 1, 2.., N);

3.3) m order prediction error Power P_mCan be expressed as: p_m＝E{e_k·y_kWhere E {. is a mathematical expectation, in y_kMultiplying both sides of the formula in 3.1 and taking the mathematical expectation of both sides yields:

$P_m=R\left(0\right)-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{a}_j^{\left(m\right)}R\left(j\right)$

simultaneous 3.2) is given by the formula:

$\left[\begin{array}{cccccc}R\left(0\right)& R\left(1\right)& \&CenterDot;& \&CenterDot;& \&CenterDot;& R\left(m\right)\\ R\left(1\right)& R\left(0\right)& \&CenterDot;& \&CenterDot;& \&CenterDot;& R(m-1)\\ \&CenterDot;& \&CenterDot;& & & & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & & & \&CenterDot;\\ \&CenterDot;& \&CenterDot;& & & & \&CenterDot;\\ R\left(m\right)& R(m-1)& \&CenterDot;& \&CenterDot;& \&CenterDot;& R\left(0\right)\end{array}\right]\left[\begin{array}{c}1\\ -a_1^{\left(m\right)}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ -a_m^{\left(m\right)}\end{array}\right]=\left[\begin{array}{c}{P}_m\\ 0\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ 0\end{array}\right]$

3.4) solving the matrix equation in 3.3) to obtain a recursion calculation formula as follows:

$a_0^{\left(m\right)}=1$

$a_j^{\left(m\right)}=a_j^{(m-1)}-a_m^{\left(m\right)}\&CenterDot;a_{m-j}^{(m-1)},j=\mathrm{1,2},...,m-1$

$a_m^{\left(m\right)}=[\underset{k=1}{\overset{m-1}{\mathrm{\&Sigma;}}}{a}_k^{(m-1)}\&CenterDot;R(m-k)-R\left(m\right)]/P_{m-1}$

$P_m=P_{m-1}\&CenterDot;(1-{\left|a_m^{\left(m\right)}\right|}^2)$

wherein, the initial value is: $P_0=R\left(0\right)=\frac{1}{N}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{y}_j^2$

3.5) obtaining the m-order prediction error power P by applying the successive recursion operation of the recursion formula in 3.4)_mAnd prediction error filter coefficients of each order

The maximum entropy of the sequence Y, i.e. the maximum entropy of the log power spectrum LG (f), is calculated by the following formula,

$S\left(\mathrm{\&tau;}\right)=\frac{P_m\&CenterDot;\mathrm{\&Delta;t}}{{|1-\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{a}_i^{\left(m\right)}\&CenterDot;e^{-j2\mathrm{\&pi;\&tau;i\&Delta;t}}|}^2}$

where Δ t is the sampling time interval.

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