CN114580480A - Fault diagnosis method for spindle box of numerical control high-speed gear milling machine - Google Patents

Fault diagnosis method for spindle box of numerical control high-speed gear milling machine Download PDF

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CN114580480A
CN114580480A CN202210223343.9A CN202210223343A CN114580480A CN 114580480 A CN114580480 A CN 114580480A CN 202210223343 A CN202210223343 A CN 202210223343A CN 114580480 A CN114580480 A CN 114580480A
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洪荣晶
刘海北
张建坤
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Nanjing Tech University
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    • B23Q—DETAILS, COMPONENTS, OR ACCESSORIES FOR MACHINE TOOLS, e.g. ARRANGEMENTS FOR COPYING OR CONTROLLING; MACHINE TOOLS IN GENERAL CHARACTERISED BY THE CONSTRUCTION OF PARTICULAR DETAILS OR COMPONENTS; COMBINATIONS OR ASSOCIATIONS OF METAL-WORKING MACHINES, NOT DIRECTED TO A PARTICULAR RESULT
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Abstract

The invention discloses a fault diagnosis method for a main shaft box of a numerical control high-speed gear milling machine, which comprises the following steps: 1) collecting a vibration signal 2) of a spindle box of the gear milling machine by using a vibration sensor, and setting preset parameters of a sine and cosine optimization algorithm (SCA). 3) And optimizing high and low quality factors of a resonance sparse decomposition method (RBSSD) by using the SCA, wherein the maximum value of the kurtosis value of the low resonance component after resonance sparse decomposition of the original fault vibration signal is an optimization target. 4) And carrying out resonance sparse decomposition on the original fault vibration signal by using the optimized optimal high and low quality factors to obtain high and low resonance components of the vibration signal. 5) And carrying out envelope spectrum analysis on the low resonance component containing the transient impact signal, extracting fault characteristics, and carrying out fault diagnosis on the spindle box. The invention improves the randomness of manually selecting quality factors by the traditional RBSSD method by utilizing the SCA algorithm, separates signals into high resonance components containing background noise and low resonance components containing transient impact signals, and accurately extracts fault characteristics so that the decomposition of the signals is more accurate.

Description

Fault diagnosis method for spindle box of numerical control high-speed gear milling machine
Technical Field
The invention relates to the field of fault diagnosis, in particular to a fault diagnosis method for a spindle box of a machine tool, and particularly relates to a fault diagnosis method for the spindle box of a numerical control high-speed gear milling machine.
Background
The main shaft box of the numerical control gear milling machine is driven by multi-stage gears, and power generated by a main shaft servo motor is transmitted to a main shaft cutter disc through transmission gears and transmission shafts at all stages in the main shaft box, so that the main shaft obtains corresponding rotating speed and direction. The milling cutter runs under severe conditions of high speed, heavy load and the like for a long time, simultaneously, the milling cutter belongs to intermittent dry cutting, and the cutter can generate large impact load and cutting heat during cutting. In the actual machining process of a machine tool, stress deformation of a gear, a shaft, a bearing and the like in a main shaft box occurs sometimes, the development and the operation efficiency of the numerical control gear milling machine are seriously influenced, and vibration signals collected in the running process of the gear milling machine usually contain abundant state information and can be used for fault diagnosis.
Signal processing means have been a common technique for performing fault diagnosis. The signal processing method proposed by Ivan w Selesnick decomposes a complex signal into a high resonance component containing periodic signals and a low resonance component containing transient impulse signals by high and low quality factors, and the accuracy of the decomposition depends on the selection of the quality factors to a large extent. At present, quality factors are mostly selected through human experience, so how to quickly and accurately obtain the optimal quality factors has important significance for improving the accuracy of signal decomposition and subsequent fault characteristic signal extraction.
Disclosure of Invention
The invention aims to provide an accurate and reliable fault diagnosis method for a spindle box of a numerical control high-speed gear milling machine, which is used for processing vibration signals polluted by a large amount of background noise.
In order to achieve the purpose, the invention adopts the technical scheme that: the method for diagnosing the fault of the spindle box of the numerical control high-speed gear milling machine comprises the following steps:
step S1: collecting a vibration signal of a main shaft box of the gear milling machine by using a vibration sensor;
step S2: setting preset parameters of a sine and cosine optimization algorithm (SCA), including a cost function, maximum iteration times and upper and lower variable limits;
step S3: optimizing high and low quality factors of a resonance sparse decomposition method (RBSSD) by using an SCA optimization algorithm with the maximum kurtosis value of the low resonance component after resonance sparse decomposition of the original fault vibration signal as an optimization target;
step S4: carrying out resonance sparse decomposition by using the optimized optimal quality factor to obtain high and low resonance components of the vibration signal;
step S5: and carrying out envelope spectrum analysis on the low resonance component containing the transient impact signal, extracting fault characteristics, and carrying out fault diagnosis on the spindle box.
Further, in step S1: the model of the vibration sensor selects a PCB SN40166 one-way acceleration sensor, and data are acquired through an LMS test.
Further, in step S2: the SCA optimization algorithm is a random optimization algorithm, a plurality of random initial solutions are generated in the algorithm and are fluctuated towards the direction of the optimal solution based on sine and cosine waveforms, different areas in a space are searched by utilizing a plurality of random variables and fitness, local optimization is effectively avoided, and convergence to global optimization is achieved. The method has the advantages of high flexibility, simple principle, easy realization and convenient application to optimization problems in different fields. The specific iterative formula is as follows:
Figure BDA0003538305950000021
Figure BDA0003538305950000022
wherein X is the initial solution, r2Is 0 to 2 piThe number of machines; r is3A random number between 0 and 2; r is4A random number between 0 and 1; a is a constant, typically taken as 2; t is the current iteration number; and T is the maximum iteration number.
Further, in step S3: the kurtosis of the low resonance component is sensitive to the impact signal and can represent the strength of the transient impact signal, and when the kurtosis value is larger, the transient impact component in the low resonance component is stronger, and the extracted fault feature is more obvious.
Kurtosis values are defined as follows:
assuming that the original vibration signal collected is x, kurtosis K is a time domain statistic used to describe the degree of waveform spiking, which is defined as:
Figure BDA0003538305950000023
wherein mu is the mean value of the vibration signal x; σ is the standard deviation of the vibration signal x, E [ (x- μ)4]Is (x-mu)4Is measured.
Further, in step S4: decomposing the vibration signal into high and low resonance components by using a resonance sparse decomposition method, which comprises the following specific steps:
(1) suppose that the original signal x consists of a high-resonance-component signal x1And low resonance component signal x2The method comprises the following steps:
x＝x1+x2,x,x1,x2∈RN
x1and x2Can be respectively composed of two base function libraries S with low correlation1，S2Expressing that resonance sparse decomposition borrows the thought of form component analysis (MCA) of a nonlinear decomposition algorithm in the field of digital image processing, two different redundant dictionaries are selected, a basis function is constructed, nonlinear sparse separation is carried out on high resonance components and low resonance components in target vibration signals, and the objective function can be expressed as:
J(w1,w2)＝||x-S1w1-S2w2||2 2+λ1||w1||1+λ2||w2||2
in the formula, w1And w2Is a signal x1、x2In the library of basis functions S1，S2Matrix of transform coefficients, λ, of down1And λ2Is a regularization parameter.
(2) Deriving a base function library S by a TQWT filter bank1，S2. In TQWT, important parameters are quality factor Q, redundancy γ, and the number of decomposition layers L, where the quality factor Q is defined as:
Figure BDA0003538305950000024
the redundancy gamma represents the oversampling frequency of a multilayer TQWT filter bank, gamma is usually greater than or equal to 3, and filters with different oscillation attributes can be obtained by changing Q and gamma, so that resonance sparse decomposition is realized.
The number of decomposition layers L represents the number of iterations of the dual-channel filter, and for different signals, the maximum value of the number of decomposition layers L is:
Figure BDA0003538305950000025
wherein N is the original signal sampling number, beta is a high-pass scale factor, and alpha is a low-pass scale factor, which is defined as follows:
Figure BDA0003538305950000031
the decomposition and reconstruction filter bank of TWQT is shown in fig. 4.
Low pass sub-band signal v0(n) has a sampling frequency of α fsHigh-pass subband signal v1(n) has a sampling frequency of β fs，fsIs the original sampling frequency of the signal x (n). TWQT utilizes the decomposition and reconstruction filter bank shown in FIG. 4The decomposition and reconstruction of the original signal is carried out in an iterative manner, the filter bank after the iteration of the multi-layer TWQT being shown in fig. 5.
The original signal x is decomposed into a series of high-pass scale sub-bands v after passing through a plurality of layers of TWQT filters1(n) and the low-pass scale sub-band v0(n) of (a). When a high quality factor Q is adoptedHReconstructing the signal, the reconstructed signal of the high-pass sub-band signal is S1(ii) a Using a low quality factor QLReconstructing the signal, wherein the reconstructed signal of the low-pass sub-band signal is S2。
(3) Library of basis functions S1、S2Substituting the objective function of MCA, solving the objective function becomes extremely difficult due to the existence of a norm of irreducible parameters and a plurality of parameters, so that the objective function is solved by iteratively updating a transformation coefficient matrix by adopting a split augmented Lagrange contraction algorithm (SALSA). The definition of SALSA is:
Figure BDA0003538305950000032
Figure BDA0003538305950000033
the iterative formula is as follows:
Figure BDA0003538305950000034
Figure BDA0003538305950000035
d(k+1)＝d(k)-u(k+1)+w(k+1)
wherein k is an iteration number, and the parameter mu is 0.5 lambda.
To obtain w1*，w2Make objective function J (w)1，w2) Minimized to realize separation of high and low resonance components, and high obtained at the timeThe estimates of the low resonance component are:
Figure BDA0003538305950000036
the invention has the beneficial effects that: the invention provides a fault diagnosis method for a spindle box of a numerical control high-speed gear milling machine, which can effectively decompose vibration signals polluted by a large amount of noise, extract fault characteristics, optimize quality factors of the traditional RBSSD by using an SCA optimization algorithm, improve the uncertainty of artificially selecting the quality factors and better extract the fault characteristics of the spindle box of the numerical control high-speed gear milling machine.
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FIG. 1 is a flow chart of the proposed method of the present invention;
FIG. 2 is a diagram of a fault component in a spindle box;
FIG. 3 is a diagram of the raw time domain and frequency spectrum of the signal acquired by the present invention;
FIG. 4 is a TWQT decomposition and reconstruction filter bank of the present invention;
FIG. 5 is a multi-layer TWQT filter bank of the present invention;
FIG. 6 shows the high and low resonance components of the original signal after conventional RBSSD decomposition;
FIG. 7 shows the high and low resonance components of the original signal after SCA-RBSSD decomposition;
FIG. 8 is an envelope spectrum of a low resonance component of an original signal after SCA-RBSSD decomposition;
Detailed Description
The data adopted in the embodiment is actually measured vibration data of a gap eliminating spindle box of a high-speed numerical control gear milling machine of Nanjing industry and large numerical control technology Limited company, the model of a bearing used in the spindle box is NN3016 of NSK company, the number of rolling bodies is 26, the diameter of the rolling body is 10mm, the inner ring of a spindle bearing fails, the bearing load under an idling condition is 0, and the tooth surface of a spindle gear in the box body fails to peel. Data are collected in a workshop, environmental noise is large, and experimental requirements are met. The method comprises the steps of selecting the milling rotation speed under the actual working condition, wherein the rotation speed of a cutter main shaft is 90r/min, the sampling frequency is 800Hz, taking 262144 data points, and obtaining the fault characteristic frequency of a main shaft bearing inner ring through theoretical calculation to be 21.39Hz, the main shaft rotation frequency to be 1.5HZ, and the meshing frequency of the main shaft and an idler shaft gear to be 34.5 HZ.
The invention will be described with reference to fig. 1 to 8, a flowchart of a fault diagnosis method for a main shaft box of a numerical control high-speed gear milling machine according to the embodiment is shown in fig. 1, and a fault component to be implemented is shown in fig. 2, and the method includes the following specific steps:
step S1: collecting a fault main spindle box vibration signal of the gear milling machine by using a vibration sensor;
step S2: setting preset parameters of a sine and cosine optimization algorithm (SCA), including a cost function, maximum iteration times and upper and lower variable limits;
step S3: optimizing high and low quality factors of a resonance sparse decomposition method (RBSSD) by using an SCA optimization algorithm with the maximum kurtosis value of the low resonance component after resonance sparse decomposition of the original fault vibration signal as an optimization target;
step S4: carrying out resonance sparse decomposition by using the optimized optimal quality factor to obtain high and low resonance components of the vibration signal;
step S5: and carrying out envelope spectrum analysis on the low resonance component containing the transient impact signal, extracting fault characteristics, and carrying out fault diagnosis on the spindle box.
As a possible implementation manner, in the step S1, the model of the vibration sensor is selected from a PCB SN40166 unidirectional acceleration sensor, and data is collected through an LMS test.
As a possible implementation manner, in step S2, the preset parameters of the SCA algorithm are:
an objective function: the maximum kurtosis value of the low resonance component;
maximum number of iterations: 500, a step of;
variable upper and lower limits: qLIs 1 to 3; qHIs 3 to 8;
as a possible implementation manner, in step S3, the kurtosis value is sensitive to the impulse signal, and is a parameter capable of reflecting the strength of the transient impulse component in the signal, and the specific calculation steps are as follows:
the original signal acquired by the sensor is x, the time domain diagram and the frequency spectrum of the original signal are shown in fig. 3, and the kurtosis K is calculated:
Figure BDA0003538305950000041
wherein mu is the mean value of the vibration signal x; σ is the standard deviation of the vibration signal x, E [ (x- μ)4]Is (x-mu)4Of the average value of (a). As a possible implementation manner, in step S4, the resonance sparse decomposition specifically includes the following steps:
1) decomposing the original signal x into high-resonance components x1And a low resonance component x2：
x＝x1+x2,x,x1,x2∈RN
x1And x2Can be respectively composed of two base function libraries S with low correlation1，S2Expressing that resonance sparse decomposition borrows the thought of nonlinear decomposition algorithm Morphological Component Analysis (MCA) in the field of digital image processing, selects two different redundant dictionaries, constructs a basis function, and carries out high-resonance component x in an original signal x1And a low resonance component x2Carrying out nonlinear sparse separation, wherein the objective function is as follows:
J(w1,w2)＝||x-S1w1-S2w2||2 2+λ1||w1||1+λ2||w2||2
in the formula, w1And w2Is a signal x1、x2In the library of basis functions S1，S2Matrix of transform coefficients, λ, of down1And λ2For regularization parameters, take λ respectively1And λ2Is 0.5.
2) Deriving a base function library S by a TQWT filter bank1，S2. In TQWT, important parameters include a quality factor Q, a redundancy gamma, and a decomposition layer number L, wherein the quality factor Q of the conventional RBSSD method is taken asH＝3，Q L1, redundancy y 3, in which case K3.54 × 10-5The quality factor Q of the SCA-RBSSD method is obtained by an SCA optimization algorithm, QH＝4.38,QL1.91, redundancy y is 3, and K is 4.00 × 10-5The kurtosis value K is improved.
The redundancy gamma represents the oversampling frequency of a multilayer TQWT filter bank, gamma is usually greater than or equal to 3, and filters with different oscillation attributes can be obtained by changing Q and gamma, so that resonance sparse decomposition is realized.
The number of decomposition layers L represents the number of iterations of the dual-channel filter, and for different signals, the maximum value of the number of decomposition layers L is:
Figure BDA0003538305950000051
where N is the number of samples of the original signal, α is the low-pass scale factor, β is the high-pass scale factor, and its value is:
Figure BDA0003538305950000052
in this embodiment, the number of decomposition layers of the high-Q wavelet transform is taken to be 15, and the number of decomposition layers of the low-Q wavelet transform is taken to be 8.
The decomposition and reconstruction filter bank of TWQT is shown in fig. 4.
Low pass sub-band signal v0(n) has a sampling frequency of α fsHigh-pass subband signal v1(n) has a sampling frequency of β fs，fsIs the original sampling frequency of signal x (n). TWQT performs decomposition and reconstruction of the original signal in an iterative manner using the decomposition and reconstruction filter bank shown in fig. 2, the filter bank after iteration of the multi-layer TWQT being shown in fig. 5.
An original signal x is decomposed into a series of high-pass scale sub-bands v after passing through a plurality of layers of TWQT filters1(n) and the low-pass scale sub-band v0(n) of (a). When a high quality factor Q is adoptedHReconstructing the signal, wherein the reconstructed signal of the high-pass sub-band signal is S1(ii) a By using a lower levelQuality factor QLReconstructing the signal, wherein the reconstructed signal of the low-pass sub-band signal is S2。
3) Library of basis functions S1、S2The objective function substituted into the MCA is extremely difficult to solve due to the immutability of a norm and the existence of a plurality of parameters, so the solution is carried out by iteratively updating a transformation coefficient matrix by adopting a split-augmented Lagrange shrinkage algorithm (SALSA). The SALSA is calculated as follows:
Figure BDA0003538305950000053
Figure BDA0003538305950000054
the iterative formula is as follows:
Figure BDA0003538305950000055
Figure BDA0003538305950000056
d(k+1)＝d(k)-u(k+1)+w(k+1)
wherein k is an iteration number, and the parameter mu is 0.5 lambda.
To obtain w1*，w2Make objective function J (w)1，w2) And minimizing to separate high and low resonance components, wherein the obtained estimated values of the high and low resonance components are respectively as follows:
Figure BDA0003538305950000057
the high-low resonance components obtained after the conventional RBSSD decomposition are shown in fig. 6, and the high-low resonance components obtained after the SCA-RBSSD decomposition are shown in fig. 7.
In a possible implementation manner, in step S5, envelope spectrum analysis is performed on the low resonance component containing the transient impulse signal, so as to extract the fault feature. The envelope spectrums of low resonance components of original signals after being decomposed by a traditional RBSSD method and an SCA-RBSSD are respectively shown in fig. 8, and the fact that although the low resonance component envelope spectrums obtained by the traditional RBSSD method can highlight faults of a main shaft gear, faults of an inner ring of a main shaft bearing still do not highlight, faults of the inner ring of the main shaft bearing can be accurately judged by 20.92HZ highlighted by the low resonance component envelope spectrums obtained by the traditional RBSSD method and a side frequency band which is very close to a main shaft frequency conversion and has a difference value of 1.63HZ, 1 frequency multiplication of the main shaft bearing is very obvious, 3, 4 and 9 frequency multiplication of the main shaft bearing is highlighted, 1, 2, 6 and 10 frequency multiplication of the main shaft gear frequency is also obvious, uncertainty of artificially selected quality factors is effectively improved, and fault characteristics are accurately extracted.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and the preferred embodiments of the present invention are described in the above embodiments and the description, and are not intended to limit the present invention. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (6)

1. A fault diagnosis method for a main shaft box of a numerical control high-speed gear milling machine is characterized by comprising the following steps:
step S1: collecting a vibration signal of a main shaft box of the gear milling machine by using a vibration sensor;
step S2: setting preset parameters of a sine and cosine optimization algorithm (SCA), including a cost function, maximum iteration times and upper and lower variable limits;
step S3: optimizing high and low quality factors of a resonance sparse decomposition method (RBSSD) by using an SCA optimization algorithm with the maximum kurtosis value of the low resonance component after resonance sparse decomposition of the original fault vibration signal as an optimization target;
step S4: carrying out resonance sparse decomposition by using the optimized optimal quality factor to obtain high and low resonance components of the vibration signal;
step S5: and carrying out envelope spectrum analysis on the low resonance component containing the transient impact signal, extracting fault characteristics, and carrying out fault diagnosis on the spindle box.
2. The fault diagnosis method for the spindle box of the gear milling machine according to claim 1, wherein the SCA algorithm in step S2 has the following specific iterative formula:
Figure FDA0003538305940000011
Figure FDA0003538305940000012
wherein X is the initial solution, r2A random number of 0 to 2 pi; r is3A random number between 0 and 2; r is4A random number between 0 and 1; a is a constant, typically taken as 2; t is the current iteration number; and T is the maximum iteration number.
3. The SCA-RBSSD-based fault diagnosis method as claimed in claim 1, wherein the kurtosis value in step S3 is defined as follows:
assuming that the acquired original vibration signal is x, the kurtosis K is a time domain statistic for describing the degree of waveform peak, which is defined as:
Figure FDA0003538305940000013
wherein mu is the mean value of the vibration signal x; σ is the standard deviation of the vibration signal x, E [ (x- μ)4]Is (x-mu)4Is measured.
4. The fault diagnosis method for the spindle box of the numerical control high-speed gear milling machine according to claim 1, wherein the resonance sparse decomposition method in the step S4 comprises the following steps:
(1) suppose that the original vibration signal x is composed of a high-resonance-component signal x1And low resonance component signal x2The method comprises the following steps:
x＝x1+x2,x,x1,x2∈RN
x1and x2Can be respectively composed of two base function libraries S with low correlation1，S2Expressing that resonance sparse decomposition borrows the thought of form component analysis (MCA) of a nonlinear decomposition algorithm in the field of digital image processing, two different redundant dictionaries are selected, a basis function is constructed, nonlinear sparse separation is carried out on high resonance components and low resonance components in target vibration signals, and the objective function can be expressed as:
J(w1,w2)＝||x-S1w1-S2w2||2 2+λ1||w1||1+λ2||w2||2
in the formula, w1And w2Is a signal x1、x2In the library of basis functions S1，S2Matrix of transform coefficients, λ, of down1And λ2Is a regularization parameter.
(2) Deriving a base function library S by a TQWT filter bank1，S2. The original signal x is decomposed into a series of high-pass scale sub-bands v after passing through a plurality of layers of TWQT filters1(n) and the low-pass scale sub-band v0(n) of (a). When a high quality factor Q is adoptedHReconstructing the signal, wherein the reconstructed signal of the high-pass sub-band signal is S1(ii) a Using a low quality factor QLReconstructing the signal, wherein the reconstructed signal of the low-pass sub-band signal is S2。
(3) Library of basis functions S1、S2An objective function substituted into MCA, the objective function being due to a norm and the presence of a plurality of parametersThe solution becomes extremely difficult, so the w is obtained by iteratively updating a transformation coefficient matrix by adopting a Splitting Augmented Lagrange Shrinkage Algorithm (SALSA)1、w2So that the objective function J (w)1，w2) Minimizing to separate high and low resonance components, wherein the corresponding transformation coefficient matrix is w1*，w2The obtained estimated values of the high and low resonance components are respectively:
Figure FDA0003538305940000021
5. the fault diagnosis method for the spindle box of the numerical control high-speed gear milling machine according to claim 1, wherein the TWQT filter bank is defined as follows:
in TQWT, important parameters are quality factor Q, redundancy γ, and the number of decomposition layers L, where quality factor Q is defined as:
Figure FDA0003538305940000022
wherein f iscIs the center frequency of the signal, BwFor bandwidth, the redundancy γ represents the oversampling frequency of the multi-layer TQWT filter bank, and γ is usually equal to or greater than 3, and by changing Q and γ, filters with different oscillation properties can be obtained, thereby realizing resonance sparse decomposition.
The number of decomposition layers L represents the number of iterations of the dual-channel filter, and for different signals, the maximum value of the number of decomposition layers L is as follows:
Figure FDA0003538305940000023
wherein N is the original signal sampling number, beta is a high-pass scale factor, and alpha is a low-pass scale factor, which is defined as follows:
Figure FDA0003538305940000024
6. the fault diagnosis method for the spindle box of the numerical control high-speed gear milling machine according to claim 1, wherein the split augmented lagrangian shrinkage algorithm is defined as:
Figure FDA0003538305940000025
f2(w)＝λ1||w1||1+λ2||w2||1
H＝[S1 S2],
Figure FDA0003538305940000026
the iterative formula is as follows:
Figure FDA0003538305940000027
Figure FDA0003538305940000028
d(k+1)＝d(k)-u(k+1)+w(k+1)
wherein k is an iteration number, and the parameter mu is 0.5 lambda.
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Application publication date: 20220603