On-line measurement system for contact area of worm pair based on wear law modeling

Abstract

The present application belongs to the field of length and area measurement, and relates to a worm pair contact area online measurement system based on wear law modeling. The system comprises a sound and vibration signal synchronous acquisition end for acquiring acoustic emission and vibration mixed signals; a time-varying working condition feature extraction end for carrying out variational modal decomposition and extracting multi-scale energy entropy as an observation vector; a physical constraint state space modeling end for setting a real contact area as a state vector, embedding a mapping relationship between wear volume, normal load and sliding distance in the Archard wear law into a state transition equation, and establishing a nonlinear observation equation with multi-scale energy entropy as an observation matrix; and a hidden state Bayesian inversion end adopting an unscented Kalman filtering algorithm. The present application overcomes the problem of direct measurement failure caused by the shielding of a closed box, realizes online measurement without shutdown, introduces a physical wear law into state constraints, eliminates data-driven model drift, improves the robustness of variable working conditions, suppresses interference through feature extraction, and improves the inversion signal-to-noise ratio.

Description

Technical Field

[0001] This invention belongs to the field of length and area measurement, and relates to an online measurement system for the contact area of ​​worm gear pairs based on wear law modeling. Background Technology

[0002] As a key component in mechanical transmission systems, the contact area of ​​worm gear pairs directly reflects the meshing state and wear degree of the tooth surfaces. Current technologies primarily employ static offline methods to measure the contact area of ​​worm gear pairs. The most typical conventional approach is the red lead imprint method, which requires applying red lead powder to the tooth surfaces while the worm gear pair is stopped, followed by manual rotation to engage the teeth, and then disassembly to observe the contact imprint and calculate the area. Another conventional approach is image recognition based on industrial cameras, using a vision sensor installed inside the gearbox to capture images of the tooth surface contact spots and perform pixel statistics to obtain the area. Both of these approaches rely on direct physical or optical observation of the tooth surfaces, requiring an unobstructed observation path. However, worm gear pairs typically operate within enclosed gearboxes filled with lubricating oil, where the optical line of sight is severely affected by oil film obstruction and reflection. Furthermore, the limited space inside the gearbox makes it impossible to install a vision sensor. Therefore, existing direct observation-based methods cannot achieve online measurement while the worm gear pair is running continuously, failing to reflect the dynamic contact state under actual operating loads.

[0003] To overcome the limitations of direct observation, existing technologies have developed indirect monitoring schemes based on vibration signals. These schemes collect vibration signals during transmission by mounting vibration acceleration sensors on the outer surface of the gearbox, extracting time-domain and frequency-domain features such as the root mean square value of vibration or the amplitude of the meshing frequency. The trends of these features are then used to establish an empirical mapping relationship with the degree of wear, thereby assessing the wear state of the worm gear pair. While this indirect monitoring scheme achieves online data acquisition, it has inherent limitations. Vibration signals contain a large amount of interference from the resonance of the motor, bearings, and gearbox. Simply extracting conventional features cannot remove interference information unrelated to the contact area. Furthermore, there is only a rough qualitative correlation between vibration energy and the degree of wear; a quantitative analytical mapping between vibration response and contact area is not established, making it impossible to output a specific value for the contact area. Moreover, this invention does not consider the physical evolution of wear. When the load and speed change dynamically, the changes in vibration characteristics due to fluctuations in operating conditions mask the subtle changes caused by wear, leading to distorted monitoring results.

[0004] Based on the aforementioned implementation methods and shortcomings of existing technologies, the following core technical problems exist in this field: In enclosed worm gear pairs under lubrication and dynamic shielding conditions, the contact area cannot be directly measured online. Furthermore, existing indirect monitoring methods based on vibration signals lack a quantitative inversion mechanism that deeply integrates multimodal observation signals with the physical evolution of wear. Existing indirect monitoring schemes only remain at the level of feature extraction and qualitative correlation of wear degree, failing to finely decouple the multimodal signals reflecting micro-friction and macro-impact, failing to construct a state space with contact area as a latent variable, and failing to use the physical laws reflecting the essence of wear as constraints for state evolution. This results in an insurmountable gap between the observed signal and the contact area, making it impossible to accurately obtain the dynamic true contact area under complex and variable working conditions. Summary of the Invention

[0005] The purpose of this invention is to provide an online measurement system for the contact area of ​​a worm gear pair based on wear law modeling, which can effectively solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: The online measurement system for the contact area of ​​a worm gear pair based on wear law modeling includes: a synchronous acquisition terminal for acoustic and vibration signals, used to acquire mixed acoustic emission signals and mixed vibration signals during the operation of the worm gear pair; The time-varying operating condition feature extraction end is used to perform variational mode decomposition on the acoustic emission mixed signal and the vibration mixed signal to obtain the intrinsic mode functions reflecting macroscopic impact and microscopic friction, and extract multi-scale energy entropy as the observation vector; The physical constraint state space modeling end is used to set the actual contact area as the state vector, embed the mapping relationship between wear volume, normal load and sliding distance in Arcard wear law into the state transition equation, and establish a nonlinear observation equation with the multi-scale energy entropy as the observation matrix. The hidden-state Bayesian inversion end is used to employ an unscented Kalman filter algorithm to drive the state transition equation and the nonlinear observation equation with the observation vector to perform recursive estimation and output the continuous-time evolution value of the true contact area.

[0007] Preferably, when the time-varying operating condition feature extraction end performs variational mode decomposition on the acoustic emission mixed signal and the vibration mixed signal, it adopts a variational mode decomposition adaptive optimization method based on the minimum value of envelope entropy to determine the penalty factor and the number of decomposition layers of variational mode decomposition. The acoustic emission mixed signal and the vibration mixed signal are divided into frequency bands to separate the high-frequency intrinsic mode functions containing meshing impact characteristics and the low-frequency intrinsic mode functions containing friction and wear characteristics. The envelope spectral entropy of the high-frequency intrinsic mode functions and the singular spectral entropy of the low-frequency intrinsic mode functions are calculated. The envelope spectral entropy and the singular spectral entropy are combined to form the multi-scale energy entropy.

[0008] Preferably, when the physical constraint state space modeling end embeds the mapping relationship between wear volume, normal load, and sliding distance in Arcard's wear law into the state transition equation, it introduces a time-varying wear coefficient that decays with running time. The time-varying wear coefficient is used as an extended state variable in the state vector to construct an exponential decay constraint relationship between the time-varying wear coefficient and the oil film thickness change rate during the operation of the worm gear pair. The exponential decay constraint relationship is used as an auxiliary evolution equation for the state transition equation, so that the wear volume dynamically adjusts the time-varying wear coefficient according to the oil film thickness change rate at the current moment.

[0009] Preferably, when the physical constraint state space modeling end establishes the nonlinear observation equation with the multi-scale energy entropy as the observation matrix, a composite kernel function of polynomial kernel function and Gaussian kernel function is used to construct the mapping relationship between the multi-scale energy entropy and the actual contact area. The weight coefficients and bias terms of the composite kernel function are solved offline using calibration data obtained from the worm gear bench test. The solved composite kernel function is used as the observation matrix of the nonlinear observation equation. The observation vector is input into the nonlinear observation equation, and the residual between the output value of the composite kernel function and the state vector is calculated as the basis for updating the measurement noise covariance of the nonlinear observation equation.

[0010] Preferably, when the hidden state Bayesian inversion end uses the unscented Kalman filter algorithm for recursive estimation, a Sigma point set is constructed based on the state vector, and the Sigma point set is substituted into the state transition equation and the nonlinear observation equation for nonlinear transmission. The prior state estimation error covariance matrix output by the state transition equation is subjected to exponential weighted decay processing using the fading factor. The weights of historical states in the current state prediction are adjusted according to the fading factor, the Kalman gain is calculated using the attenuated prior state estimation error covariance matrix, and the actual contact area is updated based on the Kalman gain.

[0011] Preferably, when the time-varying working condition feature extraction end combines the envelope spectrum entropy and the singular spectrum entropy to form the multi-scale energy entropy, it adopts a dynamic weight allocation strategy based on mutual information to calculate the first mutual information between the envelope spectrum entropy and the change rate of the true contact area of ​​the worm gear pair, and the second mutual information between the singular spectrum entropy and the change rate of the true contact area of ​​the worm gear pair. The first mutual information and the second mutual information are normalized to obtain the first dynamic weight corresponding to the envelope spectral entropy and the second dynamic weight corresponding to the singular spectral entropy. The sum of the product of the envelope spectral entropy and the first dynamic weight and the product of the singular spectral entropy and the second dynamic weight is used as the final observation vector element of the multi-scale energy entropy.

[0012] Preferably, when the physical constraint state space modeling end constructs the exponential decay constraint relationship between the time-varying wear coefficient and the oil film thickness change rate during the operation of the worm gear pair, the acoustic emission energy accumulation value is extracted based on the high-frequency continuous component in the acoustic emission mixed signal. By combining the root mean square value in the time domain of the vibration mixed signal, a relative change index of oil film thickness is constructed. The derivative of the relative change index of oil film thickness with respect to running time is used as the rate of change of oil film thickness. The rate of change of oil film thickness is substituted into a preset exponential decay function to calculate the real-time decay step size of the time-varying wear coefficient, so as to dynamically correct the time-varying wear coefficient.

[0013] Preferably, when the hidden state Bayesian inversion end calculates the Kalman gain using the attenuated prior state estimation error covariance matrix, an adaptive adjustment mechanism for measurement noise covariance based on innovation covariance is introduced to extract the innovation vector between the observation vector at the current time and the observation prediction value predicted by the nonlinear observation equation. The cross product of the innovation vector and the mean cross product of historical innovation vectors within a preset sliding window are calculated as the real-time innovation covariance. The difference between the real-time innovation covariance and the theoretical innovation covariance calculated based on the nonlinear observation equation is added to the measurement noise covariance of the previous time step by a scaling factor to obtain the adaptive measurement noise covariance of the current time step.

[0014] Preferably, before the acoustic emission mixed signal and vibration mixed signal are acquired by the acoustic and vibration signal synchronous acquisition terminal during the operation of the worm gear pair, an end face runout compensation preprocessing terminal is added to acquire the axial movement signal of the main shaft through a displacement sensor installed next to the rotating main shaft of the worm gear pair; The spindle axial movement signal is subjected to a fast Fourier transform to extract the fundamental frequency component and harmonic component that are in the same frequency as the spindle rotation frequency, and an axial movement interference template is constructed. The axial movement interference template is then subtracted from the acoustic emission mixed signal and the vibration mixed signal to eliminate the periodic low-frequency modulation interference of the spindle end face runout on the acoustic and vibration signals.

[0015] Preferably, the acoustic and vibration signal synchronous acquisition end includes multiple acoustic emission sensors and multiple vibration sensors distributed in a ring array on the outer wall of the worm gear pair housing. When acquiring the acoustic emission mixed signal and the vibration mixed signal, the meshing point of the worm gear pair is used as the spatial reference point. The acoustic wave propagation delay and stress wave propagation delay of each acoustic emission sensor and vibration sensor relative to the spatial reference point are calculated. The original signals collected by each sensor are time-shifted and aligned using the acoustic wave propagation delay and stress wave propagation delay. The aligned signals of the same type of sensor are coherently averaged and superimposed. The superimposed signal is used as the acoustic emission mixed signal and vibration mixed signal and input into the time-varying working condition feature extraction terminal.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention acquires a mixture of acoustic emission and vibration signals through a synchronous acoustic and vibration signal acquisition terminal. It then uses a time-varying operating condition feature extraction terminal to perform variational mode decomposition on the signals and extract multi-scale energy entropy as the observation vector. In the physical constraint state space modeling terminal, the actual contact area is set as the state vector. The mapping relationship between wear volume, normal load, and sliding distance in the Akard wear law is embedded into the state transition equation, and a nonlinear observation equation with multi-scale energy entropy as the observation matrix is ​​established. Finally, the hidden state Bayesian inversion terminal uses an unscented Kalman filter algorithm to recursively estimate the continuously evolving value of the actual contact area. This invention overcomes the direct measurement failure problem caused by oil film obstruction and space limitations inside the closed gearbox, achieving online continuous acquisition of the contact area of ​​the worm gear pair under non-stop operation. By introducing the Akard wear law into the state transition equation and combining it with the exponential decay constraint relationship between the time-varying wear coefficient and the rate of change of oil film thickness, the solution space of the state evolution is limited, eliminating the drift phenomenon of the pure data-driven model during long-term operation and improving the robustness of the measurement system under complex and variable operating conditions. The prior state estimation error covariance matrix is ​​exponentially weighted and decayed using a fading factor. An adaptive adjustment mechanism for measurement noise covariance based on innovation covariance is introduced to dynamically adjust the weights of historical states and real-time observations, thereby improving the dynamic tracking response speed and inversion accuracy.

[0017] 2. This invention introduces multiple improvements in the feature extraction and signal preprocessing stages, further enhancing the quality of the inverted input signal and the system reliability. By using a variational mode decomposition adaptive optimization method based on the minimum envelope entropy, decomposition parameters are determined, separating high-frequency intrinsic mode functions (IMMs) containing meshing impact characteristics from low-frequency IMMs containing friction and wear characteristics. Envelope spectral entropy and singular spectral entropy are calculated, and a dynamic weight allocation strategy based on mutual information is used to determine the first and second dynamic weights of both, combining them to form a multi-scale energy entropy. This suppresses the influence of interference signals from non-meshing parts in the mechanical transmission chain, improving the signal-to-noise ratio of the hidden state inversion. An end-face runout compensation preprocessing stage is added at the signal front end. The axial runout signal of the main shaft is acquired through a displacement sensor, and the fundamental frequency component and harmonic components are extracted to construct an axial runout interference template, which is then subtracted from the original signal, eliminating the periodic low-frequency modulation interference generated by the main shaft end-face runout on the acoustic vibration signal. By using multiple acoustic emission sensors and multiple vibration sensors distributed in a ring array to calculate the propagation delay of acoustic waves and stress waves, time-shift alignment and coherent averaging superposition are performed to enhance the effective signal energy, offset the signal distortion caused by differences in spatial propagation paths, and provide high signal-to-noise ratio observation input for subsequent state-space models. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating the overall operation of the online measurement system for the contact area of ​​a worm gear pair based on wear law modeling, as described in this invention. Figure 2 This is a flowchart of the preprocessing steps for end face runout compensation and multi-sensor time delay alignment of the worm gear pair acoustic vibration signal according to the present invention. Figure 3 This is a flowchart of the adaptive variational mode decomposition and multi-scale energy entropy extraction based on the minimum value of envelope entropy of the present invention. Figure 4 Flowchart for building the basic physical constraint state-space model of the present invention that incorporates Arcard's wear law; Figure 5 A flowchart for constructing the exponential decay constraint of the time-varying wear coefficient related to the rate of change of oil film thickness in this invention; Figure 6 This is a flowchart of the unscented Kalman filter inversion process of the present invention, which integrates the fading factor and the adaptive adjustment of the innovation covariance. Figure 7 This is a schematic diagram of the arrangement of the acoustic and vibration signal synchronous acquisition terminal of the present invention.

[0019] The above figures include the following reference numerals: 1. Gearbox housing; 2. Vibration sensor; 3. Acoustic emission sensor. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] Please refer to Figure 1 This embodiment provides an online measurement system for the contact area of ​​a worm gear pair based on wear law modeling, including a synchronous acoustic and vibration signal acquisition terminal, a time-varying operating condition feature extraction terminal, a physical constraint state space modeling terminal, and a hidden state Bayesian inversion terminal. The synchronous acoustic and vibration signal acquisition terminal adopts a passive data acquisition method to acquire the mixed acoustic emission signal and the mixed vibration signal during the operation of the worm gear pair. The mixed acoustic emission signal includes the elastic stress wave signal generated during the meshing of the worm gear teeth, and the mixed vibration signal includes the structural vibration response signal of the gearbox housing. Specifically, as shown... Figure 7 As shown, the synchronous acquisition terminal for acoustic and vibration signals includes a vibration sensor 2 and an acoustic emission sensor 3, both of which are deployed outside the gearbox housing 1 of the worm gear transmission system. The vibration sensor 2 is used to acquire the structural vibration response signal of the gearbox housing 1, and the acoustic emission sensor 3 is used to acquire the elastic stress wave signal generated during the meshing of the worm gear teeth.

[0022] The time-varying operating condition feature extraction end receives the acoustic emission mixed signal and vibration mixed signal output from the acoustic and vibration signal synchronous acquisition end. Variational mode decomposition is performed on both signals to obtain the intrinsic mode functions reflecting macroscopic impact and microscopic friction. Multi-scale energy entropy is extracted from each intrinsic mode function as the observation vector. The physical constraint state-space modeling end sets the actual contact area of ​​the worm gear pair as the state vector. The mapping relationship between wear volume, normal load, and sliding distance in Arcard's wear law is embedded into the state transition equation, establishing a nonlinear observation equation with multi-scale energy entropy as the observation matrix. The hidden state Bayesian inversion end uses an unscented Kalman filter algorithm to recursively estimate the state transition equation and nonlinear observation equation driven by the observation vector, outputting the continuous-time evolution value of the actual contact area.

[0023] In this embodiment, the acoustic emission and vibration signal synchronous acquisition terminal acquires acoustic emission and vibration signals respectively through an acoustic emission sensor and a vibration sensor. The acoustic emission sensor is a piezoelectric ceramic sensor with a resonant frequency covering the 100kHz to 1MHz frequency band, capable of capturing high-frequency stress waves generated by micro-friction and macro-impact on the worm gear tooth surface. The vibration sensor is a piezoelectric accelerometer with a frequency response range covering the 10Hz to 10kHz frequency band, capable of capturing low-frequency structural vibrations of the gearbox housing 1. The acoustic emission and vibration sensors are amplified and filtered by a signal conditioning circuit, which includes a preamplifier, a bandpass filter, and an analog-to-digital converter. The preamplifier amplifies the weak electrical signal output by the sensor to the input range of the analog-to-digital converter. The bandpass filter removes the DC component and high-frequency noise from the signal. The analog-to-digital converter converts the analog signal into a digital signal. The sampling frequency is set according to the signal frequency range; the sampling frequency of the acoustic emission signal is not less than 2MHz, and the sampling frequency of the vibration signal is not less than 20kHz.

[0024] The time-varying operating condition feature extraction terminal performs variational mode decomposition (VMD) on the acoustic emission and vibration mixed signals. VMD is an adaptive signal decomposition method that can decompose a non-stationary signal into several eigenmode functions (EMFs) with different center frequencies. The goal of VMD is to find a set of EMFs such that the sum of the estimated bandwidths of all EMFs is minimized, while the sum of the EMFs equals the original signal. The mathematical model of VMD is expressed as:

[0025] in, The number of decomposition layers, For the first One eigenmode function For the first The center frequencies of the eigenmode functions For the Dirac function, This represents the convolution operation. The original signal, Indicates time Find the partial derivative.

[0026] In this embodiment, the penalty factor for variational mode decomposition With the number of decomposition layers Determined through preset empirical values. Penalty factor. Controlling the bandwidth of intrinsic mode functions and decomposing the number of layers The fineness of the decomposition is controlled. The acoustic emission mixture signal and the vibration mixture signal are input into the variational mode decomposition algorithm respectively to obtain... The intrinsic mode functions (IMFs) are categorized into several types. Based on the center frequency of the IMFs, IMFs with a center frequency higher than a preset threshold are classified as high-frequency components, while those with a center frequency lower than the preset threshold are classified as low-frequency components. The high-frequency components mainly reflect the macroscopic impact characteristics during the meshing process of the worm gear teeth, while the low-frequency components mainly reflect the microscopic friction and wear characteristics of the worm gear teeth.

[0027] Multi-scale energy entropy is extracted from high-frequency and low-frequency intrinsic mode functions (EMFs). Multi-scale energy entropy is a characteristic quantity that reflects the complexity of signal energy distribution. Its calculation process is as follows: First, the energy of each EMF is calculated. Then, the energy of each EMF is normalized to obtain the energy distribution probability. Finally, the multi-scale energy entropy is calculated using the information entropy formula. The formula for calculating multi-scale energy entropy is:

[0028] in, For the first The proportion of the energy of each eigenmode function to the total energy satisfies the following condition: .

[0029] refer to Figure 4 The physical constraint state-space modeling end constructs a state-space model containing the actual contact area. The state-space model consists of state transition equations and observation equations. The state transition equations describe the evolution of the state vector over time, and the observation equations describe the mapping relationship between the observation vector and the state vector. In this embodiment, the state vector... Defined as:

[0030] in, For the first The actual contact area of ​​the worm gear pair at all times. For the first The rate of change of the actual contact area at any given moment.

[0031] The Archard wear law is embedded into the state transition equation. The Archard wear law describes the relationship between wear volume and normal load, sliding distance, and material properties, and its expression is:

[0032] in, For wear volume, The wear coefficient is... For normal load, The sliding distance, The Brinell hardness of the material.

[0033] In a worm gear transmission system, the sliding distance With the rotational speed of the worm gear Running time and the pitch circle diameter of the worm gear Related, its expression is:

[0034] Wear volume Change in actual contact area and wear depth Related, its expression is:

[0035] Substituting the above two equations into Arcard's wear law, we obtain the relationship between the rate of change of the actual contact area and the normal load, rotational speed, and wear coefficient:

[0036] Based on the above relationships, the state transition equation is constructed as follows:

[0037] in, Here is the state transition matrix. Let be the process noise vector, which has a mean of zero and a covariance matrix of... The state transition matrix is ​​a Gaussian distribution. The expression is:

[0038] in, This represents the sampling time interval.

[0039] A nonlinear observation equation is established, using multi-scale energy entropy as the observation matrix. The observation equation describes the observation vector. With state vector The mapping relationship between them is expressed as follows:

[0040] in, For nonlinear observation functions, Let the measurement noise vector have a mean of zero and a covariance matrix of... The Gaussian distribution. In this embodiment, the nonlinear observation function... Using polynomial function form, its expression is:

[0041] in, The coefficients are polynomials, and the solution is obtained through offline regression analysis using calibration data obtained from worm gear bench tests.

[0042] The hidden-state Bayesian inversion stage employs an unscented Kalman filter (UKF) algorithm to recursively estimate the state vector. The UKF approximates the probability distribution of the state vector by constructing a Sigma point set, then substitutes this Sigma point set into a nonlinear function for propagation, thereby obtaining the prior and posterior estimates of the state vector. The recursive process of the UKF algorithm includes a prediction step and an update step.

[0043] In the prediction step, the posterior state estimate from the previous time step is used. and the posterior estimation error covariance matrix Construct the Sigma point set:

[0044] in, Let be the dimension of the state vector. For scale parameters, To control the distribution range of the Sigma point set, it is usually taken as... , This is a secondary scale parameter, usually set to 0.

[0045] Substituting the Sigma point set into the state transition equation, we obtain the predicted Sigma point set:

[0046] Calculate prior state estimation and the prior estimation error covariance matrix :

[0047]

[0048] in, and These are the mean weight and the covariance weight, respectively, and their expressions are:

[0049]

[0050]

[0051] in, The distribution parameters are used to consider the prior distribution information of the state vector. For a Gaussian distribution, This is the optimal value.

[0052] In the update step, the predicted Sigma point set is substituted into the nonlinear observation equation to obtain the observed predicted Sigma point set:

[0053] Calculate the observed predicted value Observation and prediction error covariance matrix and cross covariance matrix :

[0054]

[0055]

[0056] Calculate Kalman gain :

[0057] Calculate posterior state estimates and the posterior estimation error covariance matrix :

[0058]

[0059] Through the above recursive process, the estimated value of the state vector is continuously updated, and the continuous-time evolution value of the actual contact area is output.

[0060] This embodiment acquires the mixed acoustic emission and vibration signals during the operation of the worm gear pair via a synchronous acoustic and vibration signal acquisition terminal. The signals are then decomposed using variational mode decomposition, and multi-scale energy entropy is extracted as the observation vector. A state-space model incorporating Arcard's wear law is constructed, and an unscented Kalman filter algorithm is used to recursively estimate the actual contact area. This invention achieves continuous online acquisition of the contact area of ​​the worm gear pair during continuous operation, overcoming the direct measurement failure problem caused by oil film obstruction and space limitations inside the enclosed gearbox.

[0061] In a preferred embodiment, when the time-varying operating condition feature extraction end performs variational mode decomposition on the acoustic emission mixed signal and the vibration mixed signal, it employs an adaptive optimization method based on the minimum value of envelope entropy to determine the penalty factor and the number of decomposition levels. Envelope entropy is a feature quantity that reflects the strength of the signal's impact characteristics; the smaller the envelope entropy, the more obvious the impact characteristics in the signal. The basic idea of ​​the adaptive optimization method based on the minimum value of envelope entropy is: within the preset range of the penalty factor and the number of decomposition levels, it traverses all possible parameter combinations, performs variational mode decomposition on the original signal, calculates the sum of the envelope entropies of each intrinsic mode function after decomposition, and selects the parameter combination with the smallest sum of envelope entropies as the optimal parameters.

[0062] In this embodiment, the penalty factor The value range is set to Step size is 500; number of decomposition levels The value range is set to The step size is 1. For each set of parameter combinations Variational mode decomposition was performed on the acoustic emission mixture signal and the vibration mixture signal respectively to obtain... There are 10 intrinsic mode functions (EMFs). For each EMF, a Hilbert transform is performed to obtain its analytic signal. The magnitude of the analytic signal is the envelope signal of that EMF. The normalized probability distribution of the envelope signal is calculated, and then the envelope entropy is calculated using the information entropy formula. The formula for calculating the envelope entropy is:

[0063] in, The length of the envelope signal, The first in the envelope signal The normalized probability of each sample.

[0064] Calculate the sum of the envelope entropies of all intrinsic mode functions to obtain the total envelope entropy for that parameter combination. Iterate through all parameter combinations to find the one with the minimum total envelope entropy. , which serves as the optimal parameter for variational mode decomposition.

[0065] Variational mode decomposition of the acoustic emission mixture signal and the vibration mixture signal was performed using optimal parameters to obtain... The intrinsic mode functions are categorized into several intrinsic mode functions. Based on the center frequency of the intrinsic mode functions, intrinsic mode functions with a center frequency higher than a preset threshold are classified as high-frequency intrinsic mode functions containing meshing impact characteristics, while intrinsic mode functions with a center frequency lower than the preset threshold are classified as low-frequency intrinsic mode functions containing friction and wear characteristics.

[0066] Calculate the envelope spectral entropy of the high-frequency intrinsic mode functions (EMFs) and the singular spectral entropy of the low-frequency EEMs. The calculation process for the envelope spectral entropy is as follows: Perform a Hilbert transform on the high-frequency EEMs to obtain their envelope signal; perform a Fast Fourier Transform on the envelope signal to obtain the envelope spectrum; calculate the normalized probability distribution of the envelope spectrum; and then calculate the envelope spectral entropy using the information entropy formula. The calculation process for the singular spectral entropy is as follows: Reconstruct the phase space of the low-frequency EEMs to obtain the reconstruction matrix; perform singular value decomposition on the reconstruction matrix to obtain the singular value sequence; calculate the normalized probability distribution of the singular value sequence; and then calculate the singular spectral entropy using the information entropy formula.

[0067] The envelope spectral entropy and singular spectral entropy are combined to form the multi-scale energy entropy. In this embodiment, a dynamic weight allocation strategy based on mutual information is used to determine the weights of the envelope spectral entropy and the singular spectral entropy. Mutual information is a measure that reflects the correlation between two random variables; the larger the mutual information, the stronger the correlation between the two random variables. The basic idea of ​​the dynamic weight allocation strategy based on mutual information is to calculate the first mutual information between the envelope spectral entropy and the rate of change of the actual contact area of ​​the worm gear pair, and the second mutual information between the singular spectral entropy and the rate of change of the actual contact area of ​​the worm gear pair. The first and second mutual information are then normalized to obtain the first dynamic weight of the corresponding envelope spectral entropy and the second dynamic weight of the corresponding singular spectral entropy.

[0068] The formula for calculating mutual information is:

[0069] in, For random variables and The joint probability distribution, and They are random variables and The marginal probability distribution.

[0070] In this embodiment, acoustic emission signals, vibration signals, and corresponding actual contact area data at different wear stages are obtained through worm gear bench tests. The envelope spectral entropy at each moment is calculated. Singular Spectral Entropy and the rate of change of actual contact area .Will , and Discretize them separately to obtain discrete random variables. , and .calculate and The first mutual information between ,as well as and The second mutual information between .

[0071] The first mutual information and the second mutual information are normalized to obtain the first dynamic weight. Second dynamic weight :

[0072]

[0073] in, .

[0074] The sum of the product of the envelope spectral entropy and the first dynamic weight, and the product of the singular spectral entropy and the second dynamic weight, is taken as the final observation vector element of the multi-scale energy entropy:

[0075] In this embodiment, the acoustic and vibration signal synchronous acquisition end includes multiple acoustic emission sensors and multiple vibration sensors arranged in a ring array on the outer wall of the worm gear pair housing. The center of the ring array and the meshing point of the worm gear pair are on the same horizontal plane, and the acoustic emission sensors and vibration sensors are alternately and evenly distributed on the ring array. When acquiring the mixed acoustic emission signal and the mixed vibration signal, the meshing point of the worm gear pair is used as the spatial reference point, and the sound wave propagation delay and stress wave propagation delay of each acoustic emission sensor and vibration sensor relative to the spatial reference point are calculated.

[0076] The speed of sound waves in air is The propagation speed of the stress wave in the gearbox housing material 1 is . No. The distance between each acoustic emission sensor and the spatial reference point is The sound wave propagation delay is . No. The distance between each vibration sensor and the spatial reference point is The stress wave propagation delay is .

[0077] refer to Figure 2 The propagation delay of acoustic waves and the propagation delay of stress waves are used to perform time-shift alignment on the raw signals acquired by each sensor. For the raw signals acquired by the acoustic emission sensor... The time-shifted aligned signal is For the raw signal acquired by the vibration sensor The time-shifted aligned signal is .

[0078] The aligned signals from sensors of the same type are coherently averaged and superimposed. Coherent averaging and superposition enhances the effective signal energy and cancels out random noise. The acoustic emission mixture signal is the average of the time-shifted aligned signals from all acoustic emission sensors.

[0079] in, The number of acoustic emission sensors.

[0080] The vibration mixed signal is the average value of the signals from all vibration sensors after time-shift alignment:

[0081] in, This represents the number of vibration sensors.

[0082] In this embodiment, before the acoustic emission and vibration mixed signals during the operation of the worm gear pair are acquired by the acoustic and vibration signal synchronous acquisition terminal, an end face runout compensation preprocessing terminal is added. The end face runout compensation preprocessing terminal acquires the axial movement signal of the main shaft through a displacement sensor installed next to the rotating main shaft of the worm gear pair. The displacement sensor is an eddy current displacement sensor with a measurement range covering 0 to 5 mm and a resolution of not less than 1 μm. The probe of the displacement sensor is vertically aligned with the end face of the main shaft, and the distance between the probe and the end face of the main shaft is maintained within the linear measurement range of the sensor.

[0083] The spindle axial movement signal is subjected to a Fast Fourier Transform (FFT) to obtain its spectrum. The fundamental frequency and harmonics components that are in the same frequency as the spindle rotation frequency are extracted from the spectrum. Spindle rotation frequency. With spindle speed The relationship is The frequency of the fundamental frequency component is The frequency of the harmonic component is ,in This is the highest harmonic number, usually taken as 3 to 5.

[0084] Construct an axial movement interference template. The axial movement interference template is composed of the superposition of the fundamental frequency component and its harmonic components, and its expression is:

[0085] in, For the first The amplitude of the second harmonic. For the first Phase and amplitude of the subharmonic. and phase This was obtained by analyzing the spectrum of the spindle axial movement signal.

[0086] refer to Figure 3 The axial movement interference template is subtracted from the acoustic emission and vibration mixed signals to eliminate the periodic low-frequency modulation interference caused by the spindle end face runout. The compensated acoustic emission signal is as follows: The compensated vibration signal is .

[0087] To more clearly illustrate the effectiveness of the variational mode decomposition adaptive optimization method based on the minimum value of envelope entropy, this embodiment provides a comparison of envelope entropy under different parameter combinations, as shown in Table 1.

[0088] Table 1 Comparison of envelope entropy of variational mode decomposition of acoustic emission signals under different parameter combinations.

[0089] As shown in Table 1, the total envelope entropy of the acoustic emission signal after variational mode decomposition is minimized to 2.893 when the number of decomposition layers K=6 and the penalty factor α=6000. This indicates that this parameter combination can most effectively separate the impulse features in the signal and improve the accuracy of subsequent feature extraction.

[0090] This embodiment determines the optimal decomposition parameters using a variational mode decomposition adaptive optimization method based on the minimum value of envelope entropy. It separates high-frequency intrinsic mode functions (EMFs) containing meshing impact characteristics from low-frequency EMFs containing friction and wear characteristics, calculates envelope spectral entropy and singular spectral entropy, and employs a dynamic weight allocation strategy based on mutual information to construct a multi-scale energy entropy, suppressing the influence of interference signals from non-meshing parts in the mechanical transmission chain. Multiple acoustic emission sensors and vibration sensors distributed in a ring array are time-shifted and coherently averaged to enhance the effective signal energy. An end-face runout compensation preprocessing stage is added to eliminate the periodic low-frequency modulation interference generated by the spindle end-face runout on the acoustic and vibration signals, providing a high signal-to-noise ratio observation input for the subsequent state-space model.

[0091] In a preferred embodiment, reference Figure 5 When the physical constraint state-space modeling incorporates the mapping relationship between wear volume, normal load, and sliding distance from Arcard's wear law into the state transition equation, a time-varying wear coefficient that decays with operating time is introduced. In actual operation, the wear coefficient of the worm gear pair is not constant but gradually decreases with increasing operating time. This is because in the initial stage of worm gear pair operation, the tooth surface has microscopic unevenness, the contact area is small, the contact stress is large, and the wear rate is fast; as the operating time increases, the tooth surface gradually wears in, the contact area increases, the contact stress decreases, and the wear rate gradually decreases.

[0092] Using the time-varying wear coefficient as an extended state variable in the state vector, an extended state vector is constructed:

[0093] in, For the first The time-varying wear coefficient at any given moment.

[0094] An exponentially decaying constraint relationship was established between the time-varying wear coefficient and the rate of change of oil film thickness during the operation of the worm gear pair. Oil film thickness is a crucial factor affecting the wear of the worm gear pair; a thicker oil film results in better lubrication between the tooth surfaces and a smaller wear coefficient, while a thinner oil film results in poorer lubrication and a larger wear coefficient. The rate of change of oil film thickness reflects the trend of oil film thickness variation. A positive rate of change indicates an increasing oil film thickness, suggesting a decrease in the wear coefficient; a negative rate of change indicates a decreasing oil film thickness, suggesting an increase in the wear coefficient.

[0095] In this embodiment, the cumulative acoustic emission energy is extracted based on the high-frequency continuous component in the acoustic emission mixed signal, and combined with the root mean square value in the time domain of the vibration mixed signal to construct the relative change index of oil film thickness. The cumulative acoustic emission energy reflects the intensity of micro-friction on the tooth surface, while the root mean square value in the time domain reflects the intensity of macro-impact on the tooth surface. The formula for calculating the relative change index of oil film thickness is:

[0096] in, for The cumulative energy value of the high-frequency continuous components in the acoustic emission mixed signal at any given time. This represents the cumulative acoustic emission energy at the initial moment after the worm gear pair has completed its break-in period. for The root mean square value of the vibration mixed signal in the time domain at any given time. This represents the root mean square value of vibration in the time domain at the initial moment after the worm gear pair has completed its break-in period.

[0097] The derivative of the relative change index of oil film thickness with respect to running time is taken as the rate of change of oil film thickness:

[0098] Construct the exponential decay constraint relationship for the time-varying wear coefficient:

[0099] in, The attenuation coefficient was determined through bench tests on the worm gear pair. This represents the sampling time interval.

[0100] Using the aforementioned exponential decay constraint as an auxiliary evolution equation for the state transition equation, the wear volume dynamically adjusts the time-varying wear coefficient according to the rate of change of oil film thickness at the current moment. The extended state transition equation is:

[0101] in, The nonlinear state transition function is expressed as follows:

[0102] When establishing the nonlinear observation equation with multi-scale energy entropy as the observation matrix in the physical constraint state-space modeling stage, a composite kernel function of polynomial and Gaussian kernel functions is used to construct the mapping relationship from multi-scale energy entropy to the actual contact area. The composite kernel function combines the global fitting capability of the polynomial kernel function with the local fitting capability of the Gaussian kernel function, improving the accuracy of the mapping relationship. The expression of the composite kernel function is:

[0103] in, These are the weighting coefficients. , For polynomial kernel functions, This is the Gaussian kernel function.

[0104] The expression for the polynomial kernel function is:

[0105] in, For constant terms, Let be the degree of the polynomial.

[0106] The expression for the Gaussian kernel function is:

[0107] in, is the width parameter of the Gaussian kernel.

[0108] Offline regression analysis was performed on the weighting coefficients and bias terms of the composite kernel function using calibration data obtained from worm gear bench tests. The calibration data included multi-scale energy entropy observations and corresponding actual contact area measurements at different wear stages. Support vector regression was used to solve for the parameters of the composite kernel function, yielding the optimal weighting coefficients. constant term polynomial degree Gaussian kernel width and bias terms .

[0109] The solved composite kernel function is used as the observation matrix of the nonlinear observation equation, and the expression of the nonlinear observation equation is as follows:

[0110] in, The number of support vectors, For Lagrange multipliers, For the first Multiscale energy entropy observations at time t. For the first The multi-scale energy entropy value corresponding to each support vector. For measuring noise.

[0111] The observation vector is input into the nonlinear observation equation, and the residual between the composite kernel function output and the state vector is calculated. This residual serves as the basis for updating the measurement noise covariance of the nonlinear observation equation. The formula for calculating the residual is:

[0112] in, These are the observed predicted values ​​based on prior state estimation.

[0113] refer to Figure 6 When the hidden-state Bayesian inversion end uses the unscented Kalman filter algorithm for recursive estimation, a Sigma point set is constructed based on the extended state vector. This Sigma point set is then substituted into the nonlinear state transition equation and the nonlinear observation equation for nonlinear propagation. A fading factor is used to exponentially weight the covariance matrix of the prior state estimation error output by the state transition equation. The fading factor dynamically adjusts the weight of historical states in the current state prediction. When a sudden change occurs in the system state, the fading factor is increased, the weight of historical states is decreased, and the weight of the current observation is increased, thereby improving the system's dynamic tracking response speed.

[0114] Gradual decay factor The calculation formula is:

[0115] in, Represents the trace of a matrix. and The expression is:

[0116]

[0117] in, The new information covariance matrix, Let be the Jacobian matrix of the observation matrix.

[0118] The prior state estimation error covariance matrix is ​​subjected to exponential weighted decay using a decay factor:

[0119] The Kalman gain is calculated using the attenuated prior state estimation error covariance matrix. In this embodiment, an adaptive adjustment mechanism for measurement noise covariance based on innovation covariance is introduced. Innovation refers to the difference between the observed vector and the predicted observed value; the innovation covariance reflects the statistical characteristics of the observation noise. This adaptive adjustment mechanism for measurement noise covariance based on innovation covariance can dynamically adjust the measurement noise covariance according to real-time observation data, improving the robustness of the filtering algorithm.

[0120] Extract the innovation vector between the current observation vector and the predicted observation value obtained through the nonlinear observation equation:

[0121] The mean of the cross product of the new information vectors and the cross product of the historical information vectors within a preset sliding window is calculated as the real-time information covariance.

[0122] in, The length of the sliding window.

[0123] The difference between the real-time innovation covariance and the theoretical innovation covariance calculated based on the nonlinear observation equation is added to the measurement noise covariance of the previous time step by a scaling factor to obtain the adaptive measurement noise covariance of the current time step:

[0124] in, As a scaling factor, , This is the theoretical information covariance matrix.

[0125] To more clearly illustrate the relationship between the time-varying wear coefficient and the rate of change of oil film thickness, this embodiment provides the attenuation of the time-varying wear coefficient under different rates of change of oil film thickness, as shown in Table 2.

[0126] Table 2. Decrease of time-varying wear coefficient under different oil film thickness change rates.

[0127] As shown in Table 2, when the rate of change of oil film thickness is negative, the time-varying wear coefficient gradually decreases with increasing operating time; when the rate of change of oil film thickness is positive, the time-varying wear coefficient gradually increases with increasing operating time; and when the rate of change of oil film thickness is zero, the time-varying wear coefficient remains unchanged. This indicates that the exponential decay constraint relationship between the time-varying wear coefficient and the rate of change of oil film thickness can accurately reflect the influence of oil film thickness change on the wear coefficient.

[0128] To more clearly illustrate the impact of the fading factor on the performance of the unscented Kalman filter algorithm, this embodiment provides a comparison of the actual contact area estimation errors under different fading factors, as shown in Table 3.

[0129] Table 3 Comparison of estimation errors for true contact area under different fading factors.

[0130] As shown in Table 3, with the increase of the fading factor, the steady-state estimation error gradually increases, but the sudden change response time gradually shortens, and the maximum estimation error gradually decreases. This indicates that the fading factor can strike a balance between steady-state estimation accuracy and dynamic tracking response speed. By selecting an appropriate fading factor, the system can improve its response speed to sudden changes in state while maintaining a certain level of steady-state estimation accuracy.

[0131] This embodiment introduces a time-varying wear coefficient that decays over time and establishes an exponential decay constraint relationship between the time-varying wear coefficient and the rate of change of oil film thickness, thus limiting the solution space of state evolution and eliminating the drift phenomenon of pure data-driven models during long-term operation. A composite kernel function of polynomial and Gaussian kernel functions is used to construct the nonlinear observation equation, improving the accuracy of the mapping relationship between the observation vector and the state vector. A fading factor is used to exponentially weight the covariance matrix of the prior state estimation error, and an adaptive adjustment mechanism for the measurement noise covariance based on the innovation covariance is introduced to dynamically adjust the weights of historical states and real-time observations, improving the dynamic tracking response speed and inversion accuracy.

Claims

1. An online measurement system for the contact area of ​​a worm gear pair based on wear law modeling, comprising an acoustic and vibration signal acquisition end and a feature extraction end, wherein the acoustic and vibration signal acquisition end is used to acquire acoustic emission signals and vibration signals, and the feature extraction end is used to perform variational mode decomposition on the signals and extract multi-scale energy entropy; characterized in that, The acoustic and vibration signal acquisition terminal is a synchronous acoustic and vibration signal acquisition terminal, used to acquire the mixed acoustic emission signal and the mixed vibration signal during the operation of the worm gear pair. The feature extraction end is a time-varying working condition feature extraction end, used to perform variational mode decomposition on the acoustic emission mixed signal and the vibration mixed signal, obtain the intrinsic mode function reflecting macroscopic impact and microscopic friction, and extract multi-scale energy entropy as the observation vector; The system also includes a physical constraint state space modeling end and a hidden state Bayesian inversion end; The physical constraint state space modeling end is used to set the actual contact area as a state vector, embed the mapping relationship between wear volume, normal load and sliding distance in Arcard wear law into the state transition equation, and establish a nonlinear observation equation with the multi-scale energy entropy as the observation matrix. The hidden-state Bayesian inversion terminal is used to employ an unscented Kalman filter algorithm to drive the state transition equation and the nonlinear observation equation with the observation vector to perform recursive estimation and output the continuous-time evolution value of the true contact area.

2. The online measurement system for the contact area of ​​a worm gear pair based on wear law modeling according to claim 1, characterized in that, When the time-varying operating condition feature extraction end performs variational mode decomposition on the acoustic emission mixed signal and the vibration mixed signal, it adopts a variational mode decomposition adaptive optimization method based on the minimum value of envelope entropy to determine the penalty factor and the number of decomposition layers of variational mode decomposition. The acoustic emission mixed signal and the vibration mixed signal are divided into frequency bands to separate the high-frequency intrinsic mode functions containing meshing impact characteristics and the low-frequency intrinsic mode functions containing friction and wear characteristics. The envelope spectral entropy of the high-frequency intrinsic mode functions and the singular spectral entropy of the low-frequency intrinsic mode functions are calculated. The envelope spectral entropy and the singular spectral entropy are combined to form the multi-scale energy entropy.

3. The online measurement system for the contact area of ​​a worm gear pair based on wear law modeling according to claim 1, characterized in that, When the physical constraint state space modeling end embeds the mapping relationship between wear volume, normal load, and sliding distance in Arcard's wear law into the state transition equation, it introduces a time-varying wear coefficient that decays with running time. The time-varying wear coefficient is used as an extended state variable in the state vector to construct an exponential decay constraint relationship between the time-varying wear coefficient and the oil film thickness change rate during the operation of the worm gear pair. The exponential decay constraint relationship is used as an auxiliary evolution equation for the state transition equation, so that the wear volume dynamically adjusts the time-varying wear coefficient according to the oil film thickness change rate at the current moment.

4. The online measurement system for the contact area of ​​a worm gear pair based on wear law modeling according to claim 1, characterized in that, When the physical constraint state space modeling end establishes the nonlinear observation equation with the multi-scale energy entropy as the observation matrix, it uses a composite kernel function of polynomial kernel function and Gaussian kernel function to construct the mapping relationship between the multi-scale energy entropy and the actual contact area. The weight coefficients and bias terms of the composite kernel function are solved offline using calibration data obtained from the worm gear bench test. The solved composite kernel function is used as the observation matrix of the nonlinear observation equation. The observation vector is input into the nonlinear observation equation, and the residual between the output value of the composite kernel function and the state vector is calculated as the basis for updating the measurement noise covariance of the nonlinear observation equation.

5. The online measurement system for the contact area of ​​a worm gear pair based on wear law modeling according to claim 1, characterized in that, When the hidden state Bayesian inversion end uses the unscented Kalman filter algorithm for recursive estimation, a Sigma point set is constructed based on the state vector. The Sigma point set is substituted into the state transition equation and the nonlinear observation equation for nonlinear transmission. The prior state estimation error covariance matrix output by the state transition equation is subjected to exponential weighted decay processing using the fading factor. The weights of historical states in the current state prediction are adjusted according to the fading factor, the Kalman gain is calculated using the attenuated prior state estimation error covariance matrix, and the actual contact area is updated based on the Kalman gain.

6. The online measurement system for the contact area of ​​a worm gear pair based on wear law modeling according to claim 2, characterized in that, When the time-varying working condition feature extraction end combines the envelope spectrum entropy and the singular spectrum entropy to form the multi-scale energy entropy, it adopts a dynamic weight allocation strategy based on mutual information to calculate the first mutual information between the envelope spectrum entropy and the change rate of the true contact area of ​​the worm gear pair, and the second mutual information between the singular spectrum entropy and the change rate of the true contact area of ​​the worm gear pair. The first mutual information and the second mutual information are normalized to obtain the first dynamic weight corresponding to the envelope spectral entropy and the second dynamic weight corresponding to the singular spectral entropy. The sum of the product of the envelope spectral entropy and the first dynamic weight and the product of the singular spectral entropy and the second dynamic weight is used as the final observation vector element of the multi-scale energy entropy.

7. The online measurement system for the contact area of ​​a worm gear pair based on wear law modeling according to claim 3, characterized in that, When the physical constraint state space modeling end constructs the exponential decay constraint relationship between the time-varying wear coefficient and the oil film thickness change rate during the operation of the worm gear pair, it extracts the cumulative value of acoustic emission energy based on the high-frequency continuous component in the acoustic emission mixed signal. By combining the root mean square value in the time domain of the vibration mixed signal, a relative change index of oil film thickness is constructed. The derivative of the relative change index of oil film thickness with respect to running time is used as the rate of change of oil film thickness. The rate of change of oil film thickness is substituted into a preset exponential decay function to calculate the real-time decay step size of the time-varying wear coefficient, so as to dynamically correct the time-varying wear coefficient.

8. The online measurement system for the contact area of ​​a worm gear pair based on wear law modeling according to claim 5, characterized in that, When the hidden state Bayesian inversion end calculates the Kalman gain using the attenuated prior state estimation error covariance matrix, it introduces an adaptive adjustment mechanism for the measurement noise covariance based on the innovation covariance to extract the innovation vector between the observation vector at the current time and the observation prediction value predicted by the nonlinear observation equation. The cross product of the innovation vector and the mean cross product of historical innovation vectors within a preset sliding window are calculated as the real-time innovation covariance. The difference between the real-time innovation covariance and the theoretical innovation covariance calculated based on the nonlinear observation equation is added to the measurement noise covariance of the previous time step by a scaling factor to obtain the adaptive measurement noise covariance of the current time step.

9. The online measurement system for the contact area of ​​a worm gear pair based on wear law modeling according to claim 1, characterized in that, Before the acoustic emission mixed signal and vibration mixed signal are acquired by the acoustic and vibration signal synchronous acquisition terminal during the operation of the worm gear pair, an end face runout compensation preprocessing terminal is added to acquire the axial movement signal of the main shaft through a displacement sensor installed next to the rotating main shaft of the worm gear pair. The spindle axial movement signal is subjected to a fast Fourier transform to extract the fundamental frequency component and harmonic component that are in the same frequency as the spindle rotation frequency, and an axial movement interference template is constructed. The axial movement interference template is then subtracted from the acoustic emission mixed signal and the vibration mixed signal.

10. The online measurement system for the contact area of ​​a worm gear pair based on wear law modeling according to claim 1, characterized in that, The acoustic and vibration signal synchronous acquisition terminal includes multiple acoustic emission sensors and multiple vibration sensors distributed in a ring array on the outer wall of the worm gear pair housing. When acquiring the acoustic emission mixed signal and the vibration mixed signal, the meshing point of the worm gear pair is used as the spatial reference point. The acoustic wave propagation delay and stress wave propagation delay of each acoustic emission sensor and vibration sensor relative to the spatial reference point are calculated. The original signals collected by each sensor are time-shifted and aligned using the acoustic wave propagation delay and stress wave propagation delay. The aligned signals of the same type of sensor are coherently averaged and superimposed. The superimposed signal is used as the acoustic emission mixed signal and vibration mixed signal and input into the time-varying working condition feature extraction terminal.

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