Planetary gear system time-varying transmission path analysis and fault tracing method

Abstract

The invention discloses a time-varying transmission path analysis and fault tracing method for a planetary gear system. The method comprises the following steps of performing parametric decomposition on a signal of a gear ring measuring point; carrying out parameterized reconstruction on the signal; performing time-varying path decomposition based on meshing force identification on the signal; and carrying out fault tracing based on the time-varying path decomposition. According to the method, the contribution degree of each transmission path can be obtained, so that the health condition of each planet wheel is tracked, and the method can well serve health detection and fault diagnosis of the planetary gear transmission system.

Description

Technical Field

[0001] The present invention relates to the field of transmission technology, and in particular to a method for analyzing time-varying transmission paths and tracing faults of a planetary gear system. Background Art

[0002] Planetary gear transmission systems are widely used in the automotive, aerospace, manufacturing and other industries. Their health detection and fault diagnosis research is related to the stable and reliable operation of major equipment. In industry, acceleration sensors are generally arranged to detect the vibration of the system, so as to track the dynamic service performance of the system. In a typical planetary gear transmission system, for the acceleration sensor installed on the ring gear or the housing, the measuring point on the stationary part will experience periodic impact caused by the rotation of the planet carrier. This effect is called the passing effect of the planetary gear. The passing effect of the planetary gear will cause amplitude modulation and sidebands in the signal. Since the distance from the measuring point to the excitation source (gear meshing position) is time-varying, this problem is called the time-varying transfer path problem of the planetary gear.

[0003] According to the amount of physical information incorporated into the transfer path model, it can be divided into pure phenomenological model, semi-phenomenological model and physical model. In the pure phenomenological transfer path model, the excitation and transfer function of the system are described by phenomenological function expressions. The theoretical formula of the pure phenomenological model is very complex and has many parameters, especially after considering multiple influencing factors; a major drawback of the pure phenomenological model is that the theoretical formula and parameters lack physical meaning. The semi-phenomenological transfer path model refers to the excitation or transfer function in the model that incorporates part of the physical information, while the remaining part is still replaced by a phenomenological model without physical meaning; the physical information incorporated can come from both the dynamic model and the experiment. In response to the problem that these two types of models lack physical interpretability, scholars have proposed a transfer path model based on physical information, that is, to replace the expressions that lack physical meaning in the phenomenological model with dynamic model simulation results or measured results.

[0004] At present, planetary gear fault diagnosis and fault tracing mostly use pure data-driven methods such as deep learning, machine learning and signal processing, which lack physical explanation and cannot reflect the dynamic mechanism of the signal. In addition, existing fault diagnosis research generally focuses on local impact faults. How to effectively diagnose stable faults is the focus and difficulty of current research.

[0005] Therefore, technicians in this field are committed to providing a time-varying transfer path analysis and fault tracing method for a planetary gear system to achieve time-varying transfer path analysis of planetary gears. Summary of the invention

[0006] In view of the defects in the prior art, the technical problem to be solved by the present invention is how to provide a method for analyzing the time-varying transmission path and tracing the faults of planetary gears.

[0007] To achieve the above object, the present invention provides a method for analyzing time-varying transmission paths and tracing faults of a planetary gear system, which is characterized by comprising the following steps:

[0008] Step 1: parameterize and decompose the signal of the gear ring measurement point;

[0009] Step 2, performing parameterized reconstruction on the signal;

[0010] Step 3, performing time-varying path decomposition of the signal based on meshing force identification;

[0011] Step 4: perform fault tracing based on the time-varying path decomposition.

[0012] Furthermore, the signal parameter decomposition method is:

[0013]

[0014] Where N is the number of signal points, K is the number of components in the signal, and r(t) is the residual signal;

[0015] The instantaneous frequency is calculated as:

[0016]

[0017] In the formula, f i is the instantaneous frequency of the i-th signal component;

[0018]

[0019] Where, L f is the order of the Fourier model, F0=f s / NQ f , f s is the sampling frequency, Q f are the Fourier basis parameters.

[0020] Preferably, Q f The value is 2.

[0021] Furthermore, the parameterized reconstruction method of the signal is:

[0022] The amplitude parameter vector is estimated using the Tikhonov regularization method:

[0023]

[0024] In the formula, λ sis the regularization parameter;

[0025] Reconstruct signal components based on amplitude parameters:

[0026]

[0027] Furthermore, the step 3 comprises:

[0028] Step 3.1, construct the meshing force basis vector;

[0029] Step 3.2, construct the response basis matrix;

[0030] Step 3.3, identify the meshing force on each path.

[0031] Furthermore, the basis vector of the meshing force is:

[0032] F base (t) = [sin(ω m t)cos(ω m t)…sin(N m ω m t)cos(N m ω m t)]

[0033] In the formula, ω m is the meshing frequency, N m is the order of meshing frequency.

[0034] Furthermore, the substrate response signal is:

[0035]

[0036] Where, the subscripts s and c represent the responses under sine unit force and cosine unit force, respectively;

[0037] For N p planetary gears, the base matrix is:

[0038]

[0039] Furthermore, the relationship between the base response signal and the reconstructed signal is:

[0040] s base A m =s re

[0041] In the formula, A m is the meshing force magnitude vector:

[0042]

[0043] The meshing force on the i-th path is:

[0044]

[0045] Furthermore, the fault information of the planetary gear is tracked according to the change in the contribution ratio of the transmission path, and the location of the fault is traced according to the abnormality of the contribution of each path.

[0046] Furthermore, the contribution ratio of the i-th transmission path is:

[0047]

[0048] In the formula, A i m is the meshing force amplitude corresponding to the i-th transmission path.

[0049] The present invention has at least the following beneficial technical effects:

[0050] The time-varying transfer path analysis and fault tracing method of the planetary gear system of the present invention can obtain the contribution of each transfer path, so as to track the health status of each planetary gear; the time-varying path decomposition algorithm based on meshing force identification can successfully diagnose the stability fault of the planetary gear and identify the position and number of faulty planetary gears, which can well serve the health detection and fault diagnosis of the planetary gear transmission system and has broad application prospects in the fields of machinery, ships, aerospace, etc.

[0051] The concept, specific structure and technical effects of the present invention will be further described below in conjunction with the accompanying drawings to fully understand the purpose, characteristics and effects of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 is a schematic diagram of meshing force loading according to an embodiment of the present invention;

[0053] Figure 2 is a flow chart of a method for analyzing time-varying transmission paths and tracing faults of a planetary gear system according to an embodiment of the present invention;

[0054] Figure 3 is a schematic diagram of a substrate response signal according to an embodiment of the present invention;

[0055] Figure 4 It is the gear ring acceleration order spectrum of the original signal at different signal-to-noise ratios;

[0056] Figure 5 It is the gear ring acceleration order spectrum of the reconstructed signal at different signal-to-noise ratios;

[0057] Figure 6 It is a schematic diagram of the theoretical and identified meshing force fluctuation components under different signal-to-noise ratios;

[0058] Figure 7 It is a schematic diagram of the path contribution ratio. DETAILED DESCRIPTION

[0059] The following describes the preferred embodiments of the present invention to make its technical content clearer and easier to understand. The present invention can be embodied in many different forms of embodiments, and the protection scope of the present invention is not limited to the embodiments mentioned in the text.

[0060] In the drawings, components with the same structure are indicated by the same numerical reference numerals, and components with similar structures or functions are indicated by similar numerical reference numerals. The size and thickness of each component shown in the drawings are arbitrarily shown, and the present invention does not limit the size and thickness of each component. In order to make the illustration clearer, the thickness of the components is appropriately exaggerated in some places in the drawings.

[0061] The meshing force diagram of the planetary gear system is as follows: Figure 1 As shown, for this planetary gear system, the present invention provides a method for analyzing the time-varying transfer path and tracing the faults of the planetary gear system. The present invention obtains the meshing force on each planetary gear-ring gear path through a parameterized identification strategy to realize the analysis of the time-varying transfer path of the planetary gear; uses a signal parameterized decomposition and parameterized reconstruction method to pre-process the original signal to facilitate the subsequent meshing force identification; relies on a semi-analytical flexible ring gear model to carry out path decomposition and fault tracing based on meshing force identification.

[0062] against Figure 1 The planetary gear system shown in FIG. 1 is an embodiment of a method for analyzing a time-varying transmission path and tracing a fault of a planetary gear system according to the present invention. Figure 2 As shown, the method is specifically as follows.

[0063] Step 1: parameterize and classify the signals of the gear ring measurement points.

[0064] For planetary gear transmission systems, the signal of the ring gear measurement point mainly comes from the planetary gear-ring gear transmission path; the excitation of the sun gear-planetary gear pair is greatly attenuated when transmitted to the ring gear measurement point, so the contribution of the sun gear vibration to the measurement point is ignored. The number of planetary gears in the planetary gear transmission system is recorded as N p , then the signal of the gear ring measuring point can be regarded as N p The contribution of each path can be represented by the meshing force of the planetary gear-ring gear pair.

[0065] For the gear transmission system, the meshing force has the meshing frequency and its harmonics as the main frequency components. The vibration response of the measuring point is mainly composed of the modulation frequency of the meshing frequency and the planet carrier frequency, and also includes noise components of other frequencies. A set of causal relationships is formed between the meshing force and the meshing frequency components in the measuring point response. This set of causal relationships is used to identify the meshing force. By constructing the meshing force basis vector and the response basis matrix, the meshing force identification problem is transformed into a signal instantaneous amplitude estimation problem, so that the meshing force on each ring gear-planet wheel path can be identified, and then the absolute contribution of each ring gear-planet wheel path can be obtained. In order to eliminate the influence of frequency components other than the meshing frequency as much as possible, the signal parameterization decomposition is used to reconstruct the signal to achieve the purpose of noise reduction and retain only the meshing frequency components.

[0066] The signal of rotating machinery is generally a cyclostationary signal, which can be decomposed into the form of superposition of several signal components. Through decomposition and reconstruction, the influence of frequency components other than the meshing frequency can be eliminated as much as possible to achieve the purpose of noise reduction and retain only the meshing frequency components. For a signal containing N point data, it is decomposed into the form of superposition of several signal components:

[0067]

[0068] Where K is the number of components in the signal and r(t) represents the residual signal.

[0069] The instantaneous frequency related term is:

[0070]

[0071] In the formula, f i is the instantaneous frequency of the i-th signal component.

[0072] Use the Fourier series form to characterize the instantaneous amplitude function u i (t) and v i (t):

[0073]

[0074] Where, L f is the order of the Fourier model.

[0075] Frequency resolution F0 = f s / NQ f , f s is the sampling frequency, Q f = 1 is the standard Fourier basis, Q f = 2 is a redundant Fourier basis; since the redundant Fourier basis can better characterize complex signals, Q f =2.

[0076] Convert the signal model into matrix form:

[0077] s=Wy+r,(5)

[0078] W=[W1…W K ],(6)

[0079]

[0080] Where s is the signal array to be analyzed:

[0081] s=[s(t0)s(t1)…s(t N-1 )] T , (8)

[0082] r is the remaining signal array:

[0083] r=[r(t0)r(t1)…r(t N-1 )] T ,(9)

[0084] y i Contains the amplitude information of the i-th signal component:

[0085]

[0086] W i The matrix contains the instantaneous frequency information of the i-th signal component:

[0087]

[0088] In the formula, the superscripts c and s correspond to the cosine term and sine term respectively, diag represents the diagonal matrix, and F t The matrix contains the time information:

[0089]

[0090] Step 2: Reconstruct the signal parameterically.

[0091] The amplitude parameter vector is estimated using the Tikhonov regularization method:

[0092]

[0093] In the formula, the superscript “~” represents the estimated value, λ s is the regularization parameter.

[0094] Each signal component can be reconstructed according to the amplitude parameter, and the reconstructed signal is:

[0095]

[0096] Step 3: Decompose the signal into time-varying paths based on meshing force identification. This step specifically includes the following processes:

[0097] Step 3.1: Construct the meshing force basis vector.

[0098] The simple harmonic unit force is used as the basis and applied to the flexible gear ring; according to the direction of the meshing force, the meshing force is decomposed into radial component and axial component, as shown in the following figure: Figure 1 shown.

[0099] The basis vectors for the forces are:

[0100] F base (t) = [sin(ω m t)cos(ω m t)…sin(N m ω m t)cos(N m ω m t)],(19)

[0101] In the formula, ω m is the meshing frequency, N m is the order of meshing frequency.

[0102] Step 3.2: Construct the response basis matrix.

[0103] Apply each element of the force basis vector to the flexible gear ring to obtain the basis response signal:

[0104]

[0105] Where the subscripts s and c represent the responses under sine unit force and cosine unit force, respectively.

[0106] An example of a substrate response signal is Figure 3 As shown, since the path length between the meshing point and the response extraction point is time-varying, even if the amplitude of the meshing force does not change with time, the response signal on the ring gear has a very obvious amplitude modulation feature.

[0107] Planetary gear system has N p planetary gears, we need to obtain N p The base response signals are combined into a matrix:

[0108]

[0109] Step 3.3, identify the meshing force on each path.

[0110] The response of the measurement point is regarded as the linear superposition of the base response signal. The relationship between the base response signal and the reconstructed signal can be expressed as:

[0111] s base A m =s re ,(twenty two)

[0112] In the formula, A m is the meshing force amplitude vector, representing the force basis vector F base The amplitude corresponding to each element in .

[0113] A m Decompose into N p Blocks, each block vector corresponds to a planetary gear-ring gear meshing pair:

[0114]

[0115] By solving the overdetermined linear equations (Eq. (22)), we can obtain the amplitude corresponding to the basis vector of the force, and thus identify the meshing force on the i-th path:

[0116]

[0117] Step 4: Perform fault tracing based on time-varying path decomposition.

[0118] The contribution ratio of the i-th transmission path is defined as:

[0119]

[0120] In the formula, A i m is the meshing force amplitude corresponding to the i-th transmission path.

[0121] The fault condition of the planetary gear is tracked according to the change of the contribution ratio of the transmission path, and the location of the fault is traced according to the abnormal contribution of each path.

[0122] Based on the planetary gear time-varying transmission path analysis and fault tracing method of this embodiment, a simulation analysis of the planetary gear system is carried out. In the simulation analysis, the parameters of the planetary gear transmission system are shown in Table 1.

[0123] Table 1 Parameters of planetary gear transmission system

[0124]

[0125] * Refers to the outer diameter of the gear ring

[0126] For a planetary gear system with four planetary gears, the meshing force is assumed to be in the form of:

[0127]

[0128] In the subsequent meshing force identification stage, the above theoretical meshing force expression will be regarded as a benchmark and compared with the meshing force obtained by identification. The vibration acceleration on the gear ring is collected for meshing force identification. In order to analyze the anti-noise ability of the proposed algorithm, white noise of different amplitudes is added to the simulation signal. The order spectrum of the gear ring acceleration under different signal-to-noise ratios is shown in the figure below. Figure 4 As shown in Figure 2, it can be seen that when the signal-to-noise ratio (SNR) is -40dB, the signal is completely submerged in the noise.

[0129] The signal is denoised using the signal parameterized decomposition and reconstruction algorithm. The results are as follows: Figure 5 Compared with the original signal, the reconstructed signal removes a large amount of non-periodic noise and only retains the modulation components of the meshing frequency and the planet carrier frequency.

[0130] The meshing force of the planetary gear-ring gear pair is identified by using the algorithm of this embodiment. The identification results under different signal-to-noise ratios are as follows: Figure 6 As shown in the figure, it can be seen that the proposed meshing force identification algorithm has strong anti-noise ability. At the signal-to-noise ratio level of -20dB, the identified meshing force is still almost completely consistent with the theoretical meshing force; under the condition of -40dB, the signal is completely submerged in the noise, but the meshing force identification result still has a certain accuracy. The above anti-noise performance analysis fully demonstrates that the proposed meshing force identification algorithm has a certain robustness to noise.

[0131] In order to simulate the degradation process of the planetary gear throughout its life cycle, it is assumed that the meshing force of the third pair of planetary gear-ring gear pairs degrades according to the following law:

[0132]

[0133] Where N is the operation cycle, the unit is ×10 6 change.

[0134] The path contribution ratio of the third transmission path under different degradation cycles is Figure 7 As shown in the figure, with the degradation process, the proportion of the third contribution continues to increase, and the degradation speed shows a trend of first fast and then slow. The evolution of damage will destroy the equilibrium relationship between the various transmission paths, and the proportion of path contribution can reflect the degree of "imbalance" of the various transmission paths of the planetary gear.

[0135] The time-varying transfer path analysis and fault tracing method of the planetary gear system of the present invention accurately describes the flexible deformation of the ring gear and the amplitude / frequency modulation law of the ring gear measurement point signal from the perspective of dynamic mechanism; the method can obtain the contribution of each transfer path, so as to track the health status of each planetary gear; the time-varying path decomposition algorithm based on meshing force identification can successfully diagnose the stability fault of the planetary gear, and can identify the position and number of faulty planetary gears, which can well serve the health detection and fault diagnosis of the planetary gear transmission system.

[0136] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A method for time-varying transfer path analysis and fault tracing of a planetary gear system, characterized in that: The following steps are involved: Step 1: parameterize and decompose the signal of the gear ring measurement point; Step 2, performing parameterized reconstruction on the signal; Step 3, performing time-varying path decomposition of the signal based on meshing force identification; Step 4: perform fault tracing based on the time-varying path decomposition.

2. The method for time-varying transfer path analysis and fault tracing of a planetary gear system according to claim 1, characterized in that: The signal parameter decomposition method is: Where N is the number of signal points, K is the number of components in the signal, and r(t) is the residual signal; The instantaneous frequency is calculated as: In the formula, f i is the instantaneous frequency of the i-th signal component; Where, L f is the order of the Fourier model, F0 = f s / NQ f , f s is the sampling frequency, Q f are the Fourier basis parameters.

3. The method for time-varying transfer path analysis and fault tracing of a planetary gear system according to claim 2, characterized in that: Q f The value is 2.

4. The method for time-varying transfer path analysis and fault tracing of a planetary gear system according to claim 2, characterized in that: The parameterized reconstruction method of the signal is: The amplitude parameter vector is estimated using the Tikhonov regularization method: In the formula, λ s is the regularization parameter; Reconstruct signal components based on amplitude parameters:

5. The method for time-varying transfer path analysis and fault tracing of a planetary gear system according to claim 4, characterized in that: The step 3 comprises: Step 3.1, construct the meshing force basis vector; Step 3.2, construct the response basis matrix; Step 3.3, identify the meshing force on each path.

6. The method for time-varying transfer path analysis and fault tracing of a planetary gear system according to claim 5, characterized in that: The basis vector of the meshing force is: F base (t)=[sin(ω m t)cos(ω m t)…sin(N m oh m t)cos(N m oh m (t)] In the formula, ω m is the meshing frequency, N m is the order of meshing frequency.

7. The method for time-varying transfer path analysis and fault tracing of a planetary gear system according to claim 6, characterized in that: The substrate response signal is: Where, the subscripts s and c represent the responses under sine unit force and cosine unit force, respectively; For N p planetary gears, the base matrix is:

8. The method for time-varying transfer path analysis and fault tracing of a planetary gear system according to claim 7, characterized in that: The relationship between the substrate response signal and the reconstructed signal is: s base A m =s re In the formula, A m is the meshing force magnitude vector: The meshing force on the i-th path is:

9. The method for time-varying transfer path analysis and fault tracing of a planetary gear system according to claim 8, characterized in that: The fault information of the planetary gear is tracked according to the changes in the contribution ratio of the transmission path, and the location of the fault is traced according to the abnormal contribution of each path.

10. The method for time-varying transfer path analysis and fault tracing of a planetary gear system according to claim 9, characterized in that: The contribution ratio of the i-th transmission path is: In the formula, A i m is the meshing force amplitude corresponding to the i-th transmission path.

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