Mechanical fault diagnosis method based on nofrf blind identification

Abstract

The application discloses a mechanical fault diagnosis method based on NOFRF blind identification, proposes a NOFRF blind identification algorithm, extracts NOFRF blind identification values in a fault state and analyzes sensitive characteristic parameters, establishes a damage degree quantitative mapping relationship, and verifies the effectiveness of the diagnosis method through experimental data. The nonlinear output frequency response function of the system can be identified only by using the output signal, and the deficiency that the traditional nonlinear output frequency response function is identified according to the input and output is overcome. Not only can the fault be found earlier, but also the damage degree can be quantitatively evaluated through the multiple growth law of the sensitive characteristic parameters, the bottleneck problem that different faults have similar features in the spectrum and fault quantitative evaluation is solved in the traditional fault analysis method, and the application prospect in the field of mechanical fault intelligent diagnosis is wide.

Description

Technical Field

[0001] This invention relates to mechanical fault diagnosis technology, and in particular to a mechanical fault diagnosis method based on NOFRF (nonlinear output frequency response function) blind identification. Background Technology

[0002] As core load-bearing components in rotating machinery such as aero engines and generators, rolling bearings operate under the combined effects of high speed, high temperature, and complex loads, making them prone to typical failures such as wear, spalling, and fracture. Statistics show that these bearing failures account for more than 30% of all mechanical equipment failures. Therefore, research on rolling bearing fault diagnosis technology has significant engineering implications.

[0003] Currently, traditional methods for diagnosing rolling bearing faults often rely on the characteristic frequencies of rolling bearing faults and their harmonic components for differentiation. However, these methods have significant limitations in practical applications: when the bearing is in the early stage of faulting or when the amplitudes of fault characteristics at different damage levels (early, moderate, and severe) are similar, the differences in the amplitudes of the harmonics in the envelope spectrum are not obvious, making it difficult to accurately quantify the degree of damage. For example, in inner ring faults, the increase in envelope spectrum amplitude is gradual from moderate to severe, and the amplitude alone cannot reliably distinguish the fault; in outer ring faults, the changes in the harmonic amplitudes of the envelope spectrum are not very regular in the early and moderate stages. Furthermore, these methods typically only utilize the system's output signal and cannot reflect the essential transmission characteristics of the system under unknown input excitation, which may lead to misjudgment when the input changes.

[0004] Methods based on nonlinear models can overcome some of the aforementioned shortcomings. The Nonlinear Output Frequency Response (NOFRF) function can describe the nonlinear characteristics of a system in the frequency domain using a one-dimensional function, accurately reflecting the relationship between the output spectrum and nonlinear parameters. However, traditional NOFRF identification methods rely on known system input signals. In practical engineering, the input excitations of mechanical systems (such as complex and variable loads) are often difficult to observe directly and cannot be designed artificially, severely restricting the engineering application of NOFRF methods. Blind identification techniques, on the other hand, extract unknown information solely from the system output, providing a new approach to solving the problem of unmeasurable inputs. Therefore, it is necessary to combine blind identification theory with the NOFRF method to develop a nonlinear system feature extraction technique that relies solely on the output response to effectively identify the fault type and damage degree of rolling bearings. Summary of the Invention

[0005] To address the problem that existing fault diagnosis methods rely on system input signals and are difficult to accurately quantify and assess the degree of damage to rolling bearings, this invention provides a mechanical fault diagnosis method based on NOFRF blind identification. By constructing a NOFRF blind identification algorithm that only utilizes the output vibration response, high-order nonlinear feature parameters that are sensitive to faults are extracted, and a quantitative mapping relationship between the feature parameters and the degree of damage is established based on the exponential growth law of the feature parameters.

[0006] This invention achieves the above objectives using the following technical solution: A mechanical fault diagnosis method based on NOFRF blind identification, with the following specific steps: 1) Taking the inner and outer ring failures of rolling bearings as an example, establish and simulate their dynamic models: establish a four-degree-of-freedom nonlinear dynamic model of the rolling bearing, calculate the elastic restoring force between the balls and the raceway according to Hertz contact theory; set the bearing structural parameters and operating parameters, and simulate the damage levels of inner ring failure and outer ring failure by setting different simulation damage sizes; solve the dynamic model, obtain the vibration acceleration response signal under the fault state, and analyze its envelope spectrum. 2) Propose a NOFRF blind identification algorithm: Introduce the concept of blind system identification, and derive a normalized NOFRF blind identification value calculation formula using only the system's output vibration response signal: ; In the formula: i It is a nonlinear order. Angular frequency, The largest eigenvalue, For the first i The largest eigenvalue corresponds to the eigenvector. The eigenvector corresponding to the first-order largest eigenvalue; 3) Extract NOFRF blind identification values ​​under fault conditions and analyze sensitive feature parameters: Input the vibration response signals obtained from the simulation of inner ring fault and outer ring fault damage levels in step 1) into the NOFRF blind identification algorithm in step 2) respectively, calculate the first four normalized NOFRF blind identification values ​​under each state; by comparing the variation law of each order parameter under the damage level, identify the sensitive feature order that is sensitive to specific faults. 4) Establish a quantitative mapping relationship for damage level: Calculate the growth factor of sensitive NOFRF parameters relative to the normal state under the damage level, plot the relative growth factor relationship curve and scatter plot, and establish a quantitative mapping relationship with the damage level; 5) Verify the effectiveness of the diagnostic method using experimental data: Based on the changes in amplitude and standard deviation of acceleration of the whole-life vibration signal of the inner and outer ring faults of the rolling bearing obtained from the experiment, the experimental data are divided into normal stage, early fault stage, general fault stage, and severe fault stage; firstly, traditional envelope spectrum analysis is performed on the experimental signals, and then normalized NOFRF blind identification values ​​for each stage are extracted; the experimental results are compared with the simulation results to verify the consistency of the growth law of the sensitive feature parameters and the effectiveness of the NOFRF blind identification method in quantitatively assessing the degree of fault damage.

[0007] Furthermore, the elastic deformation between the ball and the raceway is: ; middle: j For the ball bearing serial number, c r For the radial clearance of the bearing, δ This represents the change in contact gap when the ball passes through a damaged area. θ j For the first j The position angle of each ball bearing n The number of balls x i This refers to the horizontal displacement between the bearing inner ring and the shaft. x i and y i These represent the horizontal and vertical displacements of the bearing inner ring relative to the shaft, respectively. x o and y o These represent the horizontal and vertical displacements of the base and the outer ring of the bearing, respectively. The elastic restoring force between the ball and the raceway can be derived from Hertzian contact theory as follows: ; In the formula: K c For contact stiffness, ; In the formula: K ci and K co These represent the contact stiffness of the balls and the inner and outer raceways, respectively. η =1.5; H ( δ j ) is the Hertzian contact function. ; when δ jWhen the value is greater than 0, the Hertzian contact force generated by the elastic deformation of the balls and raceways is: ; In the formula: F x and F y These are the resultant forces of all rolling element contact forces in the horizontal and vertical directions, respectively. Based on Newton's second law, the dynamic model equation for bearing failure is established, and its formula is as follows: ; In the formula: W x For external loads on horizontal bearing systems, W y External load on the bearing system in the vertical direction. and Let be the acceleration of the inner ring in the horizontal and vertical directions. and Let be the acceleration of the outer ring in the horizontal and vertical directions. and These represent the horizontal velocities of the inner and outer rings, respectively. and X represents the vertical velocity of the inner and outer rings, respectively. i and X o Y represents the horizontal displacement of the inner and outer rings, respectively. i and Y o K represents the vertical displacements of the inner and outer rings, respectively. si and K so C represents the equivalent support stiffness of the inner and outer rings, respectively. i and C o M represents the equivalent damping coefficients of the inner and outer rings, respectively. i and M o These are the equivalent masses of the inner and outer rings, respectively. When the inner ring of a rolling bearing is damaged, its total radial deformation changes to: ; In the formula: δ i This refers to the displacement caused when the rolling element rolls over a fault in the inner race. When the outer ring of a rolling bearing is damaged, its total radial deformation changes to: ; In the formula: δ o This refers to the additional displacement of the rolling element when it passes through an outer ring fault.

[0008] Furthermore, the inner ring fault sensitive feature parameters in the sensitive feature order are second-order parameters. and fourth-order parameters The outer ring fault-sensitive characteristic parameters are second-order parameters. Fourth-order parameters and third-order parameters .

[0009] Furthermore, the quantization mapping relationship is specifically as follows: for inner-circle faults, the sensitive characteristic parameter increases approximately 10 times from normal to early-stage faults; from normal to moderate faults, the sensitive characteristic parameter increases 30-40 times; and from normal to severe faults, the sensitive characteristic parameter increases 50-60 times. For outer-circle faults, the sensitive characteristic parameter increases 25-35 times from normal to early-stage faults, and from normal to moderate faults, the second-order parameter... and fourth-order parameters Growth of 165 to 185 times, third-order parameters Increased by 40 to 60 times; from normal to severe fault, second-order parameters and fourth-order parameters Growth of 300 to 320 times, third-order parameters Increased by 200 to 220 times.

[0010] Furthermore, the verification diagnosis includes: performing traditional envelope spectrum analysis and NOFRF blind identification analysis on the experimental signals respectively, and determining the effectiveness of the NOFRF blind identification method for fault type identification and quantitative assessment of damage degree based on the comparison of the two analysis results.

[0011] This invention, by introducing blind identification theory into the NOFRF framework, successfully overcomes the dependence of traditional methods on system input signals, extracting the nonlinear essential characteristics of the system using only the output response. Diagnostic experiments on the inner and outer rings of rolling bearings demonstrate that the proposed method not only detects faults earlier but also quantifies the degree of damage through the exponential growth law of sensitive characteristic parameters. It can identify the nonlinear output frequency response function of the system using only the output signal, overcoming the shortcomings of traditional methods that rely on input and output for identification. This approach not only detects faults earlier but also quantifies the degree of damage through the exponential growth law of sensitive characteristic parameters, solving the bottleneck problem in traditional fault analysis methods where different faults exhibit similar spectral characteristics and quantitative fault assessment is difficult. It has broad application prospects in the field of intelligent mechanical fault diagnosis. Attached Figure Description

[0012] Figure 1 This is the rolling bearing dynamics model in the embodiments of the present invention; Figure 2 This is a mechanical fault diagnosis method based on NOFRF blind identification in the embodiments of the present invention; Figure 3a This is a scatter plot showing the multiplier relationship of various parameters under different damage levels of inner ring faults in the embodiments of the present invention. Figure 3b This is a scatter plot showing the multiplier relationship of various parameters under different damage levels of the simulated outer ring fault in this embodiment of the invention. Figure 4a This is a scatter plot showing the multiplier relationship of various parameters under different damage levels of inner ring faults in the embodiments of the present invention. Figure 4b This is a scatter plot showing the multiplier relationship of various parameters under different damage levels of the outer ring fault in the embodiments of the present invention. Detailed Implementation

[0013] The present invention will be further described below with reference to the accompanying drawings and embodiments. See also: Figures 1 to 4b Since early diagnosis and quantification of damage levels in rolling bearings are crucial for ensuring the reliable operation of rotating machinery, this invention systematically elucidates the implementation process and advantages of the proposed NOFRF-based blind identification method for mechanical fault diagnosis through a combination of simulation and experimentation. The steps are as follows (e.g.) Figure 2 (as shown) Step 1: Establish and simulate the dynamic models of the inner and outer ring faults of the rolling bearing. This invention proposes a 4-DOF rolling bearing system (such as...) Figure 1 As shown in the figure, the contact between the inner and outer rings of the bearing and the balls is equivalent to Hertzian contact, and the horizontal displacement between the inner ring of the bearing and the shaft... x i Vertical displacement of the bearing inner ring relative to the shaft y i Horizontal displacement of the base and the outer ring of the bearing x o Vertical displacement of the base and the outer ring of the bearing y o .

[0014] When a bearing is working, there is radial clearance between the balls and the inner and outer raceways, and it is subjected to radial loads, which will produce corresponding contact deformation. j The elastic deformation of each ball and raceway is: ; In the formula: j For the ball bearing serial number, c r For the radial clearance of the bearing, δ This represents the change in contact gap when the ball passes through a damaged area. θ j For the first j The position angle of each ball bearing n The number of balls xi and y i These represent the horizontal and vertical displacements of the bearing inner ring relative to the shaft, respectively. x o and y o These represent the horizontal and vertical displacements of the base and the outer ring of the bearing, respectively.

[0015] According to Hertzian contact theory, we can obtain the... j The elastic restoring force between each ball and the raceway is: ; In the formula: K c For contact stiffness, ; In the formula: K ci and K co These represent the contact stiffness of the balls and the inner and outer raceways, respectively. η =1.5, H ( δ j ) is the Hertzian contact function. ; when δ j When the value is greater than 0, the Hertzian contact force generated by the elastic deformation of the balls and raceways is: ; In the formula: F x and F y These are the resultant forces of all rolling element contact forces in the horizontal and vertical directions, respectively.

[0016] Based on Newton's second law, the dynamic model equation for bearing failure is established, and its formula is as follows: ; In the formula: W x For external loads on horizontal bearing systems, W y External load on the bearing system in the vertical direction. and Let be the acceleration of the inner ring in the horizontal and vertical directions. and Let be the acceleration of the outer ring in the horizontal and vertical directions. and These represent the horizontal velocities of the inner and outer rings, respectively. and X represents the vertical velocity of the inner and outer rings, respectively. i and X o Y represents the horizontal displacement of the inner and outer rings, respectively. i and Y o K represents the vertical displacements of the inner and outer rings, respectively. si and K so C represents the equivalent support stiffness of the inner and outer rings, respectively. i and C o M represents the equivalent damping coefficients of the inner and outer rings, respectively. i and M o These are the equivalent masses of the inner and outer rings, respectively.

[0017] When the inner ring of a rolling bearing is damaged, its total radial deformation changes to: ; In the formula: δ i This refers to the displacement caused when the rolling element rolls over the inner ring fault.

[0018] When the outer ring of a rolling bearing is damaged, its total radial deformation changes to: ; In the formula: δ o This refers to the additional displacement of the rolling element when it passes through an outer ring fault.

[0019] The bearing parameters were set as follows: ball diameter 7.92 mm, pitch circle diameter 34.55 mm, contact angle 0°, number of balls 8, equivalent damping coefficient 200 N·s / m, and rotational speed 2100 rpm (rotor rotational frequency 35 Hz). Theoretical calculations yielded characteristic frequencies of 172.1 Hz and 107.9 Hz for inner and outer ring faults, respectively.

[0020] To simulate the progression of rolling bearing failure from minor to severe, this embodiment sets different simulated damage dimensions for inner ring and outer ring failures, and classifies the damage levels into normal, early-stage, general, and severe failures. The simulated damage dimensions include damage depth, damage length, and damage width, with the damage length and width gradually increasing with the severity of the failure. It should be noted that the simulated damage dimensions are only used to characterize different damage levels in the dynamic model and do not limit the actual damage dimensions at each failure stage during real bearing operation.

[0021] The built-in Runge-Kutta (4,5) algorithm in MATLAB was used to solve the constructed model, obtaining the vibration acceleration response signals of the inner and outer rings of the rolling bearing under fault conditions. Analysis of the envelope spectra revealed that the amplitude of the fault frequency in the inner ring increased with the severity of damage. The amplitude increase of the inner ring fault tended to level off in the stage from general to severe fault, with a significantly lower increase than in the early to general fault stage. The amplitude response of the outer ring fault frequency was positively correlated with the degree of damage. The amplitude increase was relatively slow in the early to general fault stage, but showed a significant increasing trend when the fault condition escalated to severe fault. Therefore, relying solely on envelope spectrum amplitude analysis is insufficient to accurately determine the degree of bearing damage.

[0022] Step 2: Propose the NOFRF blind identification algorithm 202: To overcome the limitations of traditional envelope spectrum analysis in quantitative fault assessment, this invention proposes a NOFRF blind identification algorithm that utilizes only the output signal.

[0023] No. n The NOFRF formula is: ; In the formula: for n First-order output frequency components, for n First-order input frequency components.

[0024] Assume the system has two input signals. u (k) ( t )and u (l) ( t The excitation generates two corresponding output signals. y (k) ( t )and y (l) ( t Their cross-correlation function is: ; In the formula: t For time, τ For time delay, for The i A sub-signal, for The j A sub-signal, N The highest nonlinear order considered for the system.

[0025] and The cross-correlation function is: ; Its output signal's first i Rank and number j The cross-power spectral density (CPSD) function between the first and second order components is: ; In the formula: and They are respectively u (k) ( t )and u (l) ( t The frequency domain expression of ) For the system number i Volterra frequency domain kernel, For the system number j Volterra frequency domain kernel, T This represents the duration of signal observation.

[0026] and The cross-correlation function is: ; Its and They are of the same order.

[0027] The first input signal i Rank and number j The cross-power spectral density (CPSD) function between the first and second order components is: ; The ratio of output CPSD to input CPSD is: ; available The direct relationship with NOFRF is as follows: ; In the formula: For the first i NOFRF, For the first j NOFRF.

[0028] To obtain NOFRF, it is necessary to determine Through derivation, the two output signals and The cross-power spectral density can be expressed as: ; and It can be calculated using the formula above.

[0029] To eliminate the influence of input amplitude and reveal the nonlinearity of the system through the output signal, a normalized NOFRF is proposed, the process of which is as follows: Assumption and For specific inputs Multiples of can be used to obtain: ; In the formula: and i Power of 1 For the first k The amplitude coefficient of each input relative to the reference input; yes of j Power of 1 For the first l The magnitude coefficient of each input relative to the reference input.

[0030] The frequency domain expression for the reference input is: ; in: It can be decomposed into: ; In the formula: and The corresponding reference inputs are the first i Rank and first j Equivalent input of order.

[0031] Normalized n The order NOFRF is defined as: ; Related to the inherent properties of the system, It does not change with the input amplitude, therefore It can reflect the inherent properties of the system to a certain extent. If the system is linear, then... It is zero, therefore The value is also zero.

[0032] Power spectral density (PSD) was used. The average value of the roots establishes a normalized NOFRF output-only signal estimation method. k The average value of the square root of the PSD of each output signal in the frequency domain is: ; In the formula: [0,Ω] is the frequency domain range under study.

[0033] The results obtained from the preceding CPSD relationship and input amplitude scaling assumption It can be written as: ; therefore It can be rewritten as: ; In the formula: An artificially defined coefficient related to the input amplitude. The function.

[0034] When the PSD value of the signal is small and the system nonlinearity is not strong, the influence of higher-order terms is weak. The terms of intermediate and higher powers can be approximately ignored; only the terms of intermediate and higher powers are retained. i =1, j For a first-order linear term where =1, then: ; In the formula: β For normalized scaling parameters, The frequency transfer relationship of the first-order linear response part. The first-order input power spectral density is used as the reference input.

[0035] therefore, and The CPSD can be rewritten as:

[0036] ; make: ; In the formula: ; but: ; Then By rank i , j Reconstructed into a matrix: ; right Perform eigenvalue decomposition: ; In the formula: It is the eigenvalue matrix; For the first matrix N Each feature value.

[0037] Let the largest eigenvalue be... The corresponding feature vector is: ; In the formula: For the first N The largest eigenvalue corresponds to the eigenvector.

[0038] in It can be calculated as follows: ; The normalized NOFRF blind identification is defined as follows: ; In the formula: i It is a nonlinear order. For frequency position, The largest eigenvalue, For the first i The largest eigenvalue corresponds to the eigenvector. This is the eigenvector corresponding to the first-order largest eigenvalue.

[0039] Thus, this invention completes the algorithm construction for obtaining the blind identification feature parameters of each order of NOFRF using only the output vibration signal.

[0040] Step 3: Extract NOFRF blind identification values ​​under fault conditions and analyze sensitive feature parameters 203: The vibration response signals of different damage levels (normal a1, early b1, moderate c1, severe d1) of the inner ring fault and different damage levels (normal a2, early b2, moderate c2, severe d2) of the outer ring fault obtained from simulation are input into the NOFRF blind identification algorithm in step two, respectively, to calculate the first four normalized NOFRF blind identification values ​​for each state. Since different orders of NOFRF can form effective features at different combination frequencies, this paper selects... As candidate feature parameters, the calculation results are shown in Tables 1 and 2. In the tables, the inner ring fault sensitive feature parameters are second-order parameters. and fourth-order parameters The outer ring fault-sensitive characteristic parameters are second-order parameters. Fourth-order parameters and third-order parameters .

[0041] To facilitate comparison, all data were normalized.

[0042] ; ; Analyzing the data trends in Tables 1 and 2, when the bearing is in the early stage of failure, and The amplitudes increased by 11 times and 10 times respectively during the general fault stage; during the severe fault stage, the amplitudes increased by 31 times and 33 times respectively; and during the serious fault stage, they further increased to 53 times and 57 times. When damage occurs to the outer ring, in addition to... , outside, The parameters also showed a clear upward trend and phased characteristics. When the bearing is in the early stage of failure, , and The amplitudes of the three parameters increased by 27, 29, and 30 times respectively during the general fault stage; 168, 173, and 54 times respectively during the general fault stage; and 313, 307, and 211 times respectively during the severe fault stage. In stark contrast, the growth rates of the other characteristic parameters were relatively gradual, and the dispersion of the increase factors in different fault stages was low.

[0043] Step 4: Establish a quantitative mapping relationship for damage level 204: Through repeatability verification of multiple sets of data, a scatter plot of the relationship between damage level and parameter multiples was further plotted. This plot reveals, in a quantitative form, the nonlinear growth law of each characteristic parameter under different fault severity levels, such as... Figure 3a , Figure 3b As shown in the diagram. ● indicates… 、■ indicates 、▼ indicates ▲ indicates 、◆ indicates .

[0044] For inner ring faults: from normal to early faults, the sensitive characteristic parameters increase by about 10 times; from normal to moderate faults, the sensitive characteristic parameters increase by 30 to 40 times; from normal to severe faults, the sensitive characteristic parameters increase by 50 to 60 times.

[0045] For outer ring faults: from normal to early faults, the sensitive characteristic parameters increase by 25 to 35 times; from normal to general faults, the parameters... and Growth of 165 to 185 times Parameters increase 40 to 60 times; from normal to severe fault, parameters... and Growth of 300 to 320 times The parameters increased by 200 to 220 times.

[0046] Therefore, this invention identifies sensitive characteristic parameters for rolling bearing fault diagnosis: inner ring faults are primarily monitored. and NOFRF blind identification value; outer ring fault monitoring , , NOFRF blind identification value.

[0047] Step 5: Verify the effectiveness of the diagnostic method using experimental data 205: To verify the accuracy of the simulation results, actual measurements were conducted using a rolling bearing test bench. The experiment used an LDKUER204 bearing, with inner ring faults (Bearing2-1) and outer ring faults (Bearing2-2) set up. The bearing rotational frequency was 37.5 Hz, the number of rolling elements was 8, the rolling element diameter was 7.92 mm, the bearing pitch diameter was 34.55 mm, and the contact angle was 0°. The fault frequencies of the inner and outer rings were 184.38 Hz and 115.62 Hz, respectively.

[0048] Vibration data of the bearing throughout its entire lifespan, from normal operation to complete failure, were collected. During the data segmentation process, the maximum amplitude of the bearing's horizontal vibration signal was used as a criterion to determine whether it exceeded the maximum amplitude during normal operation. Ah Ten times the standard deviation of acceleration is used as the criterion for complete failure, and the abnormal boundary point is determined by combining the trend of acceleration standard deviation. Based on this, the entire life process of the bearing is divided into the normal stage, the early failure stage, the general failure stage, the severe failure stage, and the complete failure stage. Before complete failure, A1-D1 and A2-D2 are selected as representative samples of different damage degrees of the inner and outer rings, respectively.

[0049] First, a spectral analysis of the experimental signal was performed. When the rolling bearing was in the early stage of damage, in addition to the system fundamental frequency, the first, second, third, and fourth harmonics of the inner ring fault frequency also appeared. When it was in a moderate stage of damage, only the first harmonic of the inner ring fault frequency increased, while the other frequencies remained almost unchanged, making it difficult to determine the degree of damage to the inner ring. When it was in a severe stage of damage, the system fundamental frequency and its harmonics, as well as the harmonics of the fault frequency, increased sharply. Overall, the envelope spectrum can reflect whether the rolling bearing has an inner ring fault, but it cannot determine its severity.

[0050] When an early-stage fault exists in the outer ring of a rolling bearing, the frequency spectrum shows the first, second, third, and fourth harmonics of the fault frequency. In cases of moderate faults, the first and third harmonics increase slightly, while the second and fourth harmonics decrease slightly; these increases and decreases are negligible and cannot accurately determine the specific stage of damage. In cases of severe faults, the first, third, and fourth harmonics of the fault frequency increase further, with the second harmonic showing a more significant increase. These characteristics can indicate the presence of an outer ring fault in the rolling bearing, but they cannot accurately determine the extent of the damage.

[0051] The experimental signals were analyzed using the NOFRF blind identification algorithm proposed in this invention. The first four normalized NOFRF blind identification values ​​of the inner ring fault samples A1, B1, C1, D1 and the outer ring fault samples A2, B2, C2, D2 were calculated, and the results are shown in Tables 3 and 4.

[0052] ; ; Analyzing the data trends in the table, when the bearing is in the early stage of failure, and The amplitudes increased by approximately 8 times and 9 times respectively; during a normal fault, the amplitudes of both increased by approximately 35 times; and during a severe fault, the amplitudes of both increased by approximately 57 times. However, when damage occurs to the outer ring, except... , and The parameters also showed a clear upward trend and phased characteristics. When the bearing is in the early failure stage and the general failure stage, and The magnitude increases were the same, at 28 times and 171 times respectively. While the increase in these parameters did not reach two orders of magnitude, the increase was relatively significant compared to other parameters. When the bearing was in a severe failure stage, the amplitudes of the three parameters increased by 318 times, 319 times, and 216 times, respectively. Similarly, the increase in the other characteristic parameters was relatively gradual, with low dispersion in the increase factors at different failure stages. It should be noted that the simulation analysis was conducted under ideal constant operating conditions, while the experimental data were affected by factors such as load fluctuations, test noise, and actual assembly conditions. Therefore, a certain deviation between the experimental and simulation results is permissible.

[0053] Through repeatability verification of multiple sets of data, a scatter plot of the relationship between damage level and parameter multiples was further plotted. This plot reveals, in a quantitative form, the nonlinear growth law of each characteristic parameter under different fault severity levels, such as... Figure 4a , Figure 4b As shown in the diagram. ● indicates… 、■ indicates 、▼ indicates ▲ indicates 、◆ indicates .

[0054] For inner ring faults: from normal to early faults, the increase in sensitive characteristic parameters is roughly one order of magnitude, that is, the increase is about 10 times; from normal to general faults, the increase in sensitive characteristic parameters is 30 to 40 times; from normal to severe faults, the increase in sensitive characteristic parameters is 50 to 60 times.

[0055] For outer ring faults: from normal to early faults, the sensitive characteristic parameters increase by 25 to 35 times; from normal to general faults, the parameters... and Growth of 165 to 185 times Parameters increase 40 to 60 times; from normal to severe fault, parameters... and Growth of 300 to 320 times The parameters increased by 200 to 220 times. The experimental and simulation results are in good agreement, verifying the effectiveness and generalization ability of the NOFRF blind identification method proposed in this invention in the fault diagnosis of rolling bearings.

[0056] This invention is verified by both simulation and experiment. The results show that NOFRF parameters of a specific order are significantly sensitive to bearing inner ring faults, outer ring faults and different damage degrees. It overcomes the limitations of traditional envelope spectrum analysis in quantitative fault assessment and provides a new approach for condition monitoring and intelligent diagnosis of rolling bearings under complex working conditions.

Claims

1. A mechanical fault diagnosis method based on NOFRF blind identification, characterized in that, The specific steps are as follows: 1) Taking the inner and outer ring failures of rolling bearings as an example, a dynamic model is established and simulated: A four-degree-of-freedom nonlinear dynamic model of the rolling bearing is established, and the elastic restoring force between the balls and the raceway is calculated according to Hertz contact theory; the bearing structural parameters and operating parameters are set, and the damage levels of inner ring failure and outer ring failure are simulated by setting different simulation damage sizes; the dynamic model is solved, the vibration acceleration response signal under the fault state is obtained, and its envelope spectrum is analyzed. 2) Propose a NOFRF blind identification algorithm: Introduce the concept of blind system identification, and derive a normalized NOFRF blind identification value calculation formula using only the system's output vibration response signal: ； In the formula: i It is a nonlinear order. Angular frequency, The largest eigenvalue, For the first i The largest eigenvalue corresponds to the eigenvector. The eigenvector corresponding to the first-order largest eigenvalue; 3) Extract NOFRF blind identification values ​​under fault conditions and analyze sensitive feature parameters: Input the vibration response signals obtained from the simulation of inner ring fault and outer ring fault damage levels in step 1) into the NOFRF blind identification algorithm in step 2) respectively, calculate the first four normalized NOFRF blind identification values ​​under each state; by comparing the variation law of each order parameter under the damage level, identify the sensitive feature order that is sensitive to specific faults. 4) Establish a quantitative mapping relationship for damage level: Calculate the growth factor of sensitive NOFRF parameters relative to the normal state under the damage level, plot the relative growth factor relationship curve and scatter plot, and establish a quantitative mapping relationship with the damage level; 5) Verify the effectiveness of the diagnostic method using experimental data: Based on the changes in amplitude and standard deviation of acceleration of the whole-life vibration signal of the inner and outer ring faults of the rolling bearing obtained from the experiment, the experimental data are divided into normal stage, early fault stage, general fault stage, and severe fault stage; firstly, traditional envelope spectrum analysis is performed on the experimental signals, and then normalized NOFRF blind identification values ​​for each stage are extracted; the experimental results are compared with the simulation results to verify the consistency of the growth law of the sensitive feature parameters and the effectiveness of the NOFRF blind identification method in quantitatively assessing the degree of fault damage.

2. The mechanical fault diagnosis method based on NOFRF blind identification according to claim 1, characterized in that, The elastic deformation between the ball and the raceway is: ； In the formula: j For the ball bearing serial number, c r For the radial clearance of the bearing, δ This represents the change in contact gap when the ball passes through a damaged area. θ j For the first j The position angle of each ball bearing n The number of balls x i and y i These represent the horizontal and vertical displacements of the bearing inner ring relative to the shaft, respectively. x o and y o These represent the horizontal and vertical displacements of the base and the outer ring of the bearing, respectively. The elastic restoring force between the ball and the raceway can be derived from Hertzian contact theory as follows: ； In the formula: K c For contact stiffness, ； In the formula: K ci and K co These represent the contact stiffness of the balls and the inner and outer raceways, respectively. η =1.5; H ( δ j ) is the Hertzian contact function. ； when δ j When the value is greater than 0, the Hertzian contact force generated by the elastic deformation of the balls and raceways is: ； In the formula: F x and F y These are the resultant forces of all rolling element contact forces in the horizontal and vertical directions, respectively. Based on Newton's second law, the dynamic model equation for bearing failure is established, and its formula is as follows: ； In the formula: W x For external loads on horizontal bearing systems, W y External load on the bearing system in the vertical direction. and Let be the acceleration of the inner ring in the horizontal and vertical directions. and Let be the acceleration of the outer ring in the horizontal and vertical directions. and These represent the horizontal velocities of the inner and outer rings, respectively. and X represents the vertical velocity of the inner and outer rings, respectively. i and X o Y represents the horizontal displacement of the inner and outer rings, respectively. i and Y o K represents the vertical displacements of the inner and outer rings, respectively. si and K so C represents the equivalent support stiffness of the inner and outer rings, respectively. i and C o M represents the equivalent damping coefficients of the inner and outer rings, respectively. i and M o These are the equivalent masses of the inner and outer rings, respectively. When the inner ring of a rolling bearing is damaged, its total radial deformation changes to: ； In the formula: δ i This refers to the displacement caused when the rolling element rolls over a fault in the inner race. When the outer ring of a rolling bearing is damaged, its total radial deformation changes to: ； In the formula: δ o This refers to the additional displacement of the rolling element when it passes through an outer ring fault.

3. The mechanical fault diagnosis method based on NOFRF blind identification according to claim 1, characterized in that, The sensitive feature order in which the inner ring fault sensitive feature parameters are second-order parameters are respectively... and fourth-order parameters The outer ring fault-sensitive characteristic parameters are second-order parameters. Fourth-order parameters and third-order parameters .

4. The mechanical fault diagnosis method based on NOFRF blind identification according to claim 1, characterized in that, The quantization mapping relationship is as follows: for inner-circle faults, the sensitive characteristic parameter increases approximately 10 times from normal to early-stage faults; from normal to moderate faults, the sensitive characteristic parameter increases 30-40 times; and from normal to severe faults, the sensitive characteristic parameter increases 50-60 times. For outer-circle faults, the sensitive characteristic parameter increases 25-35 times from normal to early-stage faults, and from normal to moderate faults, the second-order parameter... and fourth-order parameters Growth of 165 to 185 times, third-order parameters Increased by 40 to 60 times; from normal to severe fault, second-order parameters and fourth-order parameters Growth of 300 to 320 times, third-order parameters Increased by 200 to 220 times.

5. The mechanical fault diagnosis method based on NOFRF blind identification according to claim 1, characterized in that, The verification diagnosis includes: performing traditional envelope spectrum analysis and NOFRF blind identification analysis on the experimental signals respectively, and determining the effectiveness of the NOFRF blind identification method for fault type identification and quantitative assessment of damage degree based on the comparison of the two analysis results.

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