Straight gear system crack fault diagnosis method based on actual crack propagation curve

Abstract

The invention provides a straight gear system crack fault diagnosis method based on an actual crack propagation curve, and the method specifically comprises the steps: building a gear dynamics analysis model based on the modal condensation of a gear; combining historical data of a gear crack fatigue propagation experiment to obtain a tooth root crack propagation path, and substituting the tooth root crack propagation path into the gear dynamics analysis model to obtain the time-varying meshing stiffness of the gear containing the cracks; simulation acceleration signal data are obtained through a gear dynamics analysis model, and tooth root crack degree identification features are established; and the tooth root crack degree identification features serve as actual signals, and the expansion degree of gear cracks is judged through a variational mode decomposition method. The invention provides a method for improving tooth root crack recognition by considering the condition that a center distance error and a misalignment error exist at the same time. According to the method, index construction is carried out through simulation, noise interference of the measurement environment is reduced through a variational mode decomposition reconstruction method, and crack vibration impact characteristics hidden in periodic signals are extracted.

Description

Technical Field

[0001] The present invention relates to the field of mechanical static characteristic analysis, and in particular to a spur gear system crack fault diagnosis method based on an actual crack propagation curve. Background Art

[0002] Gear transmission systems play a vital role in many industries such as automobiles, wind power generation, and aviation. Meshing stiffness and transmission error are key excitations within the system and are related to the stability of the transmission system. Since gears work under harsh conditions such as high speed and high load for a long time, they are often prone to severe wear and impact damage, which increases the probability of crack failure in the gear structure. Once a failure occurs, it will have very serious consequences, so it is necessary to accurately judge the degree of gear crack failure. Mastering the identification indicators of gear cracks under load can better analyze the impact of crack paths on gear meshing and ensure the reliability of the transmission system when gear cracks fail. However, due to the existence of factors such as environmental noise interference, traditional diagnostic indicators cannot identify gear cracks under variable load conditions well. From an engineering perspective, it is necessary to study crack fault diagnostic indicators for gear systems under variable conditions.

[0003] In the past, most of the research on gear crack indicators was aimed at ideal working conditions, and the research on crack indicators rarely considered the situation of variable operating conditions. In terms of dynamic modeling, most scholars use the traditional large-model finite element method with slow computational efficiency. However, when fault identification is performed on cracked gear pairs, its computational efficiency needs to be provided. In view of the above-mentioned problems, it is very necessary to establish a meshing mechanics model that takes into account the actual crack propagation path and the flexibility of the gear matrix, and to establish fault indicators based on this to solve the existing variable operating condition crack fault diagnosis problems. Summary of the invention

[0004] According to the technical problems raised above, a crack fault diagnosis method for a spur gear system based on an actual crack propagation curve is provided. Based on multiple tests and fitting the crack propagation path through polynomials, the present invention constrains the root circle through the LTCA method, obtains the time-varying meshing stiffness under the crack condition, and introduces a proposed method for constructing a dynamic model based on the tooth base condensation theory. Tests are carried out on gear conditions with different crack conditions under different torque conditions to obtain vibration acceleration signals. Indicators are constructed using simulation, and the vibration impact hidden in the periodic signal is extracted through the variational mode decomposition and reconstruction method. At the same time, the noise interference of the measurement environment is reduced. The sub-signal indicators related to the crack propagation condition and the variable load condition are determined through the Pearson correlation coefficient, and the crack propagation index considering the variable load condition is obtained.

[0005] The technical means adopted by the present invention are as follows:

[0006] A method for diagnosing crack faults in a spur gear system based on an actual crack growth curve, the specific steps comprising:

[0007] Based on the modal reduction of gears, a gear dynamics analysis model is established;

[0008] Combined with the historical data of gear crack fatigue growth experiments, the root crack growth path is obtained and substituted into the gear dynamics analysis model to obtain the time-varying meshing stiffness of the cracked gear.

[0009] Through the gear dynamics analysis model, the simulated acceleration signal data is obtained to establish the tooth root crack degree identification characteristics;

[0010] The tooth root crack degree identification feature is used as the actual signal, and the gear crack extension degree is determined by the variational mode decomposition method.

[0011] Furthermore, the modal condensation of the gear is realized by using the Guyan method to achieve static reduction of the degrees of freedom, and a condensation point is set; the shaft system of the gear is discretized into a plurality of shaft segments, coupling relationships are established between the shaft segments through Timoshenko beam units, and structural flexibility is simulated through Timoshenko beam units.

[0012] Furthermore, the establishment of the gear dynamics analysis model includes:

[0013] The gear is modally condensed, and the gear condensation transformation matrix is:

[0014]

[0015] Among them, T represents the dimension transformation matrix, K ss represents the node stiffness matrix, K sm represents the master-slave node coupling stiffness matrix, Φ sm represents the master-slave node coupling eigenvector, Φ mm represents the slave node feature vector;

[0016] The mass matrix M of the gear model after polycondensation 12 and the stiffness matrix K 12 According to the requirements of polycondensation, the modal characteristic equation and orthogonal conditions in the gear polycondensation transformation matrix are satisfied, so the polycondensed model stiffness matrix K 12 and the mass matrix M 12 The expression is:

[0017] K 12 =K mm +T T K sm +K ms T+T T K ss T

[0018] M 12 =M mm +T T M sm +M ms T+T T M ss T

[0019] Among them, K mm represents the main node stiffness matrix, K ms represents the master-slave node coupling stiffness matrix, M mm represents the master node mass matrix, M sm represents the master-slave node coupling mass matrix, M ms represents the master-slave node coupling mass matrix, M ss represents the slave node mass matrix;

[0020] The differential equation of motion of the spur gear pair is obtained as:

[0021]

[0022] Among them, F 12 is the external load vector, X 12 is the displacement vector, C is the damping matrix, using proportional damping; G is the gyro matrix, including the gyro matrix of the gear;

[0023] The dynamic equation of the total gearbox gear system transmission is obtained as:

[0024]

[0025] Among them, X is the generalized coordinate vector, M is the mass matrix of the whole system, C is the damping matrix of the whole system, K is the stiffness matrix of the whole system, and F T is the external force vector.

[0026] Furthermore, the calculation method of the time-varying meshing stiffness of the cracked gear includes:

[0027] Get the data point position information N among multiple cracks ki =(x ki ,y ki ), where k is the number of test lines, i=1,2,…n represents the number of sampling points, N represents the polynomial degree, and the mean square error is represented as Q. The calculation method of Q is as follows:

[0028]

[0029] Convert to normal equation:

[0030]

[0031] Among them, a nrepresents the polynomial coefficients, x i Indicates the horizontal coordinate of the sampling point, y i represents the ordinate of the sampling point, and A is the Vandermonde matrix of the abscissa of the sampling point;

[0032] The deformation coordination equation is introduced, and the deformation coordination equation expression is:

[0033] -(λ b +λ c )·F+I n×1 ·ste=ε

[0034] Where ste represents the static transmission error, ε represents the initial separation gap vector of each point, and λ b represents the overall bending flexibility matrix of all meshing points, λ c represents the overall contact flexibility matrix, F represents the contact force vector formed by the meshing points, and I n×1 Represents an n×1-dimensional matrix with all elements set to 1;

[0035] Iteratively solve the deformation coordination equation. If the contact force is less than zero during the iteration process, the meshing point is considered as a non-contact state. Finally, the contact force vector F and static transmission error ste of all meshing points are obtained.

[0036] The meshing stiffness of each meshing position is expressed as:

[0037]

[0038] Among them, k represents the meshing stiffness, F represents the total contact force, and nlste represents the no-load transmission error;

[0039] The gear tooth load contact analysis method is adopted to calculate the time-varying meshing stiffness of the gear pair crack by constraining the tooth root circle and bringing the fitted cubic polynomial crack propagation path into the gear tooth.

[0040] Furthermore, the establishment of the tooth root crack degree identification feature includes:

[0041] The state of the gear transmission system is detected by time-frequency domain indicators, and the indicators that are sensitive to the degree of crack extension are determined as crack fault characteristic indicators. The standard deviation, root mean square value and frequency domain indicators are selected as the initial indicators of crack fault characteristics:

[0042]

[0043] Among them, σ x represents the standard deviation, N represents the number of sample points, x(n) represents the signal value of the sampling point, represents the mean value of the sampling point signal, F represents the frequency domain index, s(k) is the spectrum of the signal x(n), k = 1, 2, ..., K; K is the number of spectral lines; fk is the frequency value of the kth spectral line, x rms represents the root mean square value;

[0044] The vibration acceleration response of the gear system under 10 load levels, torque range of 2N·m~52N·m, averagely divided into T1~T10 levels, and 7 levels of tooth root crack, S1~S7, was obtained through the dynamic model; the crack propagation stage of the model was quantified, and the sensitivity analysis of the indicators was carried out at the same time, and the root mean square error was calculated using the measured values ​​of the response indicators of each working condition and the normalized quantized value of the crack stage;

[0045]

[0046] Among them, R j represents the RMSE value; j represents different index values ​​(σ x ,x rms ,F), i represents different crack stages (S1-S7), v i,j Represents the measured values ​​of each response index and different crack stages, s i Indicates the quantitative value of each crack stage; calculates the root mean square error RMSE through the measured value of each working condition signal index and the normalized quantitative value of the crack stage, and performs sensitivity analysis on the index;

[0047] Calculate the initial indicator XT from the simulation signal d , the initial index XT d It is expressed as:

[0048]

[0049] Among them, k j and k b is the sub-indicator coefficient;

[0050] Initial indicator XT obtained from simulation signal d Establish the tooth root crack degree identification feature XT to judge the gear crack stage, and express the index XT as:

[0051]

[0052] Among them, α i and η i is the parameter of the tooth root crack degree identification feature XT, T is the gearbox working load, X1 and X2 represent T1 and T respectively. 10 The difference between the crack growth parameters at different crack stages and initial index under different load levels, k d It represents the difference between the initial index crack growth parameters and the different load levels in the crack stage.

[0053] Furthermore, the sub-index coefficient k j and kb It is expressed as:

[0054]

[0055] Among them, R j It represents the root mean square error between each sub-indicator and the quantitative crack extension value, and e is the correction factor.

[0056] Furthermore, the variational modal decomposition method takes the tooth root crack degree identification characteristics as the actual signal, and uses the VMD reconstruction method to denoise the signal before index judgment, filters and reconstructs the intrinsic mode function components obtained after VMD decomposition, and uses the denoised signal for index judgment to determine the degree of gear crack extension.

[0057] Compared with the prior art, the present invention has the following advantages:

[0058] The present invention provides a crack fault diagnosis method for a spur gear system based on an actual crack propagation curve, which takes into account the simultaneous existence of center distance error and misalignment error, and proposes an improved tooth root crack identification method. This method allows for a more realistic consideration of the actual gear working conditions, and establishes a crack propagation index under variable load conditions. First, simulation is used to construct the index, and the variational modal decomposition and reconstruction method is used to reduce the interference of measurement environment noise and extract the crack vibration impact characteristics hidden in the periodic signal.

[0059] Based on the above reasons, the present invention can be widely promoted in the field of mechanical static characteristic analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0061] Figure 1 Flow chart of the method of the present invention.

[0062] Figure 2 This is a test device for the root fatigue crack growth of spur gears.

[0063] Figure 3 is the crack path parameter of spur gear tooth root.

[0064] Figure 4 Experimental results and fitting of crack propagation path.

[0065] Figure 5 LTCA calculation process for cracked gear.

[0066] Figure 6 Meshing for calculation of gear mesh stiffness with crack faults.

[0067] Figure 7 This is a schematic diagram of gear condensation.

[0068] Figure 8 Schematic diagram of shaft segment division.

[0069] Fig. 9 It is the total stiffness matrix diagram of the gear system.

[0070] Fig.10 This is a diagram of the gear transmission system vibration acceleration test device.

[0071] Fig.11 This is the variable speed spectrum diagram of the crack fault gear system.

[0072] Fig.12 It is the acceleration spectrum diagram of the gear transmission system under the variable crack stage condition.

[0073] Fig.13 It is the acceleration spectrum of the gear transmission system under variable load level.

[0074] Fig.14 The diagram shows the establishment of crack diagnosis indicators and the diagnosis process.

[0075] Fig.15 This is a graph showing the variation of typical indicators with crack stages under variable load.

[0076] Fig.16 This is the correlation analysis diagram between the simulation signal variable load level and crack stage.

[0077] Fig.17 This is the initial indicator analysis chart of the simulation signal.

[0078] Fig.18 This is the confusion matrix of crack diagnosis between the proposed indicators and common indicators. DETAILED DESCRIPTION

[0079] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0080] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0081] like Figure 1 As shown, the present invention provides a method for diagnosing crack faults in a spur gear system based on an actual crack growth curve, and the specific steps include:

[0082] Based on the modal reduction of gears, a gear dynamics analysis model is established;

[0083] In specific implementation, as a preferred embodiment of the present invention, the modal condensation of the gear is implemented by the Guyan method to achieve static reduction of the degrees of freedom, and a condensation point is set; the shaft system of the gear is discretized into multiple shaft segments, and a coupling relationship is established between the shaft segments through the Timoshenko beam unit, and the structural flexibility is simulated by the Timoshenko beam unit.

[0084] In specific implementation, as a preferred embodiment of the present invention, the establishment of the gear dynamics analysis model includes:

[0085] In the Guyan method, the influence of inertia is ignored and the gear is modally condensed. The gear condensation transformation matrix is:

[0086]

[0087] Among them, T represents the dimension transformation matrix, K ss represents the node stiffness matrix, K sm represents the master-slave node coupling stiffness matrix, Φ sm represents the master-slave node coupling eigenvector, Φ mm represents the slave node feature vector;

[0088] The mass matrix M of the gear model after polycondensation 12 and the stiffness matrix K 12 According to the requirements of polycondensation, the modal characteristic equation and orthogonal conditions in the gear polycondensation transformation matrix are satisfied, so the polycondensed model stiffness matrix K 12 and the mass matrix M 12 The expression is:

[0089] K 12 =K mm +T T K sm +K ms T+T T K ss T

[0090] M 12 =M mm +T T M sm +M ms T+T T M ss T

[0091] Among them, K mm represents the main node stiffness matrix, K ms represents the master-slave node coupling stiffness matrix, M mm represents the master node mass matrix, M sm represents the master-slave node coupling mass matrix, M ms represents the master-slave node coupling mass matrix, M ss represents the slave node mass matrix;

[0092] The differential equation of motion of the spur gear pair is obtained as:

[0093]

[0094] Among them, F 12 is the external load vector, X 12 is the displacement vector, C is the damping matrix, using proportional damping; G is the gyro matrix, including the gyro matrix of the gear;

[0095] The dynamic equation of the total gearbox gear system transmission is obtained as:

[0096]

[0097] Among them, X is the generalized coordinate vector, M is the mass matrix of the whole system, C is the damping matrix of the whole system, K is the stiffness matrix of the whole system, and F T is the external force vector.

[0098] In implementation, the total damping matrix C of the system adopts Rayleigh damping, which is expressed as follows:

[0099] C=ξM+ηK

[0100]

[0101] Where ω1 and ω2 are the first and second order natural frequencies, ξ1 and ξ2 are the first and second order modal damping ratios.

[0102] Combined with the historical data of gear crack fatigue growth experiments, the root crack growth path is obtained and substituted into the gear dynamics analysis model to obtain the time-varying meshing stiffness of the cracked gear.

[0103] In specific implementation, as a preferred embodiment of the present invention, the method for calculating the time-varying meshing stiffness of the cracked gear includes:

[0104] Get the data point position information N among multiple cracks ki =(x ki ,y ki ), where k is the number of test lines, i=1,2,…n represents the number of sampling points, N represents the polynomial degree, and the mean square error is represented as Q. The calculation method of Q is as follows:

[0105]

[0106] Convert to normal equation:

[0107]

[0108] Among them, a n represents the polynomial coefficients, x i Indicates the horizontal coordinate of the sampling point, y i represents the ordinate of the sampling point, and A is the Vandermonde matrix of the abscissa of the sampling point;

[0109] During implementation, the polynomial coefficient a to be determined is obtained n , try to select the appropriate polynomial degree, and judge that the fitting is a cubic polynomial. Compare the obtained crack fitting path with the crack growth curve obtained by the test. The average error between the fitting and the test crack path is small, which means that the cubic polynomial fitting test path can accurately reflect the actual crack growth path. The obtained fitting cubic polynomial is used as the crack growth path and introduced into the gear tooth load analysis method for calculation.

[0110] The deformation coordination equation is introduced, and the deformation coordination equation expression is:

[0111] -(λ b +λ c )·F+I n×1 ·ste=ε

[0112] Where ste represents the static transmission error, ε represents the initial separation gap vector of each point, and λ b represents the overall bending flexibility matrix of all meshing points, λ c represents the overall contact flexibility matrix, F represents the contact force vector formed by the meshing points, and I n×1 Represents an n×1-dimensional matrix with all elements set to 1;

[0113] Iteratively solve the deformation coordination equation. If the contact force is less than zero during the iteration process, the meshing point is considered as a non-contact state. Finally, the contact force vector F and static transmission error ste of all meshing points are obtained.

[0114] The meshing stiffness of each meshing position is expressed as:

[0115]

[0116] Among them, k represents the meshing stiffness, F represents the total contact force, and nlste represents the no-load transmission error;

[0117] During implementation, the finite element model of the gear with crack fault is also established using parameter units such as eight-node hexahedral space. The gear tooth load contact analysis method is used to constrain the root circle and bring in the fitted cubic polynomial crack propagation path to calculate the time-varying meshing stiffness of the gear pair crack.

[0118] Through the gear dynamics analysis model, the simulated acceleration signal data is obtained to establish the tooth root crack degree identification characteristics;

[0119] In specific implementation, as a preferred embodiment of the present invention, the establishment of the tooth root crack degree identification feature includes:

[0120] In the implementation, a crack growth stage identification index combining simulation and experimental signals was proposed. This index can accurately identify the root crack growth stage while eliminating the interference of different load conditions, which is better than the typical crack stage identification index.

[0121] The state of the gear transmission system is detected by time-frequency domain indicators, and the indicators that are sensitive to the degree of crack extension are determined as crack fault characteristic indicators. The standard deviation, root mean square value and frequency domain indicators are selected as the initial indicators of crack fault characteristics:

[0122]

[0123] Among them, σ x represents the standard deviation, N represents the number of sample points, x(n) represents the signal value of the sampling point, represents the mean value of the sampling point signal, F represents the frequency domain index, s(k) is the spectrum of the signal x(n), k = 1, 2, ..., K; K is the number of spectral lines; f k is the frequency value of the kth spectral line, x rms represents the root mean square value;

[0124] The vibration acceleration response of the gear system under 10 load levels, torque range of 2N·m~52N·m, averagely divided into T1~T10 levels, and 7 levels of tooth root crack, S1~S7, was obtained through the dynamic model; the crack propagation stage of the model was quantified, and the sensitivity analysis of the indicators was carried out at the same time, and the root mean square error was calculated using the measured values ​​of the response indicators of each working condition and the normalized quantized value of the crack stage;

[0125]

[0126] Among them, R j represents the RMSE value; j represents different index values ​​(σ x ,x rms ,F), i represents different crack stages (S1-S7), v i,j Represents the measured values ​​of each response index and different crack stages, s i Indicates the quantitative value of each crack stage; calculates the root mean square error RMSE through the measured value of each working condition signal index and the normalized quantitative value of the crack stage, and performs sensitivity analysis on the index;

[0127] Calculate the initial indicator XT from the simulation signal d , the initial index XT d It is expressed as:

[0128]

[0129] Among them, the sub-indicator coefficient k j It is expressed as:

[0130]

[0131] Among them, R j It represents the root mean square error between each sub-index and the quantitative crack extension value, and the coefficient k b It is expressed as:

[0132]

[0133] e is the correction factor, which is set to 3.35 in this paper.

[0134] Initial indicator XT obtained from simulation signal d Establish the tooth root crack degree identification feature XT to judge the gear crack stage, and express the index XT as:

[0135]

[0136] Among them, α i and η i is the parameter of the tooth root crack degree identification feature XT, T is the gearbox working load, X1 and X2 represent T1 and T respectively. 10The difference between the crack growth parameters at different crack stages and initial index under different load levels, k d It represents the difference between the initial index crack growth parameters and the different load levels in the crack stage.

[0137] The tooth root crack degree identification feature is used as the actual signal, and the gear crack extension degree is determined by the variational mode decomposition method.

[0138] In specific implementation, as a preferred embodiment of the present invention, the variational mode decomposition method uses the tooth root crack degree identification feature as the actual signal, and uses the VMD reconstruction method to denoise the signal before the index judgment, so as to avoid the interference of external noise in the actual measurement signal when judging by the established index of this article. The intrinsic mode function components obtained after VMD decomposition are filtered and reconstructed, and the denoised signal is used for index judgment to determine the degree of gear crack extension.

[0139] Example

[0140] like Figure 1 As shown, the present invention provides a spur gear system crack fault diagnosis method based on an actual crack propagation curve. This embodiment provides a specific implementation of the present invention.

[0141] S1. Combined with the gear crack fatigue growth test, the root crack growth path is obtained.

[0142] S11. In order to achieve efficient digital-analog linkage, a gear transmission model with tooth surface faults is established with a single-stage gearbox as the object. The dynamic characteristics of the faulty gear in the gearbox are simulated, and a supplementary small sample model is constructed by combining digital and analog methods. In essence, a highly simulated equipment fault model is established, and a simulation-based data set is constructed to supplement the insufficient experimental conditions. Therefore, the constructed simulation model needs to combine accuracy and speed to achieve high-precision diagnosis.

[0143] S12, such as Figure 2 As shown in the figure, the research object is a spur gear manufactured according to the FZG standard. Six gears with the same parameters were tested on a fatigue testing machine, and the positions of the prefabricated initial tooth root cracks were exactly the same.

[0144] S13, Figure 3 This is the preparation for the crack stage division before the test. Taking the starting point of the prefabricated crack as the center of the circle and the radius as the measurement standard, by measuring the arc starting from the center of the circle and the distance from the end of the gear crack to the center of the circle, stage A is the prefabricated crack stage, and the gear crack is divided according to the crack radius, and it is expected to be divided into 8 levels from A to G.

[0145] S14, obtaining the position information of data points in multiple cracks such as Figure 4As shown, the polynomial coefficients can be obtained according to the experimental crack path, and it is judged that the polynomial is a cubic polynomial. The polynomial coefficients are determined to be a0=0.032, a1=-0.079, a2=70.252, and a3=3338.845. The obtained crack fitting path is compared with the crack growth curve obtained by the experiment. The average error between the crack path fitting and the experiment is 0.2151, and the correlation coefficient is 0.9832. It can be considered that the experimental path fitted by the cubic polynomial can more accurately reflect the actual crack growth path. The cubic polynomial obtained by fitting is introduced into the LTCA method as the crack growth path.

[0146] S15, such as Figure 5 As shown in the figure, since the overlap of the meshing gear pair is greater than or equal to 1, in order to express the load distribution and static transmission error under continuous transmission, the deformation coordination equation is introduced here to divide the mesh as follows: Figure 6 As shown, the crack path is Figure 7 shown.

[0147] S16. Iteratively solve the deformation coordination equation. If the contact force is less than zero during the iteration process, the meshing point is regarded as a non-contact state. The contact force vector F and the static transmission error ste of all meshing points are finally obtained.

[0148] S2. Establish a gear dynamics analysis model using the tooth base polycondensation method.

[0149] S21, such as Figure 8 As shown in the figure, the condensation point is the location point of the model reduction center, and the ultimate goal is to obtain the mass and stiffness matrix of the condensation point. A flexible coupling relationship is established between the main node and the condensation point, and the constraint relationship between the interface node degree of freedom and the condensation point degree of freedom adopts a displacement weighted algorithm, allowing relative deformation between the interface nodes, which has higher calculation accuracy than the rigid coupling relationship.

[0150] S22, considering axial, lateral and torsional deformation, use Timoshenko beam elements to establish the gear shaft segment, the gear shaft parameters are as follows Fig. 9 As shown in Figure 2, the stiffness matrix, mass matrix and gyro matrix of the beam unit model are obtained. This unit can not only consider the stiffness, damping and mass of the shaft, but also the bending, torsion and shear effects of the transmission shaft.

[0151] S23, test by CL-100 gear fatigue testing machine, obtain the test signal of gear. Put the healthy gear and the faulty gear into CL-100 gear fatigue testing machine respectively. The test point and the position of the test instrument are as follows: Fig.10 As shown. Obtain the variable speed experimental signal as Fig.11 shown.

[0152] S3. Construct the tooth root crack degree identification feature based on the combined simulation experimental data.

[0153] S31. According to the test process, 24 groups of experimental data under working conditions were obtained. The vibration frequency characteristics of the experimental signal are mainly the meshing frequency modulating the rotation frequency of the driving wheel and the driven wheel, f m is the meshing frequency, f r1 is the driving wheel rotation frequency, f r2 is the rotation frequency of the driven wheel. At the same time, the experimental measured acceleration signals of health and failure are compared and verified with the dynamic model of the present invention, such as Fig.12 The experiment proves that, through the comparison of simulated acceleration signals, the dynamic model can better simulate the working state of the gear system under fault conditions, providing a basis for the establishment of fault indicators.

[0154] S32, the change trend of the main frequency components of the simulation signal under the healthy state and crack state is consistent with the experimental signal change, which proves that the acceleration signal obtained by the dynamic model can effectively simulate the working conditions of different crack fault types. Fig.13 As shown in the figure, by performing spectrum analysis on different crack degrees of the test gear under three-level load conditions of 1500r / min, the rotation frequency of the driving wheel and the rotation frequency of the driven wheel can be seen in the figure.

[0155] S33, such as Fig.14 As shown, considering the frequency change of cracked gear under variable load conditions, under the condition of 3000r / min speed, ensuring the same crack degree, when the gear working condition is changed from primary load to secondary load, it is found that the amplitude of meshing frequency multiplication increases proportionally, and changes rapidly with the increase of load level. As the load increases, the modulation frequency near the meshing frequency multiplication gradually decreases. When the secondary load is converted to the tertiary load, the meshing frequency and the multiplication amplitude change to a small extent, and the meshing frequency is not obviously submerged in the modulation frequency of the rotation frequency and the meshing frequency. It can be seen that with the load change, the frequency amplitude of meshing and its multiplication changes proportionally.

[0156] S34, the proposed indicator construction is as follows Fig.14 As shown. First, according to the real crack propagation path obtained from the crack propagation experiment, the TVMS of different crack conditions is introduced into the dynamic model as the internal excitation source; the simulation signal obtained by the dynamic model can supplement the acceleration signal under the working condition missing in the experiment. And the appropriate time-frequency domain characteristic sub-indicator is obtained through sensitivity analysis. Parameters are obtained from the simulation signal to construct the crack index. After the actual signal is denoised by the VMD method, the crack stage is identified and verified by the index to complete the entire diagnosis process.

[0157] S35, such as Fig.15As shown in the figure, the frequency domain image of the vibration signal obtained with the expansion of the gear crack degree under the secondary load condition at a speed of 1450r / min is displayed. As the crack degree deepens, the excitation of the gear transmission system increases, and the amplitude and frequency components in the acceleration signal will change to a certain extent. The time domain characteristic index and frequency characteristic index reflect the time and frequency domain information corresponding to the vibration signal. The mapping relationship between the crack fault degree and the time and frequency domain index of the spur gear system dynamic signal is obtained, which proves the feasibility of creating crack indicators.

[0158] S36, in order to determine the sub-indicators for accurately judging the crack fracture stage, the dynamic model was used to obtain the gear system under 10 load levels (torque conversion range is 2N·m to 52N·m, and is evenly divided into T1-T 10 The vibration acceleration signals under the 7th level of tooth root crack (S1-S7) were used to quantify the crack propagation stage of the gear. Then, the Pearson correlation coefficient was used to analyze the correlation of various time-domain and frequency-domain fault indicators with quantified faults under variable crack stages and variable load levels.

[0159] S37, the indicator judgment result is as follows Fig.17 As shown in Figure 2, standard deviation, root mean square and frequency domain index F are selected as the criteria for index construction. These indices have a great correlation with the changes in crack stage and load state, and therefore have a higher sensitivity than the indicators of crack stage and load state changes.

[0160] S4. Establish an optimization model for gear pairs containing assembly errors.

[0161] S41. The advantages of the proposed index over the traditional index are proved by experimental data. The generalization of the proposed index is proved by the signals of different gear systems.

[0162] S42, verify the proposed indicators through the confusion matrix, such as Fig.18 As shown. The indicator showed high crack detection ability in different classification models. In particular, the classification accuracy of the back propagation neural network (BPNN) model reached 99.1%, which was significantly higher than the highest accuracy of 89.4% of other standard indicators. This shows that the proposed indicator can effectively reflect the extent of crack propagation under variable load conditions, provides a reliable basis for studying crack propagation in actual scenarios, and effectively eliminates the interference of load on crack stage identification. The practical application potential of the indicator in gear system diagnosis and maintenance is demonstrated.

[0163] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

[0164] In the above embodiments of the present invention, the description of each embodiment has its own emphasis. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0165] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. Among them, the device embodiments described above are only schematic. For example, the division of the units can be a logical function division. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of units or modules, which can be electrical or other forms.

[0166] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple units. Some or all of the units may be selected according to actual needs to achieve the purpose of the present embodiment.

[0167] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0168] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions for a computer device (which can be a personal computer, a server or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), mobile hard disk, magnetic disk or optical disk and other media that can store program codes.

[0169] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for spur gear system crack fault diagnosis based on actual crack growth curve, characterized in that: The specific steps include: Based on the modal reduction of gears, a gear dynamics analysis model is established; Combined with the historical data of gear crack fatigue growth experiments, the root crack growth path is obtained and substituted into the gear dynamics analysis model to obtain the time-varying meshing stiffness of the cracked gear. Through the gear dynamics analysis model, the simulated acceleration signal data is obtained to establish the tooth root crack degree identification characteristics; The tooth root crack degree identification feature is used as the actual signal, and the gear crack extension degree is determined by the variational mode decomposition method.

2. The spur gear system crack fault diagnosis method based on actual crack growth curve according to claim 1 is characterized in that: The modal contraction of the gear is realized by using the Guyan method to achieve static reduction of the degree of freedom, and a contraction point is set; the shaft system of the gear is discretized into multiple shaft segments, coupling relationships are established between the shaft segments through Timoshenko beam units, and structural flexibility is simulated through Timoshenko beam units.

3. The spur gear system crack fault diagnosis method based on actual crack growth curve according to claim 1, characterized in that: The establishment of the gear dynamics analysis model includes: The gear is modally condensed, and the gear condensation transformation matrix is: Among them, T represents the dimension transformation matrix, K ss represents the node stiffness matrix, K sm represents the master-slave node coupling stiffness matrix, Φ sm represents the master-slave node coupling eigenvector, Φ mm represents the slave node feature vector; The mass matrix M of the gear model after polycondensation 12 and the stiffness matrix K 12 According to the requirements of polycondensation, the modal characteristic equation and orthogonal conditions in the gear polycondensation transformation matrix are satisfied, so the model stiffness matrix K after polycondensation is 12 and the mass matrix M 12 The expression is: K 12 =K mm +T T K sm +K ms T+T T K ss T M 12 =M mm +T T M sm +M ms T+T T M ss T Among them, K mm represents the main node stiffness matrix, K ms represents the master-slave node coupling stiffness matrix, M mm represents the master node mass matrix, M sm represents the master-slave node coupling mass matrix, M ms represents the master-slave node coupling mass matrix, M ss represents the slave node mass matrix; The differential equation of motion of the spur gear pair is obtained as: Among them, F 12 is the external load vector, X 12 is the displacement vector, C is the damping matrix, using proportional damping; G is the gyro matrix, including the gyro matrix of the gear; The dynamic equation of the total gearbox gear system transmission is obtained as: Among them, X is the generalized coordinate vector, M is the mass matrix of the whole system, C is the damping matrix of the whole system, K is the stiffness matrix of the whole system, and F T is the external force vector.

4. The method for diagnosing crack faults in spur gear systems based on actual crack growth curves according to claim 1, characterized in that: The calculation method of the time-varying meshing stiffness of the cracked gear includes: Get the data point position information N among multiple cracks ki =(x ki ,y ki ), where k is the number of test lines, i=1,2,…n represents the number of sampling points, N represents the polynomial degree, and the mean square error is represented as Q. The calculation method of Q is as follows: Convert to normal equation: Among them, a n represents the polynomial coefficients, x i Indicates the horizontal coordinate of the sampling point, y i represents the ordinate of the sampling point, and A is the Vandermonde matrix of the abscissa of the sampling point; The deformation coordination equation is introduced, and the deformation coordination equation expression is: -(l b +λ c )·F+I n×1 ·ste=e Where ste represents the static transmission error, ε represents the initial separation gap vector of each point, and λ b represents the overall bending flexibility matrix of all meshing points, λ c represents the overall contact flexibility matrix, F represents the contact force vector formed by the meshing points, and I n×1 Represents an n×1-dimensional matrix with all elements being 1; Iteratively solve the deformation coordination equation. If the contact force is less than zero during the iteration process, the meshing point is considered as a non-contact state. Finally, the contact force vector F and static transmission error ste of all meshing points are obtained. The meshing stiffness of each meshing position is expressed as: Among them, k represents the meshing stiffness, F represents the total contact force, and nlste represents the no-load transmission error; The gear tooth load contact analysis method is adopted to calculate the time-varying meshing stiffness of the gear pair crack by constraining the tooth root circle and bringing the fitted cubic polynomial crack propagation path into the gear tooth.

5. The spur gear system crack fault diagnosis method based on actual crack growth curve according to claim 1, characterized in that: The establishment of the tooth root crack degree identification feature includes: The state of the gear transmission system is detected by time-frequency domain indicators, and the indicators that are sensitive to the degree of crack extension are determined as crack fault characteristic indicators. The standard deviation, root mean square value and frequency domain indicators are selected as the initial indicators of crack fault characteristics: Among them, σ x represents the standard deviation, N represents the number of sample points, x(n) represents the signal value of the sampling point, x represents the mean value of the signal of the sampling point, F represents the frequency domain index, s(k) is the spectrum of the signal x(n), k = 1, 2, ..., K; K is the number of spectral lines; f k is the frequency value of the kth spectral line, x rms represents the root mean square value; The vibration acceleration response of the gear system under 10 load levels, torque range of 2N·m~52N·m, averagely divided into T1~T10 levels, and 7 levels of tooth root crack, S1~S7, was obtained through the dynamic model; the crack propagation stage of the model was quantified, and the sensitivity analysis of the indicators was carried out at the same time, and the root mean square error was calculated using the measured values ​​of the response indicators of each working condition and the normalized quantized value of the crack stage; Among them, R j represents the RMSE value; j represents different index values ​​(σ x ,x rms ,F), i represents different crack stages (S1-S7), v i,j Represents the measured values ​​of each response index and different crack stages, s i Indicates the quantitative value of each crack stage; calculates the root mean square error RMSE through the measured value of each working condition signal index and the normalized quantitative value of the crack stage, and performs sensitivity analysis on the index; Calculate the initial indicator XT from the simulation signal d , the initial index XT d It is expressed as: Among them, k j and k b is the sub-indicator coefficient; Initial indicator XT obtained from simulation signal d Establish the tooth root crack degree identification feature XT to judge the gear crack stage, and express the index XT as: Among them, α i and η i is the parameter of the tooth root crack degree identification feature XT, T is the gearbox working load, X1 and X2 represent T1 and T respectively. 10 The difference between the crack growth parameters at different crack stages and initial index under different load levels, k d It represents the difference between the initial index crack growth parameters and the different load levels in the crack stage.

6. The method for spur gear system crack fault diagnosis based on actual crack growth curve according to claim 5, characterized in that: The sub-index coefficient k j and k b It is expressed as: Among them, R j It represents the root mean square error between each sub-indicator and the quantitative crack extension value, and e is the correction factor.

7. The method for diagnosing crack faults in spur gear systems based on actual crack growth curves according to claim 1, characterized in that: The variational modal decomposition method uses the tooth root crack degree identification feature as the actual signal, and uses the VMD reconstruction method to denoise the signal before index judgment, filters and reconstructs the intrinsic mode function components obtained after VMD decomposition, and uses the denoised signal for index judgment to determine the gear crack extension degree.

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