Drum-shaped worm grinding wheel wear state monitoring method and system considering time-varying characteristics of contact area

Abstract

The application discloses a drum-shaped worm grinding wheel wear state monitoring method and system considering time-varying characteristics of a contact area. The application synchronously collects vibration signals and acoustic emission signals in a continuous development grinding process of a face gear; performs continuous wavelet transform on the vibration signals to generate a time-frequency diagram, and extracts deep wear features in a time-frequency domain by using a convolutional neural network with an embedded cross-space learning multi-scale attention mechanism; retains the original time sequence of the acoustic emission signals, and extracts time sequence evolution wear features by using a hybrid network composed of a layered time sequence convolution network, an adaptive key feature filter and a Transformer encoder; performs feature-level fusion on the two kinds of features, and guides model training through a physical constraint loss function based on a slow evolution law of wear, so that the interference of periodic changes of the contact area on feature learning is inhibited, and finally, a classifier is input to identify a wear state. The application can improve the comprehensive recognition accuracy and effectively cope with accurate identification of the wear state under time-varying contact conditions.

Description

Technical Field

[0001] This invention belongs to the field of machining condition monitoring and fault diagnosis technology, specifically a method and system for monitoring the wear condition of a drum-shaped worm grinding wheel that considers the time-varying characteristics of the contact area. Background Technology

[0002] Face gear transmission, as a novel type of interleaved shaft transmission, boasts advantages such as high load-bearing capacity, smooth transmission, and compact structure, and has broad application prospects in aerospace, automotive, and machinery manufacturing fields. The main machining methods for face gears include gear shaping, gear hobbing, gear turning, gear milling, and gear grinding. Among these, continuous generating grinding has become the preferred method for batch processing face gears due to its high machining accuracy, high efficiency, and wide applicability.

[0003] The machining principle of Face Gear Continuous Generating Grinding (FGCGG) is essentially to simulate the conjugate meshing motion between a virtual gear shaper and a face gear. In this process, the drum-shaped worm wheel used is not a standard worm, but a specially calculated and dressed conjugate surface exhibiting complex spatial variations. Thanks to this specially designed drum-shaped tooth profile, the worm wheel can accurately reproduce the cutting edge trajectory of the virtual gear shaper during grinding, achieving precise meshing with the face gear. Through precise control of the CNC system, the worm wheel and face gear rotate synchronously according to a fixed transmission ratio; that is, for every one revolution of the worm wheel, the face gear rotates by one tooth angle, thus spatially reproducing the ideal conjugate motion between the virtual gear shaper and the face gear. Simultaneously, the worm wheel continuously feeds along the radial direction of the face gear, gradually reducing the center distance between them. The superposition of this radial low-speed feed motion and high-speed rotational motion creates a complex motion trajectory under the combined action, so that the motion trajectory of a single abrasive grain in the workpiece coordinate system is not a simple circular arc, but a complex spatial curve.

[0004] Tool wear is a crucial factor affecting machining quality. As a machining tool for continuous generating grinding of face gears, the wear degree of the drum-shaped worm wheel directly impacts key indicators such as machining efficiency, machining quality, production cost, and energy consumption. The drum-shaped worm wheel is formed by sintering abrasive grains and a bonding agent. The exit height of the abrasive grains is random; only grains with an exit height greater than the local depth of cut can actually participate in cutting. During grinding, the abrasive grains continuously wear or break. After abrasive grain breakage, the porosity on the grinding wheel surface gradually increases, and the removed metal material fills the pores, causing a dynamic change in the number of abrasive grains actually participating in cutting. These characteristics make the wear process of worm wheels more complex than that of other cutting tools, making dynamic modeling of worm wheel wear based on its wear mechanism a significant challenge.

[0005] In the field of tool wear monitoring, existing technologies are mainly divided into two categories: direct measurement methods and indirect monitoring methods. Direct measurement methods mainly include contact measurement and optical image measurement. These methods usually require machine downtime for inspection, making it difficult to achieve online real-time monitoring, and they also require significant hardware investment. Indirect monitoring methods, on the other hand, collect signals such as cutting force, vibration, acoustic emission, and motor current during the machining process, and use signal processing and machine learning methods to establish a mapping relationship between the signals and the tool wear state. They have advantages such as being non-contact and capable of being implemented online, and have been widely researched and applied.

[0006] However, in the specific scenario of continuous generating grinding of face gears, existing indirect monitoring methods face the following difficulties: First, the geometric structure of the drum-shaped worm grinding wheel is complex, and its wear degree is difficult to define and characterize using traditional tool wear parameters (such as the flank wear width VB). There is a lack of unified and objective quantitative grading standards for wear state, which brings difficulties to the training and evaluation of wear state monitoring models.

[0007] Secondly, the contact area in continuous generating grinding of face gears exhibits significant time-varying characteristics. From a macroscopic kinematic perspective, the relative position and orientation of the worm wheel and the workpiece continuously change during the machining process, and the size, shape, and position of the contact area evolve continuously. From a microscopic abrasive behavior perspective, each abrasive grain on the grinding wheel surface sequentially undergoes three stages: sliding, plowing, and cutting. The distribution density and edge height of the abrasive grains directly affect the number of abrasive grains participating in cutting and the depth of cut. It is the combined effect of these macroscopic kinematic characteristics and microscopic abrasive behavior that leads to the significant time-varying characteristics of the contact area between the worm wheel and the workpiece. This time-varying characteristic makes it very difficult to extract stable feature components related to worm wheel wear from the machining signal, severely limiting the application effectiveness of existing wear monitoring methods in this scenario.

[0008] Furthermore, vibration signals and acoustic emission signals, as two common monitoring signals, reflect processing status information from different physical fields. Vibration signals are sensitive to macroscopic dynamic responses, while acoustic emission signals are sensitive to microscopic abrasive particle breakage and material deformation. Under time-varying conditions in the contact area, a single type of signal is often insufficient to comprehensively characterize changes in wear state. How to effectively integrate multimodal information to improve the accuracy and robustness of wear identification is also a significant challenge in this field.

[0009] In summary, existing tool wear monitoring methods face several limitations in the application of continuous generating grinding of face gears: they lack a wear state definition method tailored to the characteristics of drum-shaped worm grinding wheels; they fail to fully consider the time-varying characteristics of the contact area, making it difficult to accurately extract features highly correlated with wear from machining signals; and they lack deep feature fusion of vibration and acoustic emission multimodal signals. Therefore, there is an urgent need to propose a new method that can consider the time-varying characteristics of the contact area, effectively fuse multimodal information, and achieve accurate monitoring of the wear state of drum-shaped worm grinding wheels. Summary of the Invention

[0010] In view of this, the purpose of this invention is to provide a method and system for monitoring the wear state of a drum-shaped worm grinding wheel that considers the time-varying characteristics of the contact area. By fusing vibration and acoustic emission multimodal signals, a deep feature extraction model for time-varying characteristics is constructed to achieve accurate identification of the wear state of the worm grinding wheel, providing a reliable basis for intelligent decision-making in the continuous generating grinding of face gears.

[0011] To achieve the above objectives, the present invention provides the following technical solution: This invention first proposes a method for monitoring the wear condition of a drum-shaped worm grinding wheel considering the time-varying characteristics of the contact area, comprising the following steps: Step 1: Data Acquisition: During the continuous generating grinding of face gears, vibration signals and acoustic emission signals in the worm wheel machining area are collected simultaneously to construct a multimodal raw signal dataset; Step 2: Data preprocessing: The collected vibration signal and acoustic emission signal are preprocessed respectively; continuous wavelet transform is performed on the preprocessed vibration signal to generate a time-frequency diagram of the vibration signal, and the original time sequence characteristics of the preprocessed acoustic emission signal are preserved; Step 3: Feature Extraction A vibration signal time-frequency feature extractor based on EMA-CNN is constructed. The vibration signal time-frequency map is input into the vibration signal time-frequency feature extractor to extract the deep wear features in the time-frequency domain of the vibration signal. The EMA-CNN is constructed based on cross-spatial learning multi-scale attention EMA and convolutional neural network CNN. It is a convolutional neural network CNN with embedded cross-spatial learning multi-scale attention EMA mechanism and includes an EMA module. The EMA module achieves dynamic focusing on time-varying wear features by grouping the input feature map along the channel dimension, running 1×1 and 3×3 convolution branches in parallel, and performing cross-spatial learning. An acoustic emission temporal feature extractor based on HTCN-AKFS-TE is constructed. The preprocessed acoustic emission signal is input into the extractor to extract the temporal evolution wear features of the acoustic emission signal. HTCN-AKFS-TE is constructed based on a hierarchical temporal convolutional network HTCN, an adaptive key feature filter AKFS, and a Transformer encoder TE. The hierarchical temporal convolutional network HTCN captures dynamic evolution patterns across multiple time spans through multiple convolutional layers with different dilation rates. The adaptive key feature filter AKFS filters high-value key feature fragments from the output features of the hierarchical temporal convolutional network HTCN through a learnable scoring network. The Transformer encoder TE performs deep interaction and representation enhancement on the filtered key feature fragments. Step 4: Feature Fusion: The time-frequency domain deep wear features of the extracted vibration signal are fused with the time-series evolution wear features of the acoustic emission signal to construct a multimodal joint feature vector; Step 5: Physical constraint-guided model training: The multimodal joint feature vector is input into the wear state recognition module for training and recognition; the wear state recognition module uses a physical constraint loss function to guide model training. The physical constraint loss function is constructed based on the slow evolution law of worm wheel wear. By forcing the wear state estimation of different sub-time periods within the same sample to remain consistent, the interference of periodic changes in the contact area on wear feature learning is suppressed. Step Six: Wear State Category: Input the multimodal joint feature vector into the trained wear state recognition module, and output the current wear state category of the drum worm grinding wheel; the wear state recognition module includes a fully connected layer, a batch normalization layer, a ReLU activation layer, a Dropout layer and a Softmax classification layer connected in sequence.

[0012] Furthermore, in step two, the preprocessing includes filtering and noise reduction, amplitude normalization, and equal-length signal truncation based on the rotation period of the worm gear grinding wheel. The filtering and noise reduction uses a fourth-order Butterworth bandpass filter. The passband frequency range of the vibration signal is set to 10 Hz to 5000 Hz, and the passband frequency range of the acoustic emission signal is set to 60 kHz to 400 kHz. The amplitude normalization adopts the minimum-maximum normalization method, which maps the amplitude of each channel signal to the interval [0, 1]. The equal-length signal extraction is based on five rotations of the worm wheel as a feature extraction unit, and ten signal segments are extracted from the stable grinding stage to achieve data enhancement. The continuous wavelet transform uses Morlet wavelets as the mother wavelet basis function and employs a logarithmic uniform scale step size for time-frequency transformation, making the frequency division in the low-frequency region finer than that in the high-frequency region, in order to balance time resolution and frequency resolution.

[0013] Furthermore, in step three, the EMA module includes a feature grouping unit, a parallel convolution branch unit, and a cross-space learning unit; The feature grouping unit is used to divide the input feature map into multiple non-overlapping sub-feature groups along the channel dimension to aggregate local time-frequency features in different channels; The parallel convolution branch unit is used to execute two independent convolution branches in parallel for each of the divided sub-feature groups: the first branch is a 1×1 convolution branch, which extracts position information by one-dimensional global pooling along the time axis and frequency axis respectively, and after concatenation, convolution and activation, it is multiplied element-wise with the original group features to achieve spatial feature calibration; the second branch is a 3×3 convolution branch, which expands the receptive field and extracts multi-scale detailed features in the neighborhood through local convolution. The cross-spatial learning unit is used to perform spatial attention interaction between the outputs of the 1×1 convolutional branch and the 3×3 convolutional branch. After applying global pooling, tensor reshaping and Softmax normalization to the outputs of each branch, a weight vector is obtained. This weight vector is then multiplied with the output of the other branch. The two spatial attention results are added together, processed by an activation function, and then multiplied with the original sub-feature group to obtain the output features of the EMA module.

[0014] Furthermore, in step four, the hierarchical temporal convolutional network HTCN includes three dilated convolutional layers with dilation rates of 1, 2, and 4, respectively, a kernel size of 7, and the activation function ReLU for all layers; the Transformer encoder TE includes a multi-head self-attention mechanism, and its model dimension... Set to 128, number of attention heads Set to 4, number of encoder layers Set to 2.

[0015] Furthermore, in step three, the method for the adaptive key feature filter AKFS to filter key feature fragments is as follows: Each step of the feature vector output by the hierarchical temporal convolutional network HTCN is scored. The importance score of each time step is calculated through a learnable scoring network. The M time point indices with the highest scores are selected. Based on the indices, a subset of key features is extracted from the feature sequence output by the hierarchical temporal convolutional network HTCN and used as the input of the Transformer encoder TE.

[0016] Furthermore, in step four, the feature-level fusion adopts a splicing method, which concatenates the vibration signal feature vector and the acoustic emission signal feature vector in the channel dimension to generate a joint feature vector.

[0017] Furthermore, in step five, the physical constraint loss function is specifically implemented as follows: Each sample is divided along the time axis. Each sub-segment is input into the wear condition recognition module to obtain... The predicted probability distribution of the group is transformed into a probability expression of wear state through the Softmax function; Define the continuous wear index:

[0018] in: For the first Each sub-segment is predicted to belong to category c; It reflects the model's continuous estimation of the degree of wear and tear during that period; These correspond to the initial wear stage, the normal wear stage, and the severe wear stage, respectively. Define physical constraint loss:

[0019] in: Batch size; Indicates calculation The variance of the continuous wear index of each sub-segment; For the first In the nth sample The continuous wear index of each segment; The model's total loss function is:

[0020] in: For multi-class cross-entropy loss; These are the weighting coefficients.

[0021] Furthermore, in step six, the wear state categories include the initial wear stage, the normal wear stage, and the severe wear stage; the threshold for judging the severe wear stage is predetermined by the following quantification and grading method: Collect point cloud data of the surface morphology of the worm gear grinding wheel; Calculate the average effective blade height based on the point cloud data. and abrasive passivation rate :

[0022]

[0023] The effective average height of the cutting edge After global normalization, it is compared with the wear particle passivation rate. Perform weighted summation to construct a comprehensive wear and tear index. :

[0024] in: The height of the binder reference surface is taken as the 10th percentile of the point cloud data; The effective average height of the blade after global normalization; For the first The height value of each data point; This is the preset threshold for the effective cutting height of the abrasive grains; To meet The number of valid points; This represents the total number of points in the point cloud data. To meet The number of invalid points; It is the height boundary between the effective region and the ineffective region; This is an indicator function; it takes the value 1 when the condition is true, and 0 otherwise. Based on the comprehensive wear index The evolution curve of the wear process with the number of grinding cycles was used to divide the wear process into the initial wear stage, the normal wear stage, and the severe wear stage using the K-means clustering algorithm.

[0025] This invention also proposes a drum-shaped worm grinding wheel wear condition monitoring system that considers the time-varying characteristics of the contact area, used to implement the drum-shaped worm grinding wheel wear condition monitoring method that considers the time-varying characteristics of the contact area as described above, including: The signal acquisition module is used to simultaneously acquire vibration signals and acoustic emission signals in the worm wheel machining area during the continuous generating grinding process of face gears; The signal preprocessing module is used to filter and reduce noise, normalize amplitude and truncate the acquired vibration signal and acoustic emission signal respectively, and perform continuous wavelet transform on the preprocessed vibration signal to generate a vibration signal time-frequency diagram. The vibration signal feature extraction module employs a vibration signal time-frequency feature extractor based on EMA-CNN to extract deep time-frequency wear features of the vibration signal from the vibration signal time-frequency map; the EMA-CNN is a convolutional neural network (CNN) with an embedded cross-spatial learning multi-scale attention EMA mechanism. The acoustic emission signal feature extraction module employs an HTCN-AKFS-TE-based acoustic emission temporal feature extractor to extract temporal evolution wear features from the preprocessed acoustic emission signal. The HTCN-AKFS-TE includes a hierarchical temporal convolutional network HTCN, an adaptive key feature filter AKFS, and a Transformer encoder TE. The multimodal feature fusion module is used to perform feature-level fusion of the time-frequency domain deep wear features of the vibration signal and the time-series evolution wear features of the acoustic emission signal to generate a multimodal joint feature vector; The wear condition identification module is used to input the multimodal joint feature vector into the trained classifier and output the current wear condition category of the drum worm grinding wheel.

[0026] Furthermore, the hierarchical temporal convolutional network (HTCN) includes three dilated convolutional layers with dilation rates of 1, 2, and 4, respectively, a kernel size of 7, and a ReLU activation function. The adaptive key feature filter (AKFS) calculates the importance score of each time step in the output features of the hierarchical temporal convolutional network HTCN through a learnable scoring network, selects the M time point indices with the highest scores, and extracts the corresponding key feature subsets. The multimodal feature fusion module uses a concatenation method to concatenate the vibration signal feature vector and the acoustic emission signal feature vector along the channel dimension.

[0027] The beneficial effects of this invention are as follows: The present invention provides a method for monitoring the wear condition of a drum-shaped worm grinding wheel that considers the time-varying characteristics of the contact area, and has the following technical advantages: (1) Multimodal complementary enhancement and physical constraint guidance: Simultaneously collect vibration and acoustic emission signals, integrate deep features in the time-frequency domain and time-series domain, make up for the lack of information of a single signal under time-varying conditions, and improve feature completeness; on this basis, construct a short-time stationary physical constraint loss function based on the slow evolution law of wear, force the model to maintain the temporal consistency of wear estimation under the condition of periodic changes in contact state, effectively suppress the interference of meshing periodic fluctuations on feature learning, and make the model have stronger physical consistency and interpretability under complex time-varying conditions; (2) Accurately adapt to time-varying characteristics: EMA-CNN dynamically focuses on the wear-sensitive areas that change instantaneously in the time-frequency map through channel grouping, parallel branching and cross-space learning, effectively dealing with frequency domain feature drift caused by contact geometry evolution; HTCN-AKFS-TE uses hierarchical dilated convolution to capture multi-scale temporal patterns, and combines a learnable filter to extract key segments from ultra-long sequences, effectively suppressing non-stationary background noise interference. (3) Deep feature fusion and high-precision recognition: Feature-level splicing retains the discrimination information of each mode. Through nonlinear mapping of the fully connected network, the wear state is accurately classified, which can effectively improve the overall recognition accuracy. The precision, recall and F1 score are significantly better than the single signal model and the conventional CNN, ResNet, Transformer and other comparative models.

[0028] In summary, the present invention provides a method for monitoring the wear state of a drum-shaped worm grinding wheel that considers the time-varying characteristics of the contact area. This method effectively solves the problem of difficulty in extracting wear characteristics under time-varying contact conditions and provides reliable technical support for intelligent monitoring of continuous generating grinding of face gears. Attached Figure Description

[0029] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration: Figure 1 A schematic diagram illustrating the characteristics of continuous generating grinding of face gears; Figure 2 This is a flowchart of the method for monitoring the wear state of a drum-shaped worm grinding wheel considering the time-varying characteristics of the contact area according to the present invention. Figure 3 A flowchart for data preprocessing; Figure 4 This is a schematic diagram of the FGCGG processing principle; Figure 5 This is a schematic diagram of the FGCGG contact state; Figure 6 A schematic diagram of the multi-scale attention mechanism (EMA) for cross-space learning; Figure 7 This is a schematic diagram of a vibration signal time-frequency image feature extractor based on EMA-CNN. Figure 8 This is a schematic diagram of a timing feature extractor for acoustic emission signals based on HTCN-AKFS-TE. Figure 9 A schematic diagram of the constraint loss function for the wear state identification mechanism of FGCGG; Figure 10 This is a flowchart of the experiment. Figure 11 The surface changes during the wear process of the worm gear grinding wheel; Figure 12 The results of the wear state classification for the worm gear grinding wheel; Figure 13 The confusion matrix for the image processing model; Figure 14 This is the confusion matrix for the time-series processing model. Figure 15 The confusion matrix of the model; Figure 16A comparison of performance indicators of constraint models for vibration signal mechanism; Figure 17 Comparison of performance indicators of constraint models for acoustic emission signal mechanism; Figure 18 Performance indicators for vibration signal comparison models; Figure 19 Comparison of performance indicators for acoustic emission signal input models; Figure 20 A performance comparison analysis of the multimodal feature fusion model and the single feature input model; Figure 21 Record the training process for each model. Detailed Implementation

[0030] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0031] The machining principle of continuous generating grinding of face gears is essentially to simulate the conjugate meshing motion between a virtual gear shaper and the face gear, such as... Figure 1 As shown in (a) of the diagram. The drum-shaped worm grinding wheel is not a standard worm, but a special conjugate surface obtained through precise calculation and dressing, exhibiting complex spatial variations. Thanks to this specially designed drum-shaped tooth profile, the worm grinding wheel can accurately reproduce the cutting edge trajectory of the virtual gear shaper during grinding, achieving meshing with the face gear. Through precise control by a CNC system, the worm grinding wheel and the face gear rotate synchronously according to a fixed transmission ratio; that is, for every one revolution of the worm grinding wheel, the face gear rotates by the angle of one tooth, thus spatially reproducing the ideal conjugate motion between the virtual gear shaper and the face gear. Simultaneously, the worm grinding wheel continuously feeds along the radial direction of the face gear, i.e., the center distance between the two... The radial low-speed feed motion and high-speed rotational motion superimpose to form a complex motion trajectory under combined action. The trajectory of a single abrasive grain in the workpiece coordinate system is not a simple circular arc, but a complex spatial curve. Furthermore, at the microscopic level, each abrasive grain on the worm wheel surface sequentially undergoes three stages: sliding, plowing, and cutting. The distribution density and height of the abrasive grains directly affect the number of abrasive grains participating in cutting and the cutting depth. It is the combined effect of these macroscopic motion characteristics and microscopic abrasive grain behavior that causes the contact area between the worm wheel and the workpiece to exhibit significant time-varying characteristics, with the variation pattern as follows: Figure 1 (b) is also the core feature that distinguishes continuous generating grinding of face gears from ordinary grinding methods.

[0032] Continuous generating grinding (FGCGG) of face gears is the preferred method for batch machining of face gears, and its machining quality is closely related to the wear state of the worm gear grinding wheel. The identification of tool wear state can be achieved by establishing a mapping relationship between the machining process signals and the tool wear state. However, the wear mechanism of the worm gear grinding wheel is complex, and the contact state during machining exhibits significant periodic changes, making it difficult for existing monitoring models to accurately extract wear-related information, severely limiting the accuracy and reliability of wear state identification. Therefore, this invention aims to propose a worm gear grinding wheel wear state monitoring method (PI-MFF) and system that considers the time-varying characteristics of the contact area. First, addressing the wear state definition problem, a worm gear grinding wheel wear state definition method based on multidimensional characterization is established, clarifying the criteria for different wear stages and providing clear and robust target labels for high-precision monitoring. Based on this, vibration and acoustic emission multimodal signals are integrated to complement physical field information, and short-time stationary physical constraints (PC) are introduced to suppress the interference of periodic contact changes on wear state identification, guiding the model to learn physically consistent feature expressions. Furthermore, an EMA-CNN time-frequency feature extractor for vibration signals and an HTCN-AKFS-TE time-series feature extractor for acoustic emission signals were constructed to achieve accurate mining of deep wear information. Finally, through the synergistic effect of feature-level fusion and a physically enhanced classifier, a precise mapping between wear state and multidimensional features was established. Experimental results show that the PI-MFF model achieves a comprehensive recognition accuracy of 99.29%, with precision, recall, and F1 score of 99.19%, 99.44%, and 99.31%, respectively, significantly outperforming other comparative models. The proposed method can accurately identify the wear state of drum-shaped worm gear grinding wheels, providing a reliable basis for intelligent decision-making in FGCGG.

[0033] Specifically, such as Figure 2 As shown in the figure, the method for monitoring the wear condition of a drum-shaped worm grinding wheel considering the time-varying characteristics of the contact area in this embodiment includes the following steps.

[0034] Step 1: Data Acquisition: During the continuous generating grinding of face gears, vibration signals and acoustic emission signals in the machining area of ​​the worm wheel are collected simultaneously to construct a multimodal raw signal dataset.

[0035] Specifically, the periodic evolution mechanism of the contact area between the drum-shaped worm grinding wheel and the face gear is as follows. The machining principle of continuous generating grinding of face gears is essentially a simulation of the conjugate meshing motion between a virtual gear shaper and the face gear. The face gear shaping machining principle is as follows: Figure 4As shown in (a) above, the tooth surface of the worm wheel is designed as the conjugate envelope of the virtual gear shaper tooth surface. In actual grinding, the worm wheel acts as a physical substitute for the virtual gear shaper. The machine tool reproduces the generating meshing relationship between the virtual gear shaper and the face gear by precisely controlling the relative motion between the worm wheel and the face gear. At the same time, in order to enclose the complete tooth width, the worm wheel also needs to make a continuous feed motion along the axis of the virtual gear shaper (i.e., the tooth width direction of the face gear), and its feed path is parallel to the generatrix of the face gear cone.

[0036] During the motion, the worm grinding wheel rotates around its own axis at an angular velocity High-speed rotation, while the face gear operates at a precise transmission ratio. (in This refers to the number of worm gear grinding wheel heads. (The number of teeth of the face gear) rotates around its own axis, and the worm grinding wheel rotates at an angle. Rotation angle of face gear Satisfy the transmission ratio relationship:

[0037] This superposition of rotational motion around their respective axes and feed motion along the tooth width direction causes the instantaneous contact point between the worm wheel tooth surface and the face gear tooth surface to move continuously in a specific direction on the face gear tooth surface, gradually sweeping and enveloping the entire target tooth surface. Each complete rotation of the worm wheel not only corresponds to the face gear rotating through one tooth pitch angle, but also marks a complete periodic change in the contact state between the worm wheel surface and the workpiece tooth surface.

[0038] To achieve accurate spatial mapping from worm grinding wheel to face gear, it is necessary to establish multi-level coordinate systems and complete corresponding homogeneous coordinate transformations, such as... Figure 4 As shown in (b), a moving coordinate system is established that is fixed to the worm gear grinding wheel. The moving coordinate system fixed to the face gear and auxiliary static coordinate systems fixed to the bases of both machines. and Any point on the tooth surface of the worm gear grinding wheel... The position needs to be transformed sequentially through rotation from the fixed-motion coordinate system to the static coordinate system, translation between static coordinate systems, and rotation from the static coordinate system to the moving coordinate system of the face gear, finally transforming to the face gear coordinate system. middle. arrive The homogeneous coordinate matrix is:

[0039] in:

[0040]

[0041]

[0042]

[0043] in: This is the transformation matrix from the static coordinate system to the dynamic coordinate system of the face gear; This is the transformation matrix from the static coordinate system of the virtual gear shaper to the static coordinate system of the face gear; This is the transformation matrix from the static coordinate system of the worm gear grinding wheel to the static coordinate system of the virtual gear shaper. This is the transformation matrix from the moving coordinate system of the worm grinding wheel to the stationary coordinate system of the worm grinding wheel; For the face gear rotation angle; The rotation angle of the worm gear grinding wheel; The helix angle of the worm gear grinding wheel; For feed parameters; Let be the distance between the static coordinate system of the worm gear grinding wheel and the static coordinate system of the face gear in the z-axis direction.

[0044] This coordinate transformation chain unifies the rotational motion of the worm grinding wheel, the rotational motion of the face gear, and the feed motion between them within the same mathematical framework, accurately characterizing the position and orientation of the worm grinding wheel tooth surface in the face gear coordinate system at any instant. Based on this, the worm grinding wheel tooth surface in... The envelope in the middle must simultaneously satisfy two engagement conditions:

[0045]

[0046] in, The equation for the tooth surface of a face gear is... To adjust the wheel suspension angle, These are the parameters for the involute tooth surface of a virtual gear shaper. For feed parameters, The rotation angle of the worm gear grinding wheel; and These represent the envelope condition functions of the worm grinding wheel tooth surface and the face gear tooth surface in the worm rotation and radial feed directions, respectively. A value of zero indicates that the two tooth surfaces exactly satisfy the conjugate contact condition at the instant of the motion.

[0047] During a complete meshing cycle, as the rotation angle of the worm grinding wheel changes continuously, the meshing contact state constantly changes, such as... Figure 5 As shown. Figure 5 In the middle, (a) to (c) are respectively , and This diagram illustrates the contact state during operation. Macroscopically, the number of meshing tooth pairs increases and decreases systematically: when the grinding wheel rotates to a certain angle, the number of meshing tooth pairs reaches its maximum, and the contact area increases accordingly; subsequently, some tooth pairs gradually disengage, and the contact area decreases; at another critical angle, new tooth pairs enter meshing, and the contact area increases again. Microscopically, the tooth profiles of the worm grinding wheel and the face gear are complex, the instantaneous contact area is constantly changing, and it is affected by process parameters such as the cutting depth. After the worm grinding wheel completes one revolution, the tooth profiles of each phase return to their initial configuration, and the face gear rotates through one tooth pitch angle, completing a full cycle. The coupling of macroscopic tooth pair replacement and microscopic contact area changes causes the total contact area to exhibit a continuously changing state within a cycle.

[0048] This dynamic time-varying characteristic is the essential difference in mechanism between FGCGG and other grinding methods. In profile grinding, the profile of the grinding wheel corresponds one-to-one with the shape of the tooth groove, and the contact area remains basically constant during the grinding process; its contact state can be approximated as a steady state. However, worm wheel grinding is based on continuous generating motion, and the meshing state changes continuously with the rotation angle. The time-varying characteristics of the contact area are not accidental disturbances and cannot be ignored in process analysis and condition monitoring. If it is regarded as a steady-state constant, the signal fluctuations caused by this periodic change, together with the trend drift caused by tool wear accumulation, will superimpose in the time-frequency domain. The monitoring model will find it difficult to distinguish between inherent periodic fluctuations and abnormal wear signals, thus severely weakening the accuracy of wear feature extraction and the model's generalization ability. Therefore, analyzing the periodic changes in the contact state of FGCGG is not only the theoretical core for understanding the dynamic characteristics of this process, but also a necessary prerequisite for embedding it as a deterministic physical prior into the wear condition monitoring model, achieving effective signal decoupling and accurate condition identification.

[0049] Step 2: Data Preprocessing: The acquired vibration signal and acoustic emission signal are preprocessed respectively; continuous wavelet transform is performed on the preprocessed vibration signal to generate a time-frequency diagram of the vibration signal, while retaining the original temporal characteristics of the preprocessed acoustic emission signal. Specifically, the preprocessing includes filtering and noise reduction, amplitude normalization, and equal-length signal truncation based on the rotation period of the worm gear grinding wheel.

[0050] Continuous generating grinding of face gears is not only a highly efficient and precise machining method, but also a time-varying process characterized by strong nonlinearity, strong periodicity, and high sensitivity to the morphology of the worm gear grinding wheel. During the machining process, acoustic emission signals can keenly capture high-energy physical events such as microscopic plastic deformation, crack initiation, and abrasive grain breakage during material removal, profoundly reflecting the essential mechanism of grinding and the microscopic wear behavior of the grinding wheel. Vibration signals can reflect the dynamic response of the machining system and are extremely sensitive to macroscopic state changes such as transient impacts induced by grinding wheel wear and system resonance during continuous generating motion. Therefore, this embodiment uses vibration signals and acoustic emission signals during the machining process to achieve multi-dimensional perception of the wear state of the worm gear grinding wheel.

[0051] (1) Filtering and noise reduction. A fourth-order Butterworth bandpass filter is used for filtering and noise reduction. The passband frequency range of the vibration signal is set to 10 Hz to 5000 Hz, and the passband frequency range of the acoustic emission signal is set to 60 kHz to 400 kHz.

[0052] Specifically, in the data preprocessing stage, a Butterworth filter is first used to filter and reduce noise in the original signal. Both vibration and acoustic emission signals are filtered using a fourth-order bandpass filter. The passband for the vibration signal is set to 10 Hz to 5000 Hz to eliminate low-frequency environmental interference and high-frequency electromagnetic noise, effectively preserving the core frequency band reflecting the dynamic behavior of grinding. The passband for the acoustic emission signal is set to 60 kHz to 400 kHz to accurately extract the high-frequency stress wave characteristics excited by the microscopic plastic deformation of the material and the microscopic wear of the worm wheel. This filter has the characteristic of a maximally flat passband, which can effectively eliminate environmental noise and high-frequency interference while preserving the waveform characteristics of the original vibration and acoustic emission signals to the greatest extent possible, avoiding amplitude distortion introduced by filtering.

[0053] (2) Amplitude normalization. Amplitude normalization adopts the minimum-maximum normalization method to map the amplitude of each channel signal to the interval [0, 1].

[0054] Specifically, to eliminate the impact of dimensional differences and signal amplitude fluctuations between different sensor channels on subsequent analysis, the filtered signal is normalized. This embodiment uses a minimum-maximum normalization method to map each channel signal to the [0, 1] interval. The calculation formula is as follows:

[0055] in: These are the original signal sample values; and These are the minimum and maximum values ​​of the signal sequence, respectively.

[0056] (3) Equal-length signal extraction. Equal-length signal extraction takes five rotations of the worm wheel as a feature extraction unit, and extracts ten signal segments from the stable grinding stage to achieve data enhancement.

[0057] Specifically, to ensure the consistency and sufficiency of the sample data, the continuously acquired grinding process signals are processed by equal-length truncation. In this embodiment, five rotations of the worm wheel are considered as one feature extraction unit, and 10 segments are selected from each stable grinding stage to achieve data augmentation. This not only effectively avoids transient instability interference during the grinding entry and exit stages but also covers the complete grinding cycle, thereby avoiding the randomness of feature extraction.

[0058] (4) Continuous wavelet transform. The continuous wavelet transform uses Morlet wavelet as the mother wavelet basis function and adopts a logarithmic uniform scale step size (i.e., the scale sequence increases in a geometric progression, and the corresponding frequencies are logarithmically distributed, so that the frequency intervals in the low frequency band are small and the intervals in the high frequency band are large) for time-frequency transformation, so that the frequency division in the low frequency region is finer than that in the high frequency region, in order to balance the time resolution and frequency resolution.

[0059] Specifically, given that a single time-domain waveform cannot fully reveal the instantaneous abrupt changes and frequency evolution patterns of the grinding process, this embodiment employs Continuous Wavelet Transform (CWT) for time-frequency analysis of the vibration signal. Using Morlet wavelets as the mother wavelet basis function and a logarithmically uniform step size, the low-frequency region is finely divided while the high-frequency region is relatively sparse, effectively balancing the time and frequency resolution of the time-frequency analysis. Compared with other time-frequency analysis methods, CWT exhibits significant advantages in processing non-stationary signals and revealing local features. Simultaneously, it preserves the original temporal characteristics of the acoustic emission signal to accurately capture time-varying burst information during the grinding process. The complete preprocessing workflow is as follows: Figure 3 As shown.

[0060] Step 3: Feature Extraction: Deep mining of multidimensional features considering contact time-varying characteristics.

[0061] 1. Vibration signal time-frequency feature extractor based on EMA-CNN.

[0062] The time-frequency graph of the vibration signal after CWT is rich in information about the changes in the state of the worm wheel during grinding. Features in different frequency bands have varying abilities to characterize the wear state of the worm wheel. High-frequency features reflect transient changes caused by abrasive grain shedding or minor impacts, while low-frequency features reflect the overall wear evolution trend of the grinding wheel. Both are crucial for the model to accurately identify the wear state. Due to the continuous changes in the contact area during face gear continuous generating grinding, the wear-related features in the original time-frequency graph dynamically evolve, and a large amount of redundant information and noise further interferes with the model's focus on key features. Therefore, this embodiment introduces an efficient multi-scale attention (EMA) module with cross-spatial learning to achieve accurate feature extraction from the time-frequency graph of the vibration signal under time-varying conditions. This module captures dynamic patterns at different time-frequency scales in the time-frequency graph through parallel multi-scale convolution branches and adaptively enhances the response of key regions strongly correlated with wear in the spatial dimension using a cross-spatial interaction mechanism, while suppressing redundant information and noise interference, thus effectively addressing the dynamic evolution of the frequency domain structure. Figure 6 As shown, the EMA process consists of three parts.

[0063] This embodiment constructs a vibration signal time-frequency feature extractor based on EMA-CNN. The vibration signal time-frequency map is input into the vibration signal time-frequency feature extractor to extract the deep wear features in the time-frequency domain of the vibration signal. The EMA-CNN is constructed based on Efficient Multi-Scale Attention (EMA) and Convolutional Neural Networks (CNN). It is a CNN with an embedded Efficient Multi-Scale Attention (EMA) mechanism and includes an EMA module. The EMA module achieves dynamic focusing on time-varying wear features by grouping the input feature map along the channel dimension, running 1×1 and 3×3 convolution branches in parallel, and performing cross-space learning.

[0064] like Figure 6 As shown in this embodiment, the EMA module includes a feature grouping unit, a parallel convolution branch unit, and a cross-space learning unit.

[0065] The first part of the EMA module is the feature grouping unit, which is used to divide the input feature map into multiple non-overlapping sub-feature groups along the channel dimension to aggregate local time-frequency features in different channels.

[0066] Specifically, different channels in the input feature map have varying degrees of focus on different time-frequency regions. Therefore, the input feature map is divided along the channel dimension into... Non-overlapping sub-feature groups aggregate local time-frequency features from different channels, expanding the receptive field within each group and enhancing the ability to capture time-varying wear features, as shown below:

[0067] in: The first one obtained after division Sub-feature groups, C represents the total number of channels in the input feature map. Number of groups Need to be able to be Divisible; The feature map height; This represents the width of the feature map.

[0068] The second part of the EMA module is the parallel convolution branch unit, which is used to execute two independent convolution branches in parallel for each of the divided sub-feature groups: the first branch is a 1×1 convolution branch, which extracts positional information by one-dimensional global pooling along the time axis and frequency axis respectively, and after concatenation, convolution and activation, it is multiplied element-wise with the original group features to achieve feature calibration in spatial direction; the second branch is a 3×3 convolution branch, which expands the receptive field and extracts multi-scale detailed features in the neighborhood through local convolution.

[0069] Specifically, after feature grouping, the parallel convolutional branch unit runs two computational branches in parallel. One is a 1×1 branch, which extracts the positional information of the time axis and frequency axis through one-dimensional global pooling in the horizontal and vertical directions, respectively. This information is then concatenated and subjected to 1×1 convolution to achieve cross-time-frequency interaction. A sigmoid function is then used to transform the processed feature vector into a weight vector normalized to the range of 0 to 1, and this weight vector is multiplied element-wise with the original grouped features to achieve spatial feature calibration. Finally, group normalization yields the output of this branch. The formula is expressed as follows:

[0070]

[0071]

[0072]

[0073]

[0074] in: Represents the first feature in a sub-feature group Feature maps of each channel; , This represents the result of one-dimensional global pooling for this channel; , The tensor representing the stack of all channel pooling results; It was through The cross-time-frequency features obtained after convolution; Indicates will and splicing together in the spatial dimension; Split the tensor according to its original height and width; Indicates group normalization; Use the Sigmoid activation function; Indicates the first Each sub-feature group has a 1×1 branch output.

[0075] The other branch of the parallel convolutional branch unit is a 3×3 branch, which directly expands the receptive field and captures multi-scale details within the neighborhood through local convolution. The two branches execute completely independently, focusing on long-range dependency modeling along spatial directions and local detail feature extraction, respectively, as shown below:

[0076] in: Indicates the first The output of each sub-feature group is a 3×3 branch.

[0077] The third part of the EMA module is the cross-spatial learning unit, which is used to perform spatial attention interaction between the outputs of the 1×1 convolutional branch and the 3×3 convolutional branch. The cross-spatial learning unit applies global pooling, tensor reshaping and Softmax normalization to the output of each branch to obtain a weight vector, and performs matrix multiplication with the output of another branch. The two spatial attention results are added together, processed by the activation function, and then multiplied with the original sub-feature group to obtain the output feature of the EMA module.

[0078] Specifically, each branch applies two-dimensional global average pooling, reshaping, and softmax to its own output to obtain a weight vector, which is then multiplied with the output of the other branch to obtain two spatial attention results. These two attention maps are then summed, activated by a sigmoid function, and multiplied with the original sub-feature group to extract features. The formula is expressed as follows:

[0079]

[0080]

[0081]

[0082] in: This is the global attention weight vector; hour, Corresponding to a 1×1 branch output, Corresponding to 3×3 branch output, On the contrary; It is by The reshaped two-dimensional matrix; This indicates that the feature map is flattened in the spatial dimension; This represents a spatial attention map generated by the interaction of two branches; and They are respectively and Spatial attention results obtained at that time; for Module output characteristics; Use the Sigmoid activation function; For the first Sub-feature groups.

[0083] The vibration signal feature extractor's backbone is composed of a CNN, with convolutional layers connected by an EMA module. The CNN itself possesses selective learning capabilities, enabling it to extract features highly correlated with wear conditions. The introduction of EMA further enhances the model's ability to focus on time-varying features, allowing the network to adaptively emphasize wear-sensitive features and suppress irrelevant information during training. However, adding EMA to all convolutional layers leads to a surge in parameters, prolonged training time, and compromises the model's robustness. Therefore, the vibration signal time-frequency map feature extractor framework is designed as follows: Figure 7 As shown.

[0084] 2. Acoustic emission timing feature extractor based on HTCN-AKFS-TE.

[0085] Acoustic emission time-series signals contain rich microscopic evolutionary information such as abrasive passivation and micro-fragmentation. Their temporal evolution exhibits complex characteristics, simultaneously coupling short-term local fluctuations with long-term global trends. In continuous generating grinding of face gears, the time-varying characteristics of the contact area cause the continuous changes in the generation and propagation conditions of the acoustic emission signals, further exacerbating the non-stationarity and complexity of their temporal patterns. Furthermore, the acoustic emission signals themselves have extremely high frequency bands, resulting in massively long time-series sequences. Directly inputting these sequences into a model for feature modeling would incur significant computational overhead; while blindly downsampling to compress the sequences could easily lead to irreversible loss of wear-sensitive transient features and crucial details. To address these issues, this embodiment constructs a hierarchical temporal convolutional network HTCN-adaptive key feature filter AKFS-Transformer encoder TE long sequence feature extraction module, effectively mining deep features strongly correlated with the wear state of the worm gear grinding wheel in the acoustic emission time-series signals under time-varying conditions. Figure 8 As shown, the process is divided into three parts.

[0086] Specifically, this embodiment constructs an acoustic emission temporal feature extractor based on HTCN-AKFS-TE. The preprocessed acoustic emission signal is input into the acoustic emission temporal feature extractor to extract the temporal evolution wear features of the acoustic emission signal. HTCN-AKFS-TE is constructed based on the Hierarchical Temporal Convolutional Network (HTCN), the Adaptive Key Feature Selector (AKFS), and the Transformer Encoder (TE), as shown below. Figure 8As shown, the acoustic emission temporal feature extractor includes a hierarchical temporal convolutional network (HTCN), an adaptive key feature filter (AKFS), and a Transformer encoder (TE). The hierarchical temporal convolutional network (HTCN) captures dynamic evolution patterns across multiple time spans through multiple convolutional layers with different dilation rates; the adaptive key feature filter (AKFS) filters high-value key feature fragments from the output features of the hierarchical temporal convolutional network (HTCN) through a learnable scoring network; and the Transformer encoder (TE) performs deep interaction and representation enhancement on the filtered key feature fragments.

[0087] The first part of the acoustic emission temporal feature extractor is the hierarchical temporal convolutional network (HTCN). By capturing dynamic evolution patterns across different time spans through three convolutional layers with varying dilation rates, a network structure with a wide receptive field is constructed. This allows for the capture of hierarchical features, from subtle local fluctuations to global trend evolution, while preserving the temporal integrity of the signal. The HTCN consists of three dilated convolutional layers with dilation rates of 1, 2, and 4, a kernel size of 7, and the activation function ReLU for all layers. The parameter settings for each layer are shown in Table 1.

[0088] Table 1. Parameter settings for the Hierarchical Temporal Convolutional Network (HTCN)

[0089] The second part of the acoustic emission temporal feature extractor is the adaptive key feature filter (AKFS). Specifically, the AKFS method for filtering key feature segments is as follows: each step of the feature vector output by the hierarchical temporal convolutional network (HTCN) is scored, the importance score of each time step is calculated through a learnable scoring network, the M time point indices with the highest scores are selected, and a subset of key features is extracted from the feature sequence output by the hierarchical temporal convolutional network (HTCN) based on the indices, which is then used as the input of the Transformer encoder (TE).

[0090] To further focus on key information strongly correlated with wear status while reducing computational complexity, this paper adopts the two-stage paradigm of the MUSE architecture for handling ultra-long sequences, using a "retrieval-reasoning" approach to focus on and deduplicate key information. Specifically, a learnable scoring network is introduced to score the features at each step, selecting the time point indices corresponding to higher scores, and extracting feature subsets from the previous step's output based on these indices. The formula is expressed as follows:

[0091]

[0092]

[0093] in: For the first Feature scores for each time step ; For the first Feature vectors at each time step; and These are learnable parameters; Output the score for the selector; A set of indexes for key time points; The feature sequence obtained after dilated convolution; These are the key feature fragments after filtering; Batch size; The sequence length; To take the front Indexing operations for the maximum value; The number of key time points selected.

[0094] The third part of the acoustic emission temporal feature extractor is the Transformer encoder (TE). The Transformer encoder (TE) incorporates a multi-head self-attention mechanism, and its model dimension... Set to 128, number of attention heads Set to 4, number of encoder layers Set to 2.

[0095] Specifically, the selected high-value feature sequences are input into the Transformer encoder (TE) for deep feature extraction. Leveraging the long-distance dependency modeling advantages of the self-attention mechanism, the deep interactive relationships between feature points are further explored, thereby achieving refined characterization and enhancement of wear features in acoustic emission signals.

[0096] Step 4: Feature Fusion: The time-frequency domain deep wear features of the extracted vibration signal and the time-series evolution wear features of the acoustic emission signal are fused at the feature level to construct a multimodal joint feature vector.

[0097] Multimodal signal fusion strategies mainly include three paradigms: data-level fusion, feature-level fusion, and decision-level fusion. Compared to data-level fusion, feature-level fusion effectively reduces data dimensionality and computational complexity by extracting high-dimensional feature vectors. Compared to decision-level fusion, feature-level fusion can fully explore the deep correlations and complementary information between different modalities at the feature representation level, helping the model learn more discriminative joint feature representations. Therefore, this embodiment chooses feature-level fusion to achieve multimodal signal fusion. Through feature-level fusion, the model can more precisely capture the inherent coupling relationship of multimodal signals during the grinding process, thereby improving the accuracy and robustness of wear state identification. After completing the feature extraction of each modal signal, feature-level fusion is performed using a concatenation method.

[0098] In this embodiment, feature-level fusion employs a concatenation method, which concatenates the vibration signal feature vector and the acoustic emission signal feature vector along the channel dimension to generate a joint feature vector, represented as follows:

[0099] in: It is the feature vector of the acoustic emission signal extracted by the acoustic emission timing feature extractor; It is a vibration signal feature vector extracted by a vibration signal time-frequency feature extractor. These feature vectors are concatenated along the channel dimension to generate a joint feature vector. .

[0100] Step 5: Wear State Recognition Guided by Physical Constraints: The multimodal joint feature vector is input into the wear state recognition module for training and recognition. The wear state recognition module uses a physical constraint loss function to guide model training. The physical constraint loss function is constructed based on the slow evolution law of worm wheel wear (i.e., the wear amount will not change abruptly in a short period of time, but will be a monotonous and slow cumulative degradation process over time, which can be approximately regarded as constant within the collection period of a single sample). By forcing the wear state estimation of different sub-periods within the same sample to remain consistent, the interference of periodic changes in the contact area on wear feature learning is suppressed.

[0101] During the continuous generating grinding of face gears, the contact area between the worm wheel and the face gear exhibits significant periodic changes, leading to strong fluctuations in the machining signal. If the model relies solely on data-driven learning to establish the mapping between the signal and the wear state, it is highly susceptible to misinterpreting signal fluctuations caused by changes in the contact state as changes in the degree of wear, thus affecting recognition accuracy. Therefore, this embodiment constructs a mechanism-constrained loss function based on the general laws of wear evolution, ensuring that the model's training process is guided by physical priors in addition to data fitting. The process is as follows: Figure 9 As shown.

[0102] The contact area between the worm gear and the face gear exhibits a significant periodic variation, but the absolute wear of the abrasive grains changes negligibly within a single sample (corresponding to 5 rotations of the worm gear). Therefore, the wear state within a single sample can be considered constant. Based on this physical prior, this embodiment proposes a short-term stationarity physical constraint: forcing the model to extract consistent features of the wear state corresponding to each sub-time period. Specifically, each sample is divided along the time axis into... Each sub-segment (K=5) is input into the model, such as... Figure 9 As shown in the upper right corner, we get The predicted probability distribution is then transformed into a probabilistic representation of wear states using a softmax function. To quantitatively characterize the degree of wear, a continuous wear index is defined:

[0103] in: For the first The probability that each sub-segment belongs to category c is predicted; It reflects the model's continuous estimation of the degree of wear and tear during that period; These correspond to the initial wear stage, normal wear stage, and severe wear stage, respectively. If the model correctly captures the slowly varying characteristics related to wear, then within the same sample... The continuous wear index of each sub-segment should remain highly consistent; conversely, if the model is affected by periodic changes in the contact state and misinterprets signal fluctuations as wear changes, significant discrepancies will occur. Based on this, a physical constraint loss is defined. :

[0104] in, This refers to the batch size; Indicates calculation The variance of the continuous wear index of each sub-segment; For the first In the nth sample The continuous wear index of each segment. This loss term is minimized during training, which is equivalent to forcing the model to output a consistent wear estimate within a short time window, thereby effectively suppressing the interference of contact state changes on feature learning.

[0105] Based on the above design, the model's total loss function consists of two parts: classification loss and physical constraint loss.

[0106] in: The cross-entropy loss is used for multi-class classification to ensure the model's basic ability to distinguish wear states; The weighting coefficients are used to adjust the strength of the physical constraints. This loss function is designed without relying on precise grinding forces or thermodynamic analytical formulas; it guides the model to learn physically consistent feature representations based solely on the fundamental laws of wear evolution, thereby improving recognition accuracy while enhancing the model's generalization ability and interpretability.

[0107] Step Six: Wear State Category: Input the multimodal joint feature vector into the trained wear state recognition module, and output the current wear state category of the drum worm grinding wheel; the wear state recognition module includes a fully connected layer, a batch normalization layer, a ReLU activation layer, a Dropout layer and a Softmax classification layer connected in sequence.

[0108] The worm gear grinding wheel wear state recognition module based on multimodal feature fusion (MFF) consists of two fully connected layers. All neurons in each layer are connected to all neurons in the previous layer, performing deep nonlinear mapping and dimensionality reduction on the high-dimensional fused features. Following each fully connected layer are a batch normalization layer, a ReLU activation function, and a Dropout layer. The batch normalization layer normalizes the network input to a mean of 0 and a unit variance of 1, effectively accelerating network convergence and training time. The ReLU activation layer endows the model with nonlinear representation capabilities for complex wear state information. The Dropout layer randomly discards some neurons during training, significantly reducing the risk of overfitting while retaining key discriminative information. Finally, the data processed by the fully connected layers is classified using a Softmax classification function to output a probability distribution, thereby achieving accurate recognition of the worm gear grinding wheel wear state.

[0109] The input for this part is the joint feature vector after feature extraction and fusion. The calculation process for the hidden layer is as follows:

[0110]

[0111]

[0112]

[0113] For the output layer, only a linear transformation is performed:

[0114] in: and These are the input features of the first layer and the input features of the second layer, respectively. and These are the weighted sum after linear transformation and the result after batch normalization, respectively. It is the output of the last layer; The activation function outputs features; , These are the weights and biases of the fully connected layer, which can be updated through backpropagation to achieve iterative optimization of network parameters and minimization of the loss function.

[0115] Specifically, the wear state categories include initial wear stage, normal wear stage, and severe wear stage. In this embodiment, the threshold for judging the severe wear stage is predetermined using the following quantification and grading method: Collect point cloud data of the surface morphology of the worm gear grinding wheel; Calculate the average effective blade height based on the point cloud data. and abrasive passivation rate :

[0116]

[0117] The effective average height of the cutting edge After global normalization, it is compared with the wear particle passivation rate. Perform weighted summation to construct a comprehensive wear and tear index. :

[0118] in: The height of the binder reference surface is taken as the 10th percentile of the point cloud data; For global normalization (referring to normalization based on all samples) The effective average height of the blade after Min-Max standardization; For the first The height value of each data point; In this embodiment, the preset effective cutting edge height threshold for abrasive grains is used. ; To meet The number of valid points; This represents the total number of points in the point cloud data. To meet The number of invalid points; This is an indicator function; it takes the value 1 when the condition is true, and 0 otherwise. Based on the comprehensive wear index The evolution curve of the wear process with the number of grinding cycles was used to divide the wear process into the initial wear stage, the normal wear stage, and the severe wear stage using the K-means clustering algorithm.

[0119] This embodiment also proposes a drum-shaped worm grinding wheel wear condition monitoring system that considers the time-varying characteristics of the contact area, used to implement the drum-shaped worm grinding wheel wear condition monitoring method considering the time-varying characteristics of the contact area as described in this embodiment. Specifically, the drum-shaped worm grinding wheel wear condition monitoring system considering the time-varying characteristics of the contact area in this embodiment includes a signal acquisition module, a signal preprocessing module, a vibration signal feature extraction module, an acoustic emission signal feature extraction module, a multi-modal feature fusion module, and a wear condition identification module. Specifically, the signal acquisition module is used to simultaneously acquire vibration signals and acoustic emission signals from the worm wheel machining area during the continuous generating grinding process of the face gear; the signal preprocessing module is used to filter and reduce noise, normalize amplitude, and truncate the acquired vibration and acoustic emission signals respectively, and to perform continuous wavelet transform on the preprocessed vibration signals to generate a vibration signal time-frequency map; the vibration signal feature extraction module uses an EMA-CNN-based vibration signal time-frequency feature extractor to extract the time-frequency domain deep wear features of the vibration signal from the vibration signal time-frequency map; the EMA-CNN is a convolutional neural network (CNN) with an embedded cross-spatial learning multi-scale attention EMA mechanism; acoustic emission signal features... The extraction module employs an acoustic emission temporal feature extractor based on HTCN-AKFS-TE to extract temporal evolution wear features from the preprocessed acoustic emission signal. The HTCN-AKFS-TE includes a hierarchical temporal convolutional network HTCN, an adaptive key feature filter AKFS, and a Transformer encoder TE. The multimodal feature fusion module is used to perform feature-level fusion of the time-frequency domain deep wear features of the vibration signal and the temporal evolution wear features of the acoustic emission signal to generate a multimodal joint feature vector. The wear state recognition module is used to input the multimodal joint feature vector into a trained classifier and output the current wear state category of the drum-shaped worm grinding wheel.

[0120] Furthermore, the hierarchical temporal convolutional network HTCN includes three dilated convolutional layers with dilation rates of 1, 2, and 4, respectively, a kernel size of 7, and the activation function ReLU for all layers. The adaptive key feature filter AKFS calculates the importance score of each time step in the output features of the hierarchical temporal convolutional network HTCN through a learnable scoring network, selects the M time point indices with the highest scores, and extracts the corresponding key feature subsets. The multimodal feature fusion module uses a concatenation method to concatenate the vibration signal feature vector and the acoustic emission signal feature vector in the channel dimension.

[0121] The specific implementation method of this embodiment will be further explained below with reference to specific experiments.

[0122] 1. Model performance evaluation.

[0123] In the process of model construction and optimization, the balance between network complexity and generalization ability is a core consideration. Theoretically, increasing model complexity often leads to enhanced representation ability, which can potentially result in higher classification accuracy. However, high-complexity networks typically involve a large number of parameters and computational overhead, and place higher demands on the scale and quality of training samples. To scientifically quantify the performance differences between different model architectures, this embodiment uses five core metrics—confusion matrix, accuracy, precision, recall, and F1 score—for comprehensive evaluation, aiming to objectively reflect the performance of the classification model from different perspectives. The confusion matrix visually presents the detailed distribution of classification results, while accuracy, precision, recall, and F1 score are quantitatively calculated to comprehensively characterize the model's classification performance from dimensions such as overall accuracy, positive class prediction reliability, positive class detection capability, and the harmonic mean of precision and recall. The specific calculation formulas for each metric are shown below.

[0124]

[0125]

[0126]

[0127]

[0128] in: True cases are the number of samples that the model correctly predicts as positive. True negative examples are the number of samples that the model correctly predicted as negative. False positives are the number of samples that the model incorrectly predicts as positive. False negatives are the number of samples that the model incorrectly predicts as negative. Recall rate; For accuracy.

[0129] 2. Experimental design.

[0130] 2.1 Construction of an experimental platform for continuous generating grinding of face gears.

[0131] The worm gear grinding wheel wear experiment was conducted on a face gear grinding machine. The experimental platform consisted of two main parts: a machine tool processing system and a data acquisition system. In the machine tool processing system, the worm gear grinding wheel was prepared by dressing a conventional grinding wheel with an involute profile using a diamond dressing wheel. The face gear was made of 45 steel, and its initial tooth profile was prepared by CNC milling. Detailed parameters of the cutting tool and workpiece are shown in Table 2. The data acquisition system included a vibration signal acquisition system and an acoustic emission signal acquisition system. Both consisted of sensors, signal conditioners, data acquisition units, and data processing units.

[0132] Table 2 Material parameters of the processing system

[0133] The vibration signal acquisition system sensor is mounted on the tool spindle; the data processing unit records the three-dimensional vibration of the spindle at a sampling rate of 40kHz. The acoustic emission acquisition system sensor is mounted on the front cover of the worm wheel; the data processing unit records the acoustic emission signals during the machining process at a sampling rate of 1MHz.

[0134] Furthermore, considering the complexity of the worm wheel geometry, an impression material was used to replicate the worm wheel surface, and the face gear was cut to facilitate the imaging of its surface morphology. A laser scanning confocal microscope was used to scan the worm wheel impression and the face gear cut teeth to obtain the surface morphology of the worm wheel and face gear.

[0135] 2.2 Test Scheme for Worm Grinding Wheel Wear.

[0136] Detailed process parameters for the worm gear grinding wheel wear experiment are shown in Table 3. Based on past machining experience, without dressing the worm gear grinding wheel, the workpiece surface quality cannot be guaranteed when the number of downcuts reaches 70. Therefore, this was set as the termination condition for the experiment. Continuous generating grinding of the face gear worm gear grinding wheel was performed, with each depth of cut considered as one grinding cycle, for a total of 70 grinding cycles.

[0137] Table 3 Experimental parameters

[0138] To ensure sufficient data support for subsequent model training, vibration and acoustic emission signals were collected online synchronously for each grinding cycle. After the experiment began, a monitoring node was set for every five grinding cycles to characterize the wear morphology of the worm wheel. Samples were taken from the face gear workpiece every four monitoring nodes for subsequent surface quality inspection and morphology observation. After completing the preset grinding cycles, a final sample was taken from the face gear, and the experiment terminated. The specific procedure for the worm wheel wear experiment is as follows: Figure 10 As shown.

[0139] To reduce the randomness of data caused by uneven spatial distribution of surface morphology, three locations were randomly selected on the circumference of the worm wheel at each monitoring node for actual photography and impression taking. Based on the actual morphology images, five discontinuous and non-overlapping locations were randomly selected within the grinding area corresponding to each location (i.e., 15 locations per monitoring node) to scan and collect the original point cloud data of the worm wheel impression. For the face gear of the retained sample, two non-adjacent locations were randomly selected for tooth cutting, i.e., four tooth surfaces. The surface morphology was photographed and the surface roughness value was calculated. Since the roughness values ​​differ at different locations on the face gear tooth surface, a 9-point method was used to take the average value to describe the overall tooth surface roughness. The scanning parameters are shown in Table 4.

[0140] Table 4 Topography Scanning Parameters

[0141] 2.3 Experimental data analysis and processing.

[0142] The worm wheel wear experiment consisted of 70 grinding cycles and 14 monitoring nodes. The experiment acquired 140 sets of multi-sensor signal data, 42 worm wheel surface imprints, and 4 face gear samples. In addition, 210 sets of raw point cloud data of the worm wheel imprints and 8 face gear cutting tooth samples along with their corresponding 144 sets of roughness data were obtained.

[0143] 2.3.1 Quantitative grading standard for wear degree of drum-shaped worm grinding wheel.

[0144] Existing methods for defining tool wear states include qualitative descriptions and quantitative methods. Qualitative descriptions are achieved by observing the morphological changes of abrasive grains during machining, while quantitative methods evaluate wear states by measuring or calculating specific values ​​and dividing them into intervals. However, due to the complexity and variability of actual machining scenarios and the unique structure of worm grinding wheels, existing methods are not applicable. Therefore, based on existing experimental conditions and the characteristics of drum-shaped worm grinding wheels, this embodiment innovatively proposes a method for defining wear states.

[0145] First, for the point cloud data of the surface topography of the worm gear grinding wheel, the following three parameters are defined: (1) Average effective blade extension height .

[0146] The worm gear grinding wheel is sintered from a binder and abrasive grains. The binder occupies the main area and has a relatively concentrated height distribution, while the abrasive grains are distributed on it as a few protruding high points. To reduce the influence of scanning noise, wear debris adhesion, and local morphological defects on the determination of the reference surface, the 10th quantile of the point cloud data is used as the binder reference surface. Specifically, the approximate cutting edge height of the abrasive grains is 40% of the grain size. Therefore, a 50μm elevation above the reference surface is used as the dividing line to delineate the effective cutting area and the ineffective area (the binder, low-cut abrasive grains, and other non-cutting parts). The arithmetic mean of the effective point heights above this threshold is defined as the effective cutting edge average height. The expression is as follows:

[0147] in: The height of the binder reference surface is taken as the 10th percentile of the point cloud data; For the first The height value of each data point; ; To meet The number of valid points.

[0148] The effective average protrusion height directly reflects the average protrusion height of the abrasive grains participating in cutting on the surface of the worm gear grinding wheel. A larger value indicates a higher degree of abrasive grain protrusion and better cutting sharpness of the worm gear grinding wheel; conversely, a smaller value indicates wear or dulling of the abrasive grains, resulting in decreased cutting ability. Therefore, the effective average protrusion height can be used as one of the key characteristic parameters for evaluating the wear degree of worm gear grinding wheels.

[0149] (2) Abrasive passivation rate .

[0150] Preliminary observations of the worm gear grinding wheel's surface morphology revealed that, with increasing cutting strokes, worm gear grinding wheel wear primarily manifests as abrasive grain passivation and significant slag deposition filling surface pores. Figure 11 As shown. Based on point cloud height data, invalid regions are considered as wear and passivation regions. The ratio of invalid points in wear and passivation regions to the total number of points in the point cloud is defined as the wear passivation rate. The expression is as follows:

[0151] in: This represents the total number of points in the point cloud data. To meet The number of invalid points; It is the first The height value of each data point; It is the height boundary between the effective region and the ineffective region; This is an indicator function that takes the value 1 when the condition is true, and 0 otherwise.

[0152] Abrasive passivation rate can quantitatively characterize the passivation degree of abrasive grains on the surface of worm grinding wheels and the clogging status of pores. The higher the value, the lower the proportion of effective abrasive grains participating in cutting, the wider the area filled with abrasive chips, and the more significant the decrease in grinding ability; conversely, the lower the value, the better the abrasive grain exit condition, the more unobstructed the pores, and the worm grinding wheel still has good cutting performance.

[0153] (3) Comprehensive wear index .

[0154] The effective average cutting edge height and abrasive passivation rate jointly characterize the wear degree of worm grinding wheels from different dimensions. The former reflects the average cutting edge height of the abrasive grains participating in cutting, focusing on describing the cutting sharpness of the grinding wheel; the latter quantitatively characterizes the degree of abrasive passivation and pore blockage, focusing on reflecting the state evolution of the grinding wheel's working surface and chip removal performance. To comprehensively evaluate the overall wear state of the worm grinding wheel, the two are weighted and summed to define a comprehensive wear index. As follows. To eliminate the influence of different dimensions, After global normalization, it is used in the calculation. As a ratio, it already has a normalized form, so it can be directly substituted into the formula.

[0155]

[0156] This embodiment initially adopts an equal-weighted comprehensive wear index, mainly based on the following considerations: On the one hand, the effective average cutting edge height and abrasive passivation rate characterize the wear behavior of worm grinding wheels from two independent dimensions, namely geometric morphology and functional state, and both have equally important physical significance in revealing the wear mechanism; on the other hand, since there is currently a lack of prior data to clearly define the dominant role of a single parameter, assigning equal weights to both is the most objective approach and can effectively avoid subjective bias.

[0157] Secondly, the comprehensive wear index was calculated based on 210 sets of point cloud data of the worm grinding wheel, and the average value of the data within each monitoring node was taken as the characteristic value representing the wear state of the worm grinding wheel. The calculation results are as follows: Figure 12 As shown in the figure, the blue broken line clearly illustrates the evolution of the overall wear index with increasing cutting frequency.

[0158] Combining classical wear theory, the K-means unsupervised clustering algorithm is adopted (setting the number of clusters). This method categorizes wear levels based on the inherent distribution characteristics of the data, effectively avoiding the subjectivity of manually setting thresholds. For example... Figure 12 As shown, the wear process of the worm grinding wheel is precisely divided into three distinct stages.

[0159] (1) Initial wear stage: The overall wear index is low and grows rapidly in this stage, reflecting that the abrasive grains are fully exposed but not stable. Some abrasive grains with low bonding strength fall off rapidly, resulting in a high wear rate.

[0160] (2) Normal wear stage: In this stage, the rate of increase of the comprehensive wear index tends to be slow, reflecting that the abrasive grains begin to wear and become dull. At the same time, the wear debris gradually fills the surface pores, and the cutting ability of the worm wheel enters a relatively stable decline stage, and the wear rate slows down.

[0161] (3) Severe wear stage: When the number of cutting cycles exceeds 50, the comprehensive wear index shows a significant jump, indicating that the surface morphology of the worm wheel has deteriorated drastically and has entered the severe wear stage. The effective abrasive grain ratio on the surface of the worm wheel is significantly reduced, a large number of abrasive grains are worn flat or fall off, the grinding debris is severely blocked, and the grinding performance is significantly degraded. It is necessary to repair or replace it in time.

[0162] By comparing the surface roughness values ​​of the face gears at different stages, the rationality of the above classification can be visually verified. For example... Figure 12As shown in the surface morphology and roughness values ​​at each stage, the evolution trend of workpiece surface quality exhibits a high degree of synchronicity with the three-stage characteristics of the comprehensive wear index, further confirming that this index can effectively characterize the real-time wear state of the worm grinding wheel and its direct impact on machining quality. In the transition stage from initial wear to normal wear, as the abrasive grains of the worm grinding wheel initially passivate, the workpiece surface roughness increases from 2.7267 to 2.8865. This increase is relatively gradual, confirming that although the grinding wheel has undergone break-in, its cutting performance remains within a controllable range. In the transition stage from normal wear to rapid wear... The value further increases to 3.1025. At this point, the effective cutting edge on the grinding wheel surface decreases, and the frictional squeezing effect intensifies, leading to a significant decline in the surface quality of the machined surface. During the rapid wear stage, the workpiece surface quality deteriorates significantly. The value surged to 3.2668, and more obvious grinding marks and texture disorder were visible in the surface morphology diagram. This directly reflects that the worm wheel has entered a severe failure state.

[0163] Based on the above analysis, the wear process of the worm gear grinding wheel can be divided into three stages: the initial wear stage (0-20 grinding cycles), the normal wear stage (20-50 grinding cycles), and the severe wear stage (after 50 grinding cycles). This three-stage division provides a reliable labeling basis for the wear condition monitoring model of the drum-shaped worm gear grinding wheel.

[0164] 2.3.2. Divide the processing signal dataset.

[0165] In this embodiment, the signal dataset is divided into a training set, a validation set, and a test set in a 7:2:1 ratio. The training set is used for learning and optimizing model parameters; the validation set is used for hyperparameter tuning and model selection; and the test set is used to evaluate the generalization performance of the final model. To ensure the rationality of the data partitioning and the reliability of the model evaluation, the partitioning process follows the principles of stratified sampling, mutual exclusion, and representativeness.

[0166] 2.4 Model training parameter settings.

[0167] In this embodiment, the model was developed using the PyCharm development environment and trained on an NVIDIA RTX 4060 graphics card using the Python programming language. To verify the performance gains of the proposed model, all comparison models used the same hyperparameter settings and dataset configuration. All models were trained and tested on the same computer platform.

[0168] To systematically evaluate the effectiveness of the proposed method, the experiment set up a comparative framework from three dimensions to verify the effectiveness of the mechanism constraints, the effectiveness of each feature extraction module, and the model's sophistication.

[0169] In the task of extracting vibration signal time-frequency map features, to verify the superiority and effectiveness of the proposed method, the following comparative models were trained: PI-EMA-CNN, EMA-CNN, PI-CNN, and PI-ResNet. Through these comparisons, the contribution of the EMA attention mechanism to feature enhancement, the effect of physical constraints on improving recognition accuracy, and the advancement of the proposed model compared to other models can be evaluated. All models employ a four-layer convolutional layer and two-layer fully connected layer architecture, and the relevant network parameters are consistent with PI-EMA-CNN to ensure the fairness of the comparison. The specific parameter configurations of the models are shown in Table 5.

[0170] Table 5 EMA-CNN Architecture

[0171] In the task of acoustic emission time-series signal feature extraction, to verify the superiority of the proposed HTCN-AKFS-TE method and the effectiveness of physical constraints, the following comparative models were trained: PI-HTCN-AKFS-TE, HTCN-AKFS-TE, PI-TE, and PI-iTransformer. TE relies on a multi-head self-attention mechanism and excels at capturing long-range dependencies in sequences; iTransformer has undergone fundamental architectural restructuring and is specifically designed for long sequence processing. All models adopt the same basic architecture, and the relevant hyperparameter settings are kept consistent to ensure fairness in the comparison. The specific parameter configurations of the models are shown in Table 6.

[0172] Table 6 HTCN-AKFS-TE Architecture

[0173] To verify the effectiveness of the fusion strategy, PI-MFF (the model presented in this paper), PI-EMA-CNN, and PI-HTCN-AKFS-TE were compared. Except for the input feature dimension, the three models remained strictly consistent to ensure a fair comparison.

[0174] 3. Experimental results and model performance analysis.

[0175] This embodiment comprehensively evaluates the performance of the worm gear grinding wheel wear condition identification model based on the evaluation metrics described in Section 2.1. The dataset used for testing includes 80, 120, and 80 data points for initial wear, stable wear, and severe wear, respectively. It should be noted that this embodiment focuses on the model's monitoring performance in a specific practical application scenario of FGCGG; therefore, the hyperparameter optimization process is not analyzed or discussed in detail.

[0176] 3.1 Overall performance evaluation of the model.

[0177] Figures 13-15 The confusion matrices for each model are presented. The confusion matrices describe in detail the identification results for each wear state, where 0, 1, and 2 represent initial wear, stable wear, and severe wear, respectively.

[0178] Figure 13 The confusion matrix used for the image processing model is shown. Figure 13 In the diagram, (a) to (d) represent PI-EMA-CNN, EMA-CNN, PI-CNN, and PI-ResNet, respectively. The proposed PI-EMA-CNN model outperforms the comparison models in both overall recognition accuracy and class balance, correctly recognizing 272 samples, higher than EMA-CNN's 270, PI-CNN's 262, and PI-ResNet's 260. PI-EMA-CNN demonstrates the best performance at each stage. Figure 14 The confusion matrix used for the time-series processing model is shown. Figure 14 In the figures, (a) to (d) represent PI-HTCN-AKFS-TE, HTCN-AKFS-TE, PI-TE, and PI-iTransformer, respectively. The proposed PI-HTCN-AKFS-TE model correctly identified 275 samples, significantly higher than the comparative models HTCN-AKFS-TE (262), PI-TE (216), and PI-iTransformer (260). To avoid deterioration of machining quality and potential risks, worm grinding wheels must be dressed before entering the severe wear stage; therefore, accurate identification of severe wear states by the model is crucial. PI-HTCN-AKFS-TE misidentified only one severely worn area. Both module design and mechanistic constraint strategies played a positive role in improving the model's recognition performance.

[0179] Figure 15 The confusion matrix of the single-mode signal input and the multi-mode signal fusion input model is shown. Figure 15In the diagram, (a) to (c) represent PI-EMA-CNN, PI-HTCN-AKFS-TE, and PI-MFF, respectively. The PI-MFF model presented in this paper misidentified only 2 samples out of all 280 samples in the test set, achieving an accuracy of 99.29%. All samples in the severe wear stage were accurately identified. This success is attributed to the synergistic effect of module design, mechanistic constraints, and fusion strategies. At the module design level, the EMA attention mechanism adaptively enhances the response of key regions strongly correlated with wear in the time-frequency map, suppressing periodic interference from meshing. The HTCN-AKFS structure, through hierarchical temporal convolution and key feature filtering, retains long-range dependencies while eliminating redundant information, achieving wear feature extraction from both the time-frequency and temporal domains. At the mechanistic constraint level, the short-term stationarity physical constraint forces consistent wear estimation across different sub-periods within the sample, guiding feature learning to follow the slow-changing wear pattern, effectively suppressing the modulation interference of contact state changes on feature expression, enhancing model interpretability, and reducing the risk of missed detections in the severe wear stage. At the fusion strategy level, feature-level splicing combines the global perception of macroscopic dynamic response by Gu Zhen's motion signal with the detailed characterization of microscopic damage events by acoustic emission signal, forming cross-modal information complementarity. These three aspects are progressive and mutually supportive, jointly ensuring the model's high-precision recognition under FGCGG time-varying conditions.

[0180] Table 7 presents the performance metrics for all models. The MFF model proposed in this embodiment achieves accuracy, precision, recall, and F1 score of 0.9929, 0.9919, 0.9944, and 0.9931, respectively, demonstrating significant superiority. This result fully validates the excellent recognition performance and application potential of the proposed model in the FGCGG scenario.

[0181] Table 7 Comparison of performance indicators of each model

[0182] 3.2 Analysis of the contribution of mechanistic constraints to model performance.

[0183] The effectiveness of the physical constraint strategy was verified bi-modal through two sets of comparative experiments processing vibration signals and acoustic emission signals. In terms of overall average performance, in the vibration signal task, PI-EMA-CNN improved precision, recall, and F1 score by 5.15, 4.72, and 3.00 percentage points compared to EMA-CNN, respectively. Figure 16 As shown. Figure 16 In the table, (a) to (d) represent the initial wear stage, normal wear stage, severe wear stage, and the average value of each stage, respectively. In acoustic emission signal missions, the PI-HTCN-AKFS-TE improved performance by 4.22, 4.48, and 4.50 percentage points compared to the HTCN-AKFS-TE, respectively. Figure 17As shown. Figure 17 In the figures, (a) to (d) represent the initial wear stage, normal wear stage, severe wear stage, and the average values ​​of the indicators for each stage, respectively. Both sets of experiments consistently show that the introduction of short-time stationarity physical constraints can significantly improve the model's comprehensive recognition ability, and this gain is not dependent on any specific mode, exhibiting cross-modal universality.

[0184] Further observation of the performance at different wear stages reveals a clear stage-specific difference in the contribution of physical constraints. In the initial wear stage, signal features are weak and easily aliased with background noise. Physical constraints effectively suppress the interference of meshing periodic changes on weak feature expression by forcing the model to maintain consistency in wear estimation within a short time window. In the normal wear stage, the overlap of signal features among the three wear states is highest. The constraint strategy helps the model make accurate judgments even in regions with ambiguous decision boundaries by stabilizing the feature learning direction. In the severe wear stage, the constraint strategy significantly reduces the risk of missed judgments, ensuring the reliability of key stage identification. Notably, the improvement in acoustic emission signals by physical constraints is generally higher than that of vibration signals. This stems from the difference in their physical mechanisms: vibration signals reflect the macroscopic dynamic response of the machining system, and the modulation of its features by contact geometry is relatively smooth; while acoustic emission signals originate directly from microscopic damage events at the abrasive particle scale, and their temporal evolution characteristics are more closely coupled with the contact state. Therefore, physical constraints have a more significant effect on improving the stability of its features. The above results indicate that the core mechanism of the short-time stationarity physical constraint lies in embedding the slow-varying wear law as prior knowledge into the training process, guiding the model to eliminate false features related to time-varying contact conditions during the feature learning stage, so that the prediction results have both high accuracy and physical interpretability.

[0185] 3.3 Analysis of the effectiveness of the EMA attention mechanism.

[0186] according to Figure 18 The experimental results shown demonstrate that the introduction of the EMA attention module significantly contributes to the improvement of model performance. Figure 18 In the figures, (a) to (d) represent the initial wear stage, normal wear stage, severe wear stage, and the average value of each stage, respectively. By comparing the recognition results of PI-EMA-CNN with PI-CNN and PI-ResNet under the same physical constraints, the effectiveness of the EMA module in feature extraction can be clearly evaluated.

[0187] In terms of overall average performance, PI-CNN and PI-ResNet lag behind PI-EMA-CNN in all three metrics. Specifically, PI-CNN is 2.96, 5.28, and 4.28 percentage points lower in the three metrics, respectively, while PI-ResNet performs roughly on par with PI-CNN. This phenomenon indicates that, under the time-varying conditions of FGCGG, simply increasing network depth (such as the residual structure of ResNet) does not significantly improve recognition performance, while the EMA attention mechanism, designed specifically for time-varying characteristics, has stronger feature extraction capabilities.

[0188] Analyzing the performance of the EMA module across different wear stages reveals that performance gaps primarily occur in the normal wear stage and the severe wear stage. In the normal wear stage, PI-CNN and PI-ResNet show lower precision by 10.4 and 5.78 percentage points, respectively. This stage has the largest sample size, and its signal features overlap to some extent with those in the initial and severe wear stages, making it the region with the most ambiguous classification decision boundary and placing higher demands on feature extraction capabilities. The EMA module, through a multi-scale attention mechanism that learns across spatial dimensions, adaptively enhances the response of key regions strongly correlated with wear in the time-frequency graph, while suppressing redundant information caused by contact periodic fluctuations, thus establishing a clearer discrimination boundary in this easily confused region. In the severe wear stage, the model has extremely low tolerance for missed detections. Conversely, misclassifying normal wear as severe wear, while leading to over-maintenance, is beneficial for preventing catastrophic failures. Therefore, the evaluation focus in this stage is recall. The recall rates of PI-CNN and PI-ResNet were 13.75 and 5 percentage points lower than PI-EMA-CNN, respectively, indicating that without the effective feature enhancement of the EMA module, the risk of missed detections in critical stages would significantly increase. Notably, the performance gap was relatively small in the initial wear stage, mainly because the signal features were less distinguishable from background noise at this stage. The difficulty in feature extraction lay in the signal-to-noise ratio rather than time-varying interference, and the EMA module had relatively limited room for improvement in addressing this issue. These results demonstrate that the core contribution of the EMA module lies in its adaptive time-frequency feature recalibration, effectively addressing the feature drift problem caused by the periodic changes in the contact area in FGCGG, playing a crucial role, especially in the normal wear stage with high signal feature overlap and the severe wear stage where the cost of missed detection is highest.

[0189] 3.4 Analysis of the temporal feature extraction capability of HTCN-AKFS.

[0190] By comparing the recognition results of PI-HTCN-AKFS-TE with PI-TE and PI-iTransformer under the same physical constraints, the effectiveness of the HTCN-AKFS module in feature extraction can be clearly evaluated. Figure 19The experimental results shown demonstrate that the introduction of the HTCN-AKFS module significantly contributes to the improvement of model performance. Figure 19 In the figure, (a) to (d) represent the initial wear stage, the normal wear stage, the severe wear stage, and the average value of each stage, respectively.

[0191] In terms of overall average performance, PI-TE and PI-iTransformer lag significantly behind PI-HTCN-AKFS-TE in all three metrics. Specifically, PI-TE is 15.41, 23.47, and 21.32 percentage points lower in Precision, Recall, and F1-score, respectively; even iTransformer, designed specifically for long sequence modeling, is 4.34, 5.83, and 5.27 percentage points behind, respectively. This phenomenon indicates that under specific complex conditions, relying solely on traditional temporal embedding or general architectures is insufficient to meet high-precision recognition requirements, while the HTCN-AKFS mechanism, designed for the characteristics of FGCGG signals, exhibits stronger feature mining and fusion capabilities.

[0192] The HTCN-AKFS module played a crucial role in all stages of wear and tear analysis. The model consistently maintained an accuracy rate above 97.5% across all stages, demonstrating exceptional robustness. Particularly in the normal wear and tear stage, characterized by severe feature aliasing and the greatest difficulty in extraction, and in the initial wear and tear stage, where sensitivity is paramount, the HTCN-AKFS module maintained outstanding performance, effectively overcoming the bottlenecks of traditional models in these critical intervals. These results indicate that the core contribution of the HTCN-AKFS module lies in its multi-scale temporal feature reconstruction and key information focusing, effectively addressing the balance between data scale and recognition performance. This allows it to be highly adaptable to FGCGG conditions and successfully complete wear and tear identification tasks.

[0193] 3.5 Validation of multimodal feature fusion strategy.

[0194] While feature extraction from the vibration signal time-frequency plot and acoustic emission time-series signal alone yielded good results in identifying the wear state of a worm gear grinding wheel, there is still room for improvement. To verify the effectiveness of the multimodal information fusion strategy, we conducted a comprehensive comparison between the MFF model and the single-feature input model. Experimental results confirm that the fusion model achieves a synergistic effect greater than the sum of its parts (1+1>2). Figure 20As shown, the PI-MFF model achieved the highest average accuracy, precision, recall, and F1 score of 0.9929, 0.9919, 0.9944, and 0.9931 among all comparison models. Compared to the best-performing single model PI-HTCN-AKFS-TE, the fusion model improved each evaluation metric by 1.08%, 0.84%, 1.25%, and 1.04%, respectively. More importantly, the fusion model maintained stable scores above 0.96 across all three wear stages, with minimal standard deviation. This indicates that by fusing features from different modalities, the model can simultaneously consider both the macroscopic evolution trend and microscopic transient details of the signal. This multimodal collaborative mechanism effectively adapts to the periodic time-varying conditions of dynamic time-varying conditions caused by the coupling of macroscopic generating motion and microscopic wear particle meshing depth in the FGCGG scenario, successfully overcoming the limitations of single-modality representation in complex signal features, thus constructing a state recognizer with stronger robustness and generalization ability.

[0195] 3.6 Comparative analysis of model convergence characteristics.

[0196] Figure 21 The paper presents the accuracy and loss variations of the three models (PI-MFF, PI-EMA-CNN, and PI-HTCN-AKFS-TE) on the training and validation sets. Figure 21In the figures, (a) to (d) represent the training set accuracy, validation set accuracy, training set loss, and validation set loss, respectively. The model presented in this paper exhibits the best convergence characteristics. Its accuracy rapidly climbs to over 95% in the early stages of training and then stabilizes, while the training loss decreases most rapidly. Simultaneously, the model maintains extremely high stability and smoothness on the validation set, with the loss value remaining at a very low level. This is mainly due to its multimodal fusion mechanism, which fully exploits the complementary information between different modalities, effectively accelerating feature learning and suppressing overfitting when dealing with the complex conditions of strong background noise and non-stationary signals intertwined in the FGCGG scenario. The PI-HTCN-AKFS-TE model performs second best in terms of accuracy improvement, loss reduction, and convergence speed. Although it ultimately achieves high accuracy, its validation set accuracy and loss value fluctuate slightly more in the early stages of training, indicating that the efficiency and stability of a single architecture in extracting complex meshing signal features from FGCGG are slightly inferior. In contrast, the PI-EMA-CNN model experienced dramatic fluctuations and increases in accuracy on both the training and validation sets in the early stages, with persistently high and volatile loss before a slow decline. This phenomenon reflects the difficulty of a single CNN architecture in quickly locking onto the global optimum in the early stages of training, leading to repeated fluctuations in the model's loss. This initial volatility indicates that relying solely on processing time-frequency features is insufficient to effectively decouple non-stationary disturbances during the grinding process; the model requires more iterations to trial and error and correct parameter directions, resulting in low convergence efficiency. Although the model eventually stabilizes and catches up with other models as training progresses, the overall convergence cost remains high. In conclusion, the PI-MFF model, with its superior convergence speed and high stability, demonstrates strong adaptability to complex FGCGG signals, proving its significant advantage in accurately identifying the wear state of drum-shaped worm grinding wheels under complex conditions such as continuous generating grinding.

[0197] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A method for monitoring the wear condition of a drum-shaped worm grinding wheel considering the time-varying characteristics of the contact area, characterized in that: Includes the following steps: Step 1: Data Acquisition: During the continuous generating grinding of face gears, vibration signals and acoustic emission signals in the worm wheel machining area are collected simultaneously to construct a multimodal raw signal dataset; Step 2: Data preprocessing: The collected vibration signals and acoustic emission signals are preprocessed respectively; Continuous wavelet transform is performed on the preprocessed vibration signal to generate a time-frequency diagram of the vibration signal, while preserving the original temporal characteristics of the preprocessed acoustic emission signal; Step 3: Feature Extraction A vibration signal time-frequency feature extractor based on EMA-CNN is constructed. The vibration signal time-frequency map is input into the vibration signal time-frequency feature extractor to extract the deep wear features in the time-frequency domain of the vibration signal. The EMA-CNN is constructed based on cross-spatial learning multi-scale attention EMA and convolutional neural network CNN. It is a convolutional neural network CNN with embedded cross-spatial learning multi-scale attention EMA mechanism and includes an EMA module. The EMA module achieves dynamic focusing on time-varying wear features by grouping the input feature map along the channel dimension, running 1×1 and 3×3 convolution branches in parallel, and performing cross-spatial learning. An acoustic emission temporal feature extractor based on HTCN-AKFS-TE is constructed. The preprocessed acoustic emission signal is input into the extractor to extract the temporal evolution wear features of the acoustic emission signal. HTCN-AKFS-TE is constructed based on a hierarchical temporal convolutional network HTCN, an adaptive key feature filter AKFS, and a Transformer encoder TE. The hierarchical temporal convolutional network HTCN captures dynamic evolution patterns across multiple time spans through multiple convolutional layers with different dilation rates. The adaptive key feature filter AKFS filters high-value key feature fragments from the output features of the hierarchical temporal convolutional network HTCN through a learnable scoring network. The Transformer encoder TE performs deep interaction and representation enhancement on the filtered key feature fragments. Step 4: Feature Fusion: The time-frequency domain deep wear features of the extracted vibration signal are fused with the time-series evolution wear features of the acoustic emission signal to construct a multimodal joint feature vector; Step 5: Physically Constrained Model Training: The multimodal joint feature vector is input into the wear state identification module for training and identification. The wear state identification module uses a physical constraint loss function to guide model training. The physical constraint loss function is constructed based on the slow evolution law of worm wheel wear. By forcing the wear state estimation of different sub-time periods within the same sample to remain consistent, the interference of periodic changes in the contact area on wear feature learning is suppressed. Step Six: Wear State Category: Input the multimodal joint feature vector into the trained wear state recognition module, and output the current wear state category of the drum worm grinding wheel; the wear state recognition module includes a fully connected layer, a batch normalization layer, a ReLU activation layer, a Dropout layer and a Softmax classification layer connected in sequence.

2. The method for monitoring the wear condition of a drum-shaped worm grinding wheel considering the time-varying characteristics of the contact area according to claim 1, characterized in that: In step two, the preprocessing includes filtering and noise reduction, amplitude normalization, and equal-length signal truncation based on the rotation period of the worm gear grinding wheel. The filtering and noise reduction uses a fourth-order Butterworth bandpass filter. The passband frequency range of the vibration signal is set to 10 Hz to 5000 Hz, and the passband frequency range of the acoustic emission signal is set to 60 kHz to 400 kHz. The amplitude normalization adopts the minimum-maximum normalization method, which maps the amplitude of each channel signal to the interval [0, 1]. The equal-length signal extraction is based on five rotations of the worm wheel as a feature extraction unit, and ten signal segments are extracted from the stable grinding stage to achieve data enhancement. The continuous wavelet transform uses Morlet wavelets as the mother wavelet basis function and employs a logarithmic uniform scale step size for time-frequency transformation, making the frequency division in the low-frequency region finer than that in the high-frequency region, in order to balance time resolution and frequency resolution.

3. The method for monitoring the wear condition of a drum-shaped worm grinding wheel considering the time-varying characteristics of the contact area according to claim 1, characterized in that: In step three, the EMA module includes a feature grouping unit, a parallel convolution branching unit, and a cross-space learning unit; The feature grouping unit is used to divide the input feature map into multiple non-overlapping sub-feature groups along the channel dimension to aggregate local time-frequency features in different channels; The parallel convolution branch unit is used to execute two independent convolution branches in parallel for each of the divided sub-feature groups: the first branch is a 1×1 convolution branch, which extracts position information by one-dimensional global pooling along the time axis and frequency axis respectively, and after concatenation, convolution and activation, it is multiplied element-wise with the original group features to achieve spatial feature calibration; the second branch is a 3×3 convolution branch, which expands the receptive field and extracts multi-scale detailed features in the neighborhood through local convolution. The cross-spatial learning unit is used to perform spatial attention interaction between the outputs of the 1×1 convolutional branch and the 3×3 convolutional branch. After applying global pooling, tensor reshaping and Softmax normalization to the outputs of each branch, a weight vector is obtained. This weight vector is then multiplied with the output of the other branch. The two spatial attention results are added together, processed by an activation function, and then multiplied with the original sub-feature group to obtain the output features of the EMA module.

4. The method for monitoring the wear condition of a drum-shaped worm grinding wheel considering the time-varying characteristics of the contact area according to claim 1, characterized in that: In step three, the hierarchical temporal convolutional network HTCN includes three dilated convolutional layers with dilation rates of 1, 2, and 4, respectively, a kernel size of 7, and the activation function ReLU for all layers; the Transformer encoder TE includes a multi-head self-attention mechanism, and its model dimension is... Set to 128, attention head count Set to 4, number of encoder layers Set to 2.

5. The method for monitoring the wear condition of a drum-shaped worm grinding wheel considering the time-varying characteristics of the contact area according to claim 1, characterized in that: In step three, the method of the adaptive key feature filter AKFS for filtering key feature fragments is as follows: Each step of the feature vector output by the hierarchical temporal convolutional network HTCN is scored. The importance score of each time step is calculated through a learnable scoring network. The M time point indices with the highest scores are selected. Based on the indices, a subset of key features is extracted from the feature sequence output by the hierarchical temporal convolutional network HTCN and used as the input of the Transformer encoder TE.

6. The method for monitoring the wear condition of a drum-shaped worm grinding wheel considering the time-varying characteristics of the contact area according to claim 1, characterized in that: In step four, the feature-level fusion adopts a splicing method, which concatenates the vibration signal feature vector and the acoustic emission signal feature vector in the channel dimension to generate a joint feature vector.

7. The method for monitoring the wear condition of a drum-shaped worm grinding wheel considering the time-varying characteristics of the contact area according to claim 1, characterized in that: In step five, the physical constraint loss function is implemented as follows: Each sample is divided along the time axis. Each sub-segment is input into the wear condition recognition module to obtain... The predicted probability distribution of the group is transformed into a probability expression of wear state through the Softmax function; Define the continuous wear index: in: For the first The probability that each sub-segment belongs to category c is predicted; It reflects the model's continuous estimation of the degree of wear and tear during that period; These correspond to the initial wear stage, the normal wear stage, and the severe wear stage, respectively. Define physical constraint loss: in: This refers to the batch size; Indicates calculation The variance of the continuous wear index of each sub-segment; For the first In the nth sample The continuous wear index of each segment; The model's total loss function is: in: For multi-class cross-entropy loss; These are the weighting coefficients.

8. The method for monitoring the wear condition of a drum-shaped worm grinding wheel considering the time-varying characteristics of the contact area according to claim 1, characterized in that: In step six, the wear state categories include the initial wear stage, the normal wear stage, and the severe wear stage; the threshold for judging the severe wear stage is predetermined by the following quantitative grading method: Collect point cloud data of the surface morphology of the worm gear grinding wheel; Calculate the average effective blade height based on the point cloud data. and abrasive passivation rate : The effective average height of the cutting edge After global normalization, it is compared with the wear particle passivation rate. Perform weighted summation to construct a comprehensive wear and tear index. : in: The height of the binder reference surface is taken as the 10th percentile of the point cloud data; The effective average height of the blade after global normalization; For the first The height value of each data point; This is the preset threshold for the effective cutting edge height of the abrasive grains; To meet The number of valid points; This represents the total number of points in the point cloud data. To meet The number of invalid points; It is the height boundary between the effective region and the ineffective region; This is an indicator function; it takes the value 1 when the condition is true, and 0 otherwise. Based on the comprehensive wear index The evolution curve of the wear process with the number of grinding cycles was used to divide the wear process into the initial wear stage, the normal wear stage, and the severe wear stage using the K-means clustering algorithm.

9. A drum-shaped worm grinding wheel wear condition monitoring system considering the time-varying characteristics of the contact area, used to implement the drum-shaped worm grinding wheel wear condition monitoring method considering the time-varying characteristics of the contact area as described in any one of claims 1-8, characterized in that: include: The signal acquisition module is used to simultaneously acquire vibration signals and acoustic emission signals in the worm wheel machining area during the continuous generating grinding process of face gears; The signal preprocessing module is used to filter and reduce noise, normalize amplitude and truncate the acquired vibration signal and acoustic emission signal respectively, and perform continuous wavelet transform on the preprocessed vibration signal to generate a vibration signal time-frequency diagram. The vibration signal feature extraction module employs a vibration signal time-frequency feature extractor based on EMA-CNN to extract deep time-frequency wear features of the vibration signal from the vibration signal time-frequency map; the EMA-CNN is a convolutional neural network (CNN) with an embedded cross-spatial learning multi-scale attention EMA mechanism. The acoustic emission signal feature extraction module employs an HTCN-AKFS-TE-based acoustic emission temporal feature extractor to extract temporal evolution wear features from the preprocessed acoustic emission signal. The HTCN-AKFS-TE includes a hierarchical temporal convolutional network HTCN, an adaptive key feature filter AKFS, and a Transformer encoder TE. The multimodal feature fusion module is used to perform feature-level fusion of the time-frequency domain deep wear features of the vibration signal and the time-series evolution wear features of the acoustic emission signal to generate a multimodal joint feature vector; The wear condition identification module is used to input the multimodal joint feature vector into the trained classifier and output the current wear condition category of the drum worm grinding wheel.

10. The drum-shaped worm grinding wheel wear condition monitoring system considering the time-varying characteristics of the contact area according to claim 9, characterized in that: The hierarchical temporal convolutional network (HTCN) comprises three dilated convolutional layers with dilation rates of 1, 2, and 4, respectively, all with a kernel size of 7 and an activation function of ReLU. The adaptive key feature filter (AKFS) calculates the importance score of each time step in the output features of the hierarchical temporal convolutional network HTCN through a learnable scoring network, selects the M time point indices with the highest scores, and extracts the corresponding key feature subsets. The multimodal feature fusion module uses a concatenation method to concatenate the vibration signal feature vector and the acoustic emission signal feature vector along the channel dimension.

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