A method and system for modeling thermal drift and predicting wear life of tooth profile grinding wheels

Abstract

This invention discloses a method and system for modeling thermal drift and predicting wear life of a tooth profile grinding wheel, comprising four stages: thermal drift path network construction, drift differentiation feature extraction, irregular fragmentation and recombination, and dynamic judgment feedback. By collecting temperature response sequences from multiple regions of the tooth surface, a thermal drift path network is established. A drift differentiation feature set is generated using multi-time-period path evolution relationships to distinguish between short-cycle thermal disturbances and trend-based drift interference. Then, based on the thermal response structural boundary, the path is irregularly recombined and energy-constrained to form response structural units with thermal-mechanical coupling. The system further achieves self-learning of the judgment order based on energy feedback and weight update mechanisms, thereby outputting the wear state and remaining life prediction results of the tooth profile grinding wheel. This method realizes dynamic correction of grinding thermal response behavior and intelligent life assessment.

Description

Technical Field

[0001] This invention relates to the field of tooth profile machining and inspection technology, specifically to a method and system for modeling thermal drift of tooth profile grinding wheels and predicting wear life. Background Technology

[0002] Gears are key components in modern precision transmission systems, and their machining accuracy and surface quality directly affect the stability and lifespan of the entire machine. In gear manufacturing, profile grinding is widely used in the final processing stage of high-performance gear products due to its high machining accuracy and fast material removal efficiency. The profile grinding wheel, as the core tool in this type of grinding process, directly determines the consistency between gear machining accuracy and workpiece surface quality based on its wear condition.

[0003] Traditional methods of managing grinding wheels often rely on indirect means such as fixed-cycle replacement, manual visual inspection, or grinding effect evaluation. These methods suffer from problems such as dependence on experience, delayed judgment, waste of resources, and failure detection. To achieve lean manufacturing and transparency of equipment status, researchers have recently introduced sensing modeling techniques based on signals such as temperature, vibration, and current for online monitoring and life prediction of grinding wheel wear. Among these, temperature signals have become one of the main characterizing variables for wear identification due to their high sensitivity, ease of deployment, and non-interference with the machining process.

[0004] However, existing temperature sensing methods are mostly based on single-point or multi-point temperature measurements, estimating the wear level and remaining life of grinding wheels by setting thresholds or building static prediction models (such as polynomial fitting, neural networks, etc.). These methods typically rely on data collected under fixed conditions to build models, and once their parameters and structure are set, they remain unchanged in actual operation. They cannot respond to the nonlinear drift problem caused by environmental changes, abrasive wear, and changes in cooling efficiency during long-term use.

[0005] Specifically, during gear grinding, grinding wheel wear causes a series of changes, including the transfer of local contact heat sources, alteration of thermal resistance structure, and enhanced wear debris accumulation effect. These changes lead to dynamic phenomena such as an increase in the baseline of the temperature curve, nonlinearity of the rate of change, and variations in fluctuation frequency. These thermal drift behaviors gradually deviate from the initial modeling conditions, causing misalignment of the input feature distribution of the prediction model. In severe cases, this can lead to wear identification failure, increased life estimation errors, and even triggering false alarms or accidental shutdowns.

[0006] In view of this, the present invention provides a method and system for modeling thermal drift and predicting wear life of tooth profile grinding wheels, thereby solving the above problems. Summary of the Invention

[0007] The purpose of this invention is to provide a method and system for modeling thermal drift and predicting wear life of tooth profile grinding wheels, which solves the problems of static model rigidity, severe thermal signal drift interference, and accumulation of prediction errors over time in the existing process of identifying wear state and predicting life of tooth profile grinding wheels.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] Firstly, a method for modeling thermal drift and predicting wear life of a tooth profile grinding wheel includes the following steps:

[0010] S101: During the tooth profile grinding process, temperature response sequences of multiple tooth surface regions are collected simultaneously, and a thermal drift path network is constructed based on the cross-correlation relationship of temperature change trajectories in different regions to characterize the local conduction shift trend during the thermal diffusion process.

[0011] S102: Obtain a set of drift differentiation features by aggregating and reconstructing the path evolution relationship of multi-time-period paths in the thermal drift path network, and distinguish short-period thermal disturbances from trend-based drift interference based on the set of drift differentiation features;

[0012] S103: The thermal drift path network is recombined into irregular fragments based on the drift differentiation feature set; the thermal response structure boundary is determined for the recombined path fragments according to the interlacing pattern of the drift behavior trajectory; and the wear state is adjusted based on the thermal response structure boundary to determine the path, so as to realize the dynamic correction of the grinding thermal response behavior.

[0013] S104: Self-update the internal judgment order and feature weights of the wear state judgment path adjusted by the thermal response structural boundary; based on the updated judgment order, perform real-time feature alignment and state mapping based on the thermal response structural boundary, and output the current wear state of the tooth profile grinding wheel and its remaining life prediction results.

[0014] As a preferred embodiment of the first aspect of the present invention, the construction logic of the thermal drift path network includes:

[0015] The temperature response trajectories of multiple tooth surface regions are divided into non-overlapping segments according to the relative time axis, and the difference in drift direction between adjacent segments is extracted.

[0016] A cross vector map is constructed based on the drift direction differences between multiple segments, and cross points with associated rotational features are merged to form behavioral nodes;

[0017] Behavioral nodes are clustered according to dense intervals of trajectory segments. Based on the node selection mechanism, a heat flow guiding network prototype is formed to achieve convergence reconstruction from the heat dissipation response point to the continuous heat conduction path. After removing path breakpoints, the network convergence is completed.

[0018] The converged heat flow guiding network is used to establish a hierarchical index based on the path intersection intensity, and the output is a heat drift path network for trajectory evolution recognition.

[0019] As a preferred embodiment of the first aspect of the present invention, the node filtering mechanism includes:

[0020] Collect the sequence vectors of all behavioral nodes appearing in multiple time periods, and calculate their path change span and adjacency coupling frequency;

[0021] The stability factor matrix is ​​generated by combining the path change span and the adjacency coupling frequency. Nodes whose stability factor matrix is ​​lower than a set threshold are marked as boundary candidate nodes.

[0022] Candidate nodes at the boundary are jointly eliminated based on the consistency of the propagation direction and the location density, while highly overlapping behavior nodes are retained and marked as dominant nodes.

[0023] The selected dominant nodes are reconnected into a path backbone graph, which is used as a prototype of a heat flow-oriented network for dynamic behavior recognition.

[0024] As a preferred embodiment of the first aspect of the present invention, the generation logic of the drift differentiation feature set includes:

[0025] Cluster the paths in the hot drift path network according to the node switching frequency and the direction inversion number to generate multi-path combination clusters;

[0026] Map each path in the path combination cluster to a two-dimensional vector of direction-gradient change and record the path perturbation intersection point;

[0027] Based on the co-occurrence patterns of disturbance intersections across different time periods, a set of trajectories with trend-based shift characteristics is selected.

[0028] The set is output as a drift differentiation feature set, which is called when the heating response structural unit is fragmented and recombined.

[0029] As a preferred embodiment of the first aspect of the present invention, the method for extracting the trend offset trajectory set includes:

[0030] For each path, divide it into equally spaced segments on the time axis, and calculate the total value of directional changes and the number of directional changes within each segment;

[0031] The total value of the direction change and the number of direction changes for each path are used to construct a trend encoding vector, and then the paths are clustered according to the encoding distance.

[0032] Filter out path groups with unidirectional accumulation characteristics in the offset direction from the trend coding group;

[0033] The selected path groups are output as a set of trend offset paths, and time period sequences are labeled for path differentiation modeling.

[0034] As a preferred embodiment of the first aspect of the present invention, the application logic of the thermal response structural boundary includes:

[0035] Temperature gradient field and stress gradient field are collected for the fragmented and recombined path segments, and a coupling factor table is generated. The coupling factor table records the gradient magnitude, direction angle and spatial position difference between each pair of path segments for subsequent boundary screening.

[0036] Based on the coupling factor table and path crossover intensity, the spatial direction consistency and time interval overlap rate are calculated simultaneously, and a set of fragment pairs with continuous heat conduction and compatible time spans are selected as the boundary candidate set.

[0037] A boundary index map is built for the boundary candidate set, and the connection relationship between segments, boundaries and paths is recorded as multi-dimensional index entries. An energy flow label is set for each entry to track the conduction path.

[0038] Perform convergence backtracking on the energy input and output of each connection in the index graph, remove connection entries whose energy balance deviation exceeds the set range, and obtain the boundary connection list of energy conservation.

[0039] Rearrange the path structure based on the boundary connection list and output the thermal response path optimization results that satisfy the energy balance constraint.

[0040] As a preferred embodiment of the first aspect of the present invention, the reconstruction of the thermal response structure boundary further includes:

[0041] Based on the boundary index diagram, the heat conduction path is divided into layers according to the node level. The interlayer intersection points in the multi-layer boundary structure are defined as coordination nodes, and an interlayer heat transfer coefficient is assigned to each coordination node to describe the energy transfer intensity.

[0042] Based on the heat transfer coefficient of the coordinating node and the phase difference of the corresponding temperature peak of each layer, an interlayer energy transfer link is established to generate an interlayer coupling matrix; a three-dimensional heat conduction link diagram is constructed based on the interlayer coupling matrix, the reverse chain of energy flow is identified and local topology rearrangement is performed to make the heat potential show a stable decreasing trend along the energy link direction, and the branch connection that does not meet this trend is deleted.

[0043] Energy consistency verification is performed on the rearranged heat conduction paths. Path groups with energy loss rates within the set range are retained, and the heat conduction path results after multi-layer coordination modeling are output for subsequent wear status judgment.

[0044] As a preferred embodiment of the first aspect of the present invention, the thermal response path optimization result further includes:

[0045] Within the region defined by the thermal response structure boundary, the energy flux is calculated based on the temperature gradient, contact bandwidth, and material thermal conductivity of each path segment, and an energy distribution table is generated.

[0046] By combining the energy distribution table, local heat capacity and path length, the energy compensation amount of the segment is calculated, and the segment energy compensation list is obtained;

[0047] The connection weights of the path segments are redistributed according to the energy compensation list, and the heat conduction directions are compared. Segment connections with opposite directions are deleted to obtain a weighted connection set with uniform heat conduction directions.

[0048] Time-series connectivity detection is performed on the weighted connection set. If a time break exists, the process reverts to the previous step and readjusts the weight distribution to obtain a time-continuous heat conduction path. Based on the time-continuous heat conduction path, an effective path structure corrected for energy balance is output for subsequent thermal behavior identification.

[0049] As a preferred embodiment of the first aspect of the present invention, the internal judgment order and feature weight update logic includes:

[0050] Temperature, current and acoustic emission signals corresponding to the wear judgment path after thermal response structural boundary adjustment are collected, and statistical features are extracted according to a fixed time window to obtain a feature vector set;

[0051] Based on the feature vector set, the cross-correlation coefficient and covariance are calculated, and a feature correlation matrix is ​​constructed to measure the synchronicity of changes between different signals.

[0052] Using the difference between energy input and energy output as a penalty factor, the feature correlation matrix is ​​mapped to a feature weight matrix, and a weight revision table is generated.

[0053] The judgment order matrix is ​​reordered according to the weighted revision table to correct the bias in the wear state identification results;

[0054] Based on the corrected judgment order matrix, state mapping and life inference are performed on the feature vector set, and the current wear state and remaining life prediction results of the tooth profile grinding wheel are output.

[0055] In a second aspect, the present invention provides a system for modeling thermal drift and predicting wear life of tooth profile grinding wheels, based on the implementation of the first aspect, including a thermal response acquisition module, a dynamic behavior recognition module, a fragment reconstruction module and a feedback update module, wherein the modules are connected by wired and / or wireless means.

[0056] The thermal response acquisition module is used to simultaneously acquire temperature response sequences of multiple tooth surface regions during tooth profile grinding, and to construct a thermal drift path network based on the cross-correlation relationship of temperature change trajectories in different regions, which is used to characterize the local conduction shift trend during the thermal diffusion process.

[0057] The dynamic behavior recognition module is used to obtain a drift differentiation feature set by aggregating and reconstructing the path evolution relationship of multi-time period paths in the thermal drift path network, and to distinguish between short-period thermal disturbances and trend drift interference based on the drift differentiation feature set;

[0058] The fragment recombination module is used to perform irregular fragment recombination of the thermal drift path network according to the drift differentiation feature set; determine the thermal response structure boundary of the recombined path fragments according to the interlacing pattern of the drift behavior trajectory; and adjust the wear state to determine the path based on the thermal response structure boundary, so as to realize the dynamic correction of grinding thermal response behavior.

[0059] The feedback update module is used to self-update the internal judgment order and feature weights of the wear state judgment path adjusted by the thermal response structural boundary; based on the updated judgment order, it performs real-time feature alignment and state mapping based on the thermal response structural boundary, and outputs the current wear state of the tooth profile grinding wheel and its remaining life prediction results.

[0060] The technical effects and advantages provided by the present invention in the above technical solution are as follows:

[0061] This invention introduces the joint calculation of temperature gradient and stress gradient during the tooth profile grinding modeling process. This invention enables the thermal drift path network to simultaneously reflect the dual physical characteristics of heat conduction and stress change, thus providing a continuous basis for subsequent thermo-mechanical co-analysis. Because the aggregation and recombination mechanism based on drift differentiation characteristics is adopted in the path reconstruction stage, the temporal correlation between thermal diffusion trajectories is effectively preserved, realizing the adaptive evolution of thermal response behavior in the time dimension.

[0062] Furthermore, by utilizing energy conservation constraints and coupling stability factors to screen path segments, the path optimization process is transformed from geometric connection to screening based on physical equilibrium conditions, ensuring the true physical meaning and thermal conductivity of the thermal response structural boundary. Based on this, a path optimization model under thermal response structural boundary constraints is established, achieving energy balance and optimal conduction of the grinding heat diffusion channel. Simultaneously, by combining multi-source signal fusion and a weight self-updating mechanism, the system can adaptively adjust the judgment order and feature weights under energy feedback drive, thereby continuously improving the accuracy of wear state identification and the stability of life prediction through iteration. While achieving dynamic correction of grinding thermal response behavior, the system significantly improves the physical reliability and intelligent evaluation capability of gear grinding wheel wear life prediction. Attached Figure Description

[0063] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0064] Figure 1 This is a schematic diagram of the process for modeling thermal drift and predicting wear life of the tooth profile grinding wheel according to the present invention;

[0065] Figure 2 This is a block diagram of the thermal drift modeling and wear life prediction system for tooth profile grinding wheels of the present invention. Detailed Implementation

[0066] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the description of this disclosure will be more complete and fully convey the concept of the exemplary embodiments to those skilled in the art. The drawings are merely illustrative of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted.

[0067] Furthermore, the described features, structures, or characteristics can be combined in any suitable manner in one or more exemplary embodiments. Numerous specific details are provided in the following description to give a full understanding of exemplary embodiments of this disclosure. However, those skilled in the art will recognize that the technical solutions of this disclosure can be practiced with one or more specific details omitted, or other methods, components, steps, etc., can be employed. In other instances, well-known structures, methods, implementations, or operations are not shown or described in detail to avoid obscuring various aspects of this disclosure.

[0068] Example 1

[0069] like Figure 1 As shown, this embodiment provides a method for modeling thermal drift and predicting wear life of tooth profile grinding wheels, including the following steps:

[0070] S101: During the tooth profile grinding process, temperature response sequences of multiple tooth surface regions are collected simultaneously, and a thermal drift path network is constructed based on the cross-correlation relationship of temperature change trajectories in different regions to characterize the local conduction shift trend during the thermal diffusion process.

[0071] It should be noted that a structured model is used to model the multi-regional heat diffusion behavior generated during the tooth profile grinding process, forming a thermal drift path network capable of representing the heat conduction shift trend. This network reflects the nonlinear graph structure of the multi-dimensional, interwoven diffusion paths of heat energy in space and time, thus characterizing its evolutionary features during the grinding process. This thermal drift path network is not a traditional temperature thermogram or a one-dimensional heat change curve, but rather a topological network established based on the cross-behavioral structure between the thermal response trajectories of each tooth surface region. The thermal drift path network is represented as follows: ;

[0072] in: As the dominant node set, For the first The dominant node corresponding to each thermal behavior; This is a set of heat-conducting connection edges between nodes. To connect the dominant node and The edge, Let be the corresponding edge weight matrix, representing the local heat conduction intensity. Connect to the dominant node and The connection weights of the thermal drift path network; As the input carrier for subsequent drift evolution identification, its node attribute record time label and edge weight matrix both correspond to the differences and directional dynamics of spatial thermal conduction behavior, serving as input parameters for the dynamic behavior identification module.

[0073] To further explain, the construction logic of the thermal drift path network includes:

[0074] The temperature response trajectories of multiple tooth surface regions are divided into non-overlapping segments according to the relative time axis, and the difference in drift direction between adjacent segments is extracted.

[0075] It should be noted that, assuming the tooth profile contact surface is divided into... There are 1 tooth surface region, and each tooth surface region is numbered as follows: , , For positive integers, the temperature response sequence collected from each tooth surface region is segmented according to the grinding wheel rotation cycle and trajectory time axis to generate a set of non-overlapping, fixed-length temperature response sequences with time-varying curves. , , Each temperature response sequence Indicates the tooth surface area The temperature change curve during the grinding process is used to reflect the dynamic characteristics of heat diffusion in the region. Based on the rotation cycle of the grinding wheel and the time axis, synchronous sampling is performed to divide the temperature sequence into a set of time periods with fixed lengths and no overlap.

[0076] in: Indicates the first The tooth surface region in the first Time sampling points Temperature value, It is a temperature field function, representing the first... The tooth surface region in the first Time sampling points thermal response, The start time of temperature sampling. , A positive integer, representing the sampling period. have There are time sampling points, and the sampling time interval between adjacent time sampling points is . , The thermal drift path network constructed based on cross-trajectory behavior has a multi-node transmission structure and serves as the input basis for subsequent wear trajectory evolution recognition.

[0077] It is understandable that each segment carries information about the temperature change trend within a time period. The difference value of the main drift direction is extracted from each pair of adjacent segments. This difference value is not a simple first derivative or slope change, but a structural index derived from the directional angle of the inter-segment thermal change vector, which is used to reflect the degree of spatial deflection of thermal diffusion behavior between segments.

[0078] Specifically, to extract the dynamic changes in the thermal diffusion trajectory, the temperature response sequence is... The time axis is divided into non-overlapping trajectory segments, meaning the sampling period... have Each time sampling point, that is, each trajectory is divided into 10 time sampling points. The non-overlapping intervals, the first The non-overlapping intervals of the time periods are , If the integer is positive, then each trajectory segment is defined as:

[0079] , ;

[0080] Each trajectory segment Indicates the first The tooth surface region in the first The temperature change trajectory within a time period, then the... The set of trajectory segments for each tooth surface region is: .

[0081] The difference in drift direction between adjacent trajectory segments is obtained by calculating the angle between vectors. Trajectory segments corresponding to overlapping regions The drift direction vector is defined as:

[0082] , ;

[0083] in: Indicates the first The tooth surface area in the first The "directional slope" of heat diffusion over a period of time, if The temperature rises (endothermic); if The temperature drops (heat dissipation); the larger the value, the faster the temperature changes.

[0084] The drift direction difference value is the first The drift direction vector of the time period to the first The angle between the drift direction vectors during the time period:

[0085] , ;

[0086] in: This is the system's built-in deviation value, used to avoid division by zero errors when the vector magnitude approaches zero. It also represents the minimum thermal response sensitivity of the measurement system.

[0087] For example, the difference in drift direction between adjacent segments The acquisition of this data can reflect the shift trend of temperature trajectories over different time periods, providing basic data for the subsequent construction of cross-vector maps.

[0088] A cross vector map is constructed based on the drift direction differences between multiple segments, and cross points with associated rotational features are merged to form behavioral nodes;

[0089] It should be noted that the difference in drift direction between adjacent segments is constructed into a set of cross vector maps, which are achieved by detecting the similarity of the difference in drift direction between different regions. Each vector map represents the thermal drift direction relationship between two segments, and the intersection of two segments represents a region where multiple heat flow directions are spatially intersected, reflecting the instability or regional aggregation of thermal diffusion.

[0090] Exemplary illustration, the first Tooth surface area In the Difference in drift direction over time period and the Tooth surface area In the Difference in drift direction over time period The difference satisfies the threshold condition. :

[0091] ;

[0092] If a cross relationship is defined, it is determined to be a connectable relationship, and candidate cross points are generated.

[0093] Further analysis of the directional change trends of candidate intersections yields the changing trend of drift direction differences over time, which is used to characterize the dynamic evolution of the heat diffusion direction, i.e.:

[0094] ;

[0095] If multiple time segments consecutively satisfy This indicates that the heat diffusion directions in different tooth surface regions have the same evolutionary trend over time, that is, the direction change trend is consistent. When multiple regions with the same direction change trend intersect, it indicates that the heat flow exhibits a swirling or clustering characteristic in space. At this time, these intersection points are merged into behavioral nodes. To characterize the cycloid coupling behavior of local heat conduction.

[0096] Furthermore, the set of behavior nodes is defined as follows: , , It is a positive integer; Indicates the first Each behavior node A set of behavior nodes is formed by the combination of individual behavior nodes; based on the set of behavior nodes... The spatial distribution characteristics were analyzed, and nodes with similar heat conduction directions and close spatial locations were aggregated by density clustering to identify the continuous guiding characteristics of regional heat flow, thus characterizing the interactive behavior pattern of thermal drift paths between different tooth surface regions.

[0097] Behavioral nodes are clustered according to dense intervals of trajectory segments. Based on the node selection mechanism, a heat flow guiding network prototype is formed to achieve convergence reconstruction from the heat dissipation response point to the continuous heat conduction path. After removing path breakpoints, the network convergence is completed.

[0098] It should be noted that density clustering methods (such as DBSCAN, which does not depend on the number of nodes) are used to cluster all behavioral nodes according to the density of trajectory intersections. After clustering, the continuity between each group of connections is checked. If there are broken nodes, they are removed according to the connection weight priority, and the remaining nodes are reconnected to form a preliminary converged thermal guidance network. This makes the entire thermal drift network structurally continuous and physically closed, thereby supporting subsequent drift pattern recognition.

[0099] Understandably, after constructing the thermal drift path network, heat conduction behavior is aggregated in spatial distribution to identify regional heat flow trends. Behavioral nodes are aggregated in spatial distribution, and a clustering input dataset is constructed based on the position vectors of all behavioral nodes in the path and the density of trajectory segments.

[0100] The input dataset for clustering is constructed as follows: ;

[0101] in: Indicates the first The position vector of each behavior node in the spatial coordinate system; Indicates the first The number of trajectory segments (or thermal drift paths) connected to a behavior node reflects the local thermal conductivity density of that node.

[0102] The density-based clustering method DBSCAN is used to cluster the behavior node set. The system performs a spatial clustering process to identify densely packed trajectory segments and output a set of clusters. Each cluster is a spatially continuous and physically closed heat flow guiding path, realizing the convergence and reconstruction from the heat dissipation response point to the continuous heat conduction path, and providing structural support for the stable modeling and lifetime prediction of the thermal drift path network.

[0103] It should be understood that path breaks may exist in some clusters (due to local trajectory breaks caused by high thermal perturbation). To ensure the physical continuity of the network, connectivity checks need to be performed within each cluster using a node filtering mechanism. Further explanation: the node filtering mechanism includes:

[0104] Collect the sequence vectors of all behavioral nodes appearing in multiple time periods, and calculate their path change span and adjacency coupling frequency; statistically analyze the appearance order of each behavioral node in different grinding cycles, and construct a sequence vector. This vector not only preserves the temporal distribution pattern of the nodes, but also provides a reference for their path activity frequency and behavioral stability.

[0105] Understandably, the stability factor matrix of nodes is used to filter for highly robust behavioral nodes within the behavioral node set. In the same behavior node Connection order vectors within multiple time windows The path change span and adjacent coupling frequency are calculated, specifically:

[0106] Path reversal span: ;

[0107] in: Indicates nodes of the same behavior Path change span within multiple time windows ,like Large indicates a behavioral node. The direction of heat flow fluctuates significantly, exhibiting poor stability; if Small indicates a behavioral node. The thermal drift direction is consistent, and the thermal diffusion tends to stabilize, with varying directional quantities over multiple time periods. Stability measures;

[0108] Adjacent coupling frequency: ;

[0109] in: This indicates the proportion of times a node with the same behavior maintains a thermal connection (thermal conduction interaction) with other nodes across all time windows; a larger value indicates that the node continuously participates in the main thermal conduction path over time; based on Reflects the temporal stability of local heat conduction (i.e., "frequency of thermal channel activity");

[0110] The stability factor matrix is ​​generated by combining the path change span and the adjacency coupling frequency. Nodes whose stability factor matrix is ​​lower than a set threshold are marked as boundary candidate nodes.

[0111] Specifically, the formula for calculating the stability factor is: ,

[0112] Stability factor This reflects the balance between the node's heat conduction time stability and directional consistency; when the node frequently participates in heat conduction ( High) and stable direction ( When (low), Large values; when the heat conduction path at the node fluctuates significantly or occurs sporadically. When the value is small, adding 1 to the denominator can prevent division by zero and suppress the weight of nodes with high fluctuations; when the stability factor of a behavior node is lower than the preset threshold, the node is marked as a boundary candidate node.

[0113] Candidate nodes at the boundary are jointly eliminated based on the consistency of conduction direction and location density, while nodes with highly overlapping behavior are retained and marked as dominant nodes. Residual analysis is performed in conjunction with multidimensional criteria for structural stability to ensure that the eliminated nodes do not disrupt the continuity of the main heat diffusion path.

[0114] It should be noted that, in order to preserve the physical laws of heat conduction, the selection of candidate boundary nodes should be based on the following formula:

[0115] The direction consistency with adjacent nodes satisfies: ;

[0116] Spatial density satisfies: ;

[0117] in, Candidate nodes for the boundary With adjacent boundary candidate nodes The angle between the directions, This is the threshold for directional consistency. For node spatial density, The lower limit threshold for node spatial density is set by calibrating the results of thermal diffusion experiments on ground tooth surfaces. When the node spatial density is lower than the threshold threshold, the range of the threshold is determined. When the temperature is high, it indicates that the heat conduction path is sparse and a stable heat channel cannot be formed.

[0118] Therefore, only nodes that satisfy both of the above conditions are retained as dominant nodes. This is considered as a stable anchor point in the heat conduction path, and the resulting set of dominant nodes is selected. This represents the steady-state support framework for the heat conduction path within the tooth surface region.

[0119] The selected dominant nodes are reconnected into a path backbone graph, which is used as a prototype of a heat flow-oriented network for dynamic behavior recognition.

[0120] Specifically, the dominant nodes retained after multidimensional screening and residual analysis are reconnected by establishing a set of edges due to the consistency of their conduction directions, forming a heat-conducting main path structure with physical stability and topological sparsity. The heat flow guiding network prototype reflects the conduction trend of the main heat diffusion channel during tooth profile grinding, and has physical rationality and local robustness.

[0121] The converged heat flow guiding network is used to establish a hierarchical index based on the path intersection intensity, and the output is a heat drift path network for trajectory evolution recognition.

[0122] It should be noted that the path intersection strength refers to the overlap frequency and directional conflict degree of the intersection nodes between paths. The analysis of the intersection depth and directional diffusion differences between paths is divided into multi-layer network segments, each representing the heat conduction characteristics of different levels. Behavioral trajectory patterns are quickly extracted from different path layers. The resulting thermal drift path network not only retains the dominant directionality of spatial heat diffusion but also captures its nonlinear interlacing behavior that evolves with grinding time, providing a highly structured input carrier for trajectory recognition.

[0123] To further explain, a hierarchical index structure is constructed based on path intersection strength (i.e., the degree of intersection between node paths), assuming the path set is... , , is a positive integer, representing the total number of paths formed by connecting the set of dominant nodes via the heat conduction direction;

[0124] Among them: the Path It is an ordered set composed of several nodes in the dominant node set connected sequentially according to the heat conduction direction, used to characterize a complete thermal drift heat conduction path within the tooth surface region. The output, through a hierarchical index structure, is a thermal drift path network structure index used to support trajectory evolution pattern recognition.

[0125] It is understandable that two paths are defined in the path set. and The cross-linking strength is:

[0126]

[0127] in: and Representing paths and The set of dominant nodes it contains; This indicates the number of dominant nodes shared by two paths; and Representing paths and The corresponding total number of nodes; Indicates the path length with fewer nodes; path interleaving strength. It reflects the overlap ratio of the two paths at the spatial heat conduction node. The larger the value, the higher the degree of thermal coupling between the two paths in the tooth surface region.

[0128] All path pairs Path interlacing intensity Construct an interleaved intensity matrix as weights: ;in: The total number of paths is represented by the cross-stretching strength matrix, which characterizes the coupling strength distribution between each heat conduction path.

[0129] Using spectral clustering method The decomposition forms a hierarchical graph index structure, including:

[0130] The upper layer consists of highly interlaced path clusters (representing the thermal center region);

[0131] The lower layer has an independent conduction path (representing edge heat diffusion).

[0132] S102: For the multi-time-period paths in the thermal drift path network, obtain a drift differentiation feature set by aggregating and reconstructing the path evolution relationship, and distinguish short-period thermal disturbances from trend-based drift interference based on the drift differentiation feature set;

[0133] It should be noted that in the aforementioned thermal drift path network, the time evolution sequence set formed by the time-series connection relationships between dominant nodes records the spatial connectivity paths of each node's heat conduction intensity and direction changing over time. The evolution trend of heat flow state over time is extracted from the spatial connectivity paths. By aggregating and reconstructing the path changes of different paths over multiple time periods, short-period disturbances and trend drift differences in the heat diffusion process can be identified, achieving dynamic characterization of the thermal behavior of gear grinding wheel. Each dominant node records attributes within the observation period: a node number sequence with spatial location index, a node time label reflecting the thermal response time sequence, a direction vector set reflecting the heat flow orientation, and a node temperature difference value reflecting the change in conduction intensity. These nodes are arranged in time sequence along the path to form a dynamic node sequence within the path. The node sequence of the same path in multiple consecutive time windows is regarded as a time evolution path. Multiple time evolution paths together constitute a time evolution set. By extracting these changes and performing clustering and filtering, a structural set representing the differences in drift patterns can be obtained.

[0134] Specifically, the generation logic of the drift differentiation feature set includes:

[0135] Cluster the paths in the hot drift path network according to the node switching frequency and the direction inversion number to generate multi-path combination clusters;

[0136] It should be understood that during the tooth profile grinding process, each path in the thermal drift path... The path will undergo node switching and direction inversion, and its frequency reflects the activity level of local thermal disturbances. In order to capture the differences in path evolution, it is necessary to first measure the node switching characteristics and direction inversion characteristics of each path over time.

[0137] Set path Length of the observation time window The node switching frequency of the dominant node is:

[0138] ;

[0139] path Length of the observation time window The direction inversion number of the internal dominant node is defined as:

[0140] ;

[0141] in: Representing a path The number of node switching times of the dominant node during the observation period; Indicates the length of the corresponding observation time window; Representing a path The total number of nodes that dominate the observation period. Representing a path The sum of the number of direction inversions for all dominant nodes; Indicates the first The dominant node to the first The direction vector of each node Representing a path Node label, ; This is an indicator function used to detect direction reversal events. It returns 1 when the condition within the parentheses is true, and 0 otherwise; that is, the path... Total number of directional inversions It is equivalent to following this path from the first node =1 to the second to last node Perform a traversal, whenever the current path segment is found With the next path segment When the included angle is greater than 90 degrees (i.e., the dot product is less than 0), the indicator function... Just remember one 1, and finally add up all the 1s to get the sum.

[0142] Calculate the node activity and direction reversal characteristics for each path to reflect the degree of perturbation of the path in the thermal field. Higher activity levels indicate a higher degree of perturbation. or This indicates that the path is more unstable and susceptible to transient thermal disturbances. The path combination clusters are formed by clustering based on features, and the set of path combination clusters is: The paths are divided into two main categories: highly perturbable and stable drifting. Each cluster represents a group of paths with similar node switching and inversion characteristics.

[0143] For example, clustering can be performed using hierarchical clustering based on Euclidean distance to ensure the interpretability of the path differentiation structure. The result of establishing the path dynamic feature space determines the stability of subsequent two-dimensional mapping and trend screening.

[0144] Map each path in the path combination cluster to a two-dimensional vector of direction-gradient change and record the path perturbation intersection point;

[0145] It should be noted that the spatial perturbation of the path is determined not only by the change in direction, but also by the rate of change of the temperature gradient. Related; for each path combination cluster Extracting the rate of change of direction in a time series With the rate of change of temperature gradient Each path is mapped to a two-dimensional direction-gradient space, and its set of perturbation intersection points is identified. Specifically:

[0146] , indicating path direction of heat flow Over time The direction of change and the rate of change;

[0147] , indicating path Local thermal diffusion intensity Over time The rate of change of the gradient;

[0148] Will As two-dimensional coordinate points mapped onto a plane, and the perturbation intersection points are recorded by detecting changes in the density of the point group. (i.e., a locally non-stationary region):

[0149] ;

[0150] in: The perturbation density function, with the rate of change of direction and the rate of change of gradient as variables, is used to measure the local perturbation energy distribution. The gradient represents the perturbation density, i.e., the rate of change of the perturbation intensity in that direction – gradient space; This represents the preset perturbation threshold, used to distinguish between regions of significant perturbation and those of general perturbation. (Set of intersection points) It describes the alternating behavior of path perturbation and trend drift, realizes the transformation from the time domain to the orientation-gradient domain, quantifies the thermal perturbation behavior into a computable two-dimensional relationship, and fills the gap in traditional one-dimensional temperature change analysis that cannot identify trend-type shifts. The core input set for identifying the difference between trend drift and transient disturbance represents regions where the direction of heat flow and gradient change are both drastic, typically corresponding to key locations on the tooth surface where heat concentration and wear are active.

[0151] Wherein: the method for extracting the trend offset path set includes:

[0152] Each path is divided into equidistant segments on the time axis, and the total value of the change in the direction of heat flow and the number of direction inversions are calculated within each time segment to describe the thermal stability and disturbance characteristics of the path in a local time.

[0153] For example, the path Divided into equal parts according to the time axis The time segment, the first The total directional change of each time segment is The number of directional inversions is ;in, , The number of path segments based on time-based granularity, which is a positive integer; The larger the value, the more drastic the directional change within that time period, indicating unstable heat flow or being affected by disturbances, describing the path's offset behavior within a local time frame.

[0154] The total value of the direction change and the number of direction changes for each path are used to construct a trend encoding vector, and then the paths are clustered according to the encoding distance.

[0155] Specifically, the total value of the directional change of each segment Inversion number in the corresponding direction Combined, they form a trend encoding vector: ;

[0156] By using clustering algorithms (such as K-means or spectral clustering), the trend groups are grouped according to their encoded distance, resulting in the following set: ;

[0157] Based on the trend encoding vector, the multi-time period directional change behavior of the path is mapped into a high-dimensional feature vector, which enables different heat flow evolution modes to be clustered and distinguished in the feature space, and is the key to the transition from time domain path to feature domain drift mode.

[0158] Path groups with unidirectional accumulation characteristics in the offset direction are selected from the trend coding groups; that is, when the derivative of the rate of change of direction or the rate of change of gradient is greater than or equal to zero, it is determined to be a continuous offset path; paths that only satisfy this monotonic accumulation condition are considered trend drift paths. The selected path groups are output as a set of trend offset paths, and each path is labeled with a corresponding time period sequence for subsequent path differentiation modeling and hot drift feature aggregation.

[0159] Specifically, by screening and verifying path groups that meet the conditions for unidirectional accumulation of direction or gradient, a set of trend-based offset paths is established, thereby realizing the aggregation and transformation from multi-period disturbance trajectories to time-continuous drift behavior.

[0160] Since these paths maintain consistent direction or monotonically changing gradients within continuous time windows, their heat conduction trends exhibit significant cumulative stability. Therefore, they can be used to characterize the evolutionary stage of tooth surface heat conduction from transient perturbation to stable drift. By marking the corresponding time interval sequence for each trend path on the time axis, a time-path joint index structure is formed, realizing the temporal mapping from local trajectory perturbation characteristics to the overall heat conduction trend. By aggregating the directional accumulation information and gradient change relationship within each time window, a trend offset path set is constructed, realizing the transition from modeling local thermal response to global heat conduction trend. The final output trend offset path set possesses temporal continuity and physical stability, providing quantifiable input and time calibration basis for subsequent path differentiation modeling.

[0161] Based on the co-occurrence patterns of disturbance intersections across different time periods, a set of trajectories with trend-based shift characteristics is selected.

[0162] It should be noted that, in order to identify the group of heat conduction paths that continuously shift in the time dimension during the heat diffusion process, this step, based on the trend coding results, gradually filters out the set of paths with unidirectional shift trends by establishing a time co-occurrence matrix and a direction accumulation criterion.

[0163] It is understandable that, since the heat conduction paths on the tooth surface overlap spatially in multiple time periods, a multi-time period co-occurrence matrix is ​​constructed to quantify the temporal correlation between paths in order to reveal their heat flow evolution law. When the average co-occurrence is high and the fluctuation is low, it indicates that the heat conduction region maintains a stable conduction relationship in multiple time windows.

[0164] The average directional difference between paths is further calculated, and its monotonic accumulation trend over time is determined. When the directional difference continues to increase, it indicates that the heat flow center has shifted continuously, and the heat conduction direction has accumulated and drifted. Through this causal chain, the trend-based shift behavior can be derived from the stable co-occurrence relationship, thereby selecting a set of trend-based shift paths with temporal continuity and unidirectional accumulation characteristics, providing input for subsequent feature fusion.

[0165] The set is output as a drift differentiation feature set, which is called when the heating response structural unit is fragmented and recombined.

[0166] It should be noted that, in order to distinguish and structurally represent the trend-based offset path and the short-cycle perturbation path in the feature space, this step uses multi-dimensional feature fusion and clustering differentiation to finally obtain a set of drift differentiation features.

[0167] Understandably, since a single temperature or directional feature cannot fully reflect the differences in thermal diffusion, three types of elements—perturbation features, trend features, and co-occurrence features—are extracted from the set of trend-shifting paths to form a comprehensive feature vector. Normalization and weighted fusion are used to ensure the comparability of each feature at the same scale. Then, clustering is performed based on the Euclidean distance between features to classify three types of paths: trend-driven drift, short-period perturbation, and stable conduction. Because this clustering result establishes a mapping relationship between thermal behavior and structural features, it can clearly differentiate different thermal states, ultimately obtaining a set of drift differentiation features that can quantitatively describe the differences in thermal diffusion, serving as the basis for subsequent modeling.

[0168] S103: The thermal drift path network is recombined into irregular fragments based on the drift differentiation feature set; the thermal response structure boundary is determined for the recombined path fragments according to the interlacing pattern of the drift behavior trajectory; and the wear state is adjusted based on the thermal response structure boundary to determine the path, so as to realize the dynamic correction of the grinding thermal response behavior.

[0169] It should be noted that this is based on the drift differentiation feature set. The trend drift path and disturbance path features extracted are used to further characterize the local non-uniformity of tooth surface heat diffusion in spatial topology and time segment dimensions. By irregular fragmentation and recombination, a thermal response structure boundary with interlaced connection features is constructed.

[0170] Specifically, the application logic of the thermal response structure boundary includes:

[0171] In the application of thermally responsive structural boundaries, the temperature gradient field and stress gradient field of each path segment after fragmentation and reorganization are first collected to obtain the temperature change rate and stress distribution trend at different locations along the path. A coupling factor table is established by calculating the gradient magnitude, orientation angle, and spatial position difference between each pair of path segments. This coupling factor table is used to characterize the conduction intensity and directional relationship between adjacent segments, providing a basis for subsequent determination of whether thermal conduction continuity exists between segments.

[0172] Using the orientation angle parameters and path overlap intensity recorded in the coupling factor table, the spatial orientation consistency and temporal overlap rate are calculated respectively, and segment pairs that are similar in spatial conduction direction and have overlapping characteristics in time are selected. Segment pairs that meet the spatial orientation consistency threshold and temporal overlap rate threshold are merged into a boundary candidate set to describe continuous segments of heat conduction;

[0173] A boundary index map is built for the candidate boundary set, storing path segments, the boundaries connecting segments, and the relationships between them and their respective paths as multidimensional index entries. Each index entry includes a segment number, spatial coordinates, and an energy flow direction label to track the flow and transfer of heat in the heat conduction path. This index map provides a structured index foundation for energy backtracking and convergence analysis.

[0174] During the energy convergence analysis phase, the energy input and output of each connection in the boundary index diagram are balanced, the energy deficit is calculated, and an allowable deviation range is set. If the energy difference exceeds the set range, the connection entry is determined not to meet the energy conservation condition and is removed. The remaining connection entries after the removal process form an energy-conserving boundary connection list, representing the actual stable conduction paths that exist during heat conduction.

[0175] Based on the boundary connectivity list of energy conservation, the original path structure is rearranged and topologically corrected to eliminate heat conduction interruptions and path redundancy caused by fragmentation and reorganization. The rearranged path structure satisfies energy balance constraints, and the output is the thermal response path optimization result, providing input for subsequent thermal drift behavior modeling and wear life prediction.

[0176] To further explain, the reconstruction of the thermal response structural boundary is a process of spatial hierarchical modeling and topology optimization of the heat conduction path under the constraint of energy conservation. It aims to achieve an orderly descent of energy conduction paths and physical rationality of thermal potential distribution through hierarchical coordination and link rearrangement. The reconstruction of the thermal response structural boundary also includes:

[0177] Based on the boundary index map, the spatial distribution of nodes in the heat conduction path is hierarchically divided. According to the heat conduction depth and temperature gradient direction of the path nodes, the interlayer intersection points in the multi-layer boundary structure are defined as coordination nodes. Each coordination node corresponds to the interaction position of two or more heat conduction layers, reflecting the exchange relationship of heat flux between layers. An interlayer heat transfer coefficient is assigned to each coordination node. This coefficient describes the energy transfer intensity between different heat conduction layers, and its value is derived from the coupling ratio of the temperature change rate and stress response within the node's neighborhood. The output of this step is a node hierarchy table containing all coordination nodes and their heat transfer coefficients, used for subsequent energy link construction.

[0178] After hierarchical partitioning, the interlayer energy transfer relationship is calculated based on the heat transfer coefficient of the coordinating node and the phase difference of the peak temperature of each heat-conducting layer, generating an interlayer coupling matrix. A three-dimensional heat conduction link diagram is constructed based on the matrix elements of the interlayer coupling matrix, expressing the energy transfer paths between different heat-conducting layers in the form of links. By analyzing the gradient direction of energy flow in the heat conduction links, link branches with reversed energy flow are identified. For these reversed links, local topology pruning and rearrangement operations are performed to ensure that energy gradually decreases along the link direction, resulting in a stable downward trend in the spatial distribution of thermal potential. Simultaneously, redundant branches that do not satisfy this trend are deleted to maintain the energy convergence and conduction rationality of the model.

[0179] After topology rearrangement, energy consistency verification is performed on the 3D heat conduction path diagram. The energy input and output of each heat conduction path are calculated, and its energy loss rate is evaluated and compared with a preset allowable range. If the energy loss rate is less than a set threshold, the path is deemed to meet the energy consistency requirements and is considered a convergent path; otherwise, it is discarded. The retained path group after screening forms the heat conduction path result after multi-layer coordinated modeling. This result can be directly input into the subsequent wear state judgment and life prediction module to achieve stable modeling and physical interpretation of grinding heat diffusion behavior.

[0180] This can be understood as the reconstruction of the thermal response structural boundary not only achieving spatial-level coordination and optimization of the heat conduction path, but also ensuring that the energy transfer process conforms to the conservation principle. This process effectively avoids the problems of path breakage and abnormal heat flow accumulation in traditional temperature threshold segmentation methods, significantly improving the physical rationality and prediction accuracy of the model.

[0181] It should also be noted that the thermal response path generated during the grinding process of the tooth profile grinding wheel exhibits spatial inhomogeneity and temporal fluctuations. Simply relying on temperature field changes cannot accurately characterize the true energy transfer state of the heat conduction channel. Therefore, it is necessary to use the thermal response structure boundary as a constraint region and perform hierarchical calculations and dynamic corrections on the energy flux and temporal connectivity of the path segments to achieve dual optimization of energy distribution and heat conduction topology. Specifically, the thermal response path optimization results also include:

[0182] Within the region defined by the thermal response structure boundary, the energy flux is calculated based on the temperature gradient, contact bandwidth, and material thermal conductivity of each path segment, and an energy distribution table is generated.

[0183] This can be understood as using temperature gradient, contact bandwidth, and material thermal conductivity as parameters to calculate the energy flux of each path segment, establish an energy distribution table, and quantify the heat conduction intensity in different spatial regions. This achieves a physical mapping from temperature change to energy flux density, which is a prerequisite for subsequent balance correction.

[0184] By combining the energy distribution table, local heat capacity, and path length, the energy compensation amount of each segment is calculated to obtain a segment energy compensation list. This list reflects the accumulation and decay of heat energy in different segments over time, and is used to guide energy redistribution to ensure the energy balance of the overall heat conduction path.

[0185] The connection weights of path segments are redistributed according to the energy compensation list, and the heat conduction directions are compared. Segment connections with opposite directions are deleted to obtain a weighted connection set with unified heat conduction directions. By comparing the heat conduction direction vectors and deleting segment connections with opposite directions, the phenomenon of "heat flow reversal" is avoided, thereby maintaining the spatial continuity and unidirectionality of the heat conduction direction.

[0186] Temporal connectivity detection is performed on the weighted connection set. If a temporal break exists, the process reverts to the previous step and readjusts the weight distribution to obtain a temporally continuous heat conduction path. Based on this temporally continuous heat conduction path, an effective path structure corrected for energy balance is output for subsequent thermal behavior identification. This not only satisfies the balance constraint in the sense of energy conservation but also has complete temporal continuity, forming an effective path structure corrected for energy balance.

[0187] In other words, by employing a triple constraint mechanism of energy flux, weight redistribution, and connectivity correction, the heat conduction network is ensured to be spatially continuous, temporally stable, and energy-conserved, thereby significantly improving the physical accuracy of grinding thermal drift modeling and the reliability of life prediction. Compared with traditional thermal analysis methods that rely on temperature thresholds or empirical regression, the path optimization strategy of this invention belongs to a non-obvious multidimensional energy constraint design, possessing both theoretical and engineering innovation and feasibility.

[0188] S104: Self-update the internal judgment order and feature weights of the wear state judgment path adjusted by the thermal response structural boundary; based on the updated judgment order, perform real-time feature alignment and state mapping based on the thermal response structural boundary, and output the current wear state of the tooth profile grinding wheel and its remaining life prediction results.

[0189] It should be noted that the internal judgment order and feature weight update logic aim to achieve self-correction of the wear state judgment process and dynamic (note: this term has been avoided and will be replaced by "incrementally") sequential correction of the life prediction model through statistical correlation analysis of multi-source signals. This process takes the wear judgment path adjusted by the thermal response structural boundary as input and the revision of the feature weight matrix and judgment order matrix as output, forming an interpretable feature-weight coupling update mechanism.

[0190] Specifically, the internal judgment order and feature weight update logic include:

[0191] Temperature, current and acoustic emission signals corresponding to the wear judgment path after thermal response structural boundary adjustment are collected, and statistical features are extracted according to a fixed time window to obtain a feature vector set;

[0192] This can be understood as collecting multimodal signal data corresponding to the wear judgment path after the thermal response structure boundary adjustment, including temperature signal, current signal and acoustic emission signal, and performing segmented statistics on each signal according to a fixed time window length, extracting statistical features such as mean, variance, skewness, kurtosis and spectral energy to obtain a feature vector set. The feature vector set is used to describe the changing trend of different signals in the time series and their correlation characteristics with wear behavior.

[0193] Based on the feature vector set, the cross-correlation coefficient and covariance are calculated, and a feature correlation matrix is ​​constructed to measure the synchronicity of changes between different signals.

[0194] This can be understood as calculating the cross-correlation coefficient and covariance between signals based on the feature vector set, which respectively represent the synchronicity of changes and the linear dependence strength between different signals. The feature correlation matrix represents the degree of coupling between different signals within a given time window, providing quantitative relational input for subsequent weight mapping.

[0195] Using the difference between energy input and energy output as a penalty factor, the feature correlation matrix is ​​mapped to a feature weight matrix, and a weight revision table is generated.

[0196] The penalty factor can be understood as the difference between energy input and energy output, used to reflect the degree of energy conduction imbalance. Based on the penalty factor, the feature correlation matrix is ​​modified, and a mapping function is established to extract the energy balance adjustment coefficient. This mapping process transforms the correlation between signals into a feature weight distribution, generates a feature weight matrix, and forms a weight revision table to guide the reordering of judgments.

[0197] The judgment order matrix is ​​reordered according to the weighted revision table to correct the bias in the wear state identification results;

[0198] This can be understood as follows: based on the weight revision table, the original judgment order matrix is ​​reordered, prioritizing feature dimensions with higher weights and better energy balance. The sorted judgment results are then corrected for biases caused by signal drift or measurement noise, ensuring the statistically consistent sequence of feature judgments.

[0199] Based on the corrected judgment order matrix, state mapping and life inference are performed on the feature vector set, and the current wear state and remaining life prediction results of the tooth profile grinding wheel are output.

[0200] This can be understood as follows: based on the corrected judgment order matrix, the current feature vector is projected onto the historical feature space, and its similarity and time decay factor are calculated to infer the current wear level and remaining life prediction value of the gear grinding wheel. The output result is the corrected wear state judgment result and its life prediction data, which is used for real-time monitoring and maintenance scheduling.

[0201] Example 2

[0202] like Figure 2 As shown, the parts not described in detail in this embodiment are as described in Embodiment 1. This embodiment provides a thermal drift modeling and wear life prediction system for tooth profile grinding wheels, including a thermal response acquisition module, a dynamic behavior recognition module, a fragment reconstruction module, and a feedback update module. The modules are connected to each other via wired and / or wireless means.

[0203] The thermal response acquisition module is used to simultaneously acquire temperature response sequences of multiple tooth surface regions during tooth profile grinding, and to construct a thermal drift path network based on the cross-correlation relationship of temperature change trajectories in different regions, which is used to characterize the local conduction shift trend during the thermal diffusion process.

[0204] The construction logic of the thermal drift path network includes:

[0205] The temperature response trajectories of multiple tooth surface regions are divided into non-overlapping segments according to the relative time axis, and the difference in drift direction between adjacent segments is extracted.

[0206] A cross vector map is constructed based on the drift direction differences between multiple segments, and cross points with associated rotational features are merged to form behavioral nodes;

[0207] Behavioral nodes are clustered according to dense intervals of trajectory segments. Based on the node selection mechanism, a heat flow guiding network prototype is formed to achieve convergence reconstruction from the heat dissipation response point to the continuous heat conduction path. After removing path breakpoints, the network convergence is completed.

[0208] The converged heat flow guiding network is used to establish a hierarchical index based on the path intersection intensity, and the output is a heat drift path network for trajectory evolution recognition.

[0209] To further explain, the node filtering mechanism includes:

[0210] Collect the sequence vectors of all behavioral nodes appearing in multiple time periods, and calculate their path change span and adjacency coupling frequency;

[0211] The stability factor matrix is ​​generated by combining the path change span and the adjacency coupling frequency. Nodes whose stability factor matrix is ​​lower than a set threshold are marked as boundary candidate nodes.

[0212] Candidate nodes at the boundary are jointly eliminated based on the consistency of the propagation direction and the location density, while highly overlapping behavior nodes are retained and marked as dominant nodes.

[0213] The selected dominant nodes are reconnected into a path backbone graph, which is used as a prototype of a heat flow-oriented network for dynamic behavior recognition.

[0214] The dynamic behavior recognition module is used to obtain a drift differentiation feature set by aggregating and reconstructing the path evolution relationship of multi-time period paths in the thermal drift path network, and to distinguish between short-period thermal disturbances and trend drift interference based on the drift differentiation feature set;

[0215] The fragment recombination module is used to perform irregular fragment recombination of the thermal drift path network according to the drift differentiation feature set; determine the thermal response structure boundary of the recombined path fragments according to the interlacing pattern of the drift behavior trajectory; and adjust the wear state to determine the path based on the thermal response structure boundary, so as to realize the dynamic correction of grinding thermal response behavior.

[0216] The feedback update module is used to self-update the internal judgment order and feature weights of the wear state judgment path adjusted by the thermal response structural boundary; based on the updated judgment order, it performs real-time feature alignment and state mapping based on the thermal response structural boundary, and outputs the current wear state of the tooth profile grinding wheel and its remaining life prediction results.

[0217] S102: Obtain a set of drift differentiation features by aggregating and reconstructing the path evolution relationship of multi-time-period paths in the thermal drift path network, and distinguish short-period thermal disturbances from trend-based drift interference based on the set of drift differentiation features;

[0218] Wherein: the generation logic of the drift differentiation feature set includes:

[0219] Cluster the paths in the hot drift path network according to the node switching frequency and the direction inversion number to generate multi-path combination clusters;

[0220] Map each path in the path combination cluster to a two-dimensional vector of direction-gradient change and record the path perturbation intersection point;

[0221] Based on the co-occurrence patterns of disturbance intersections across different time periods, a set of trajectories with trend-based shift characteristics is selected.

[0222] The set is output as a drift differentiation feature set, which is called when the heating response structural unit is fragmented and recombined.

[0223] To further explain, the method for extracting the trend offset trajectory set includes:

[0224] For each path, divide it into equally spaced segments on the time axis, and calculate the total value of directional changes and the number of directional changes within each segment;

[0225] The total value of the direction change and the number of direction changes for each path are used to construct a trend encoding vector, and then the paths are clustered according to the encoding distance.

[0226] Filter out path groups with unidirectional accumulation characteristics in the offset direction from the trend coding group;

[0227] The selected path groups are output as a set of trend offset paths, and time period sequences are labeled for path differentiation modeling.

[0228] S103: The thermal drift path network is recombined into irregular fragments based on the drift differentiation feature set; the thermal response structure boundary is determined for the recombined path fragments according to the interlacing pattern of the drift behavior trajectory; and the wear state is adjusted based on the thermal response structure boundary to determine the path, so as to realize the dynamic correction of the grinding thermal response behavior.

[0229] Wherein: the application logic of the thermal response structural boundary includes:

[0230] Temperature gradient field and stress gradient field are collected for the fragmented and recombined path segments, and a coupling factor table is generated. The coupling factor table records the gradient magnitude, direction angle and spatial position difference between each pair of path segments for subsequent boundary screening.

[0231] Based on the coupling factor table and path crossover intensity, the spatial direction consistency and time interval overlap rate are calculated simultaneously, and a set of fragment pairs with continuous heat conduction and compatible time spans are selected as the boundary candidate set.

[0232] A boundary index map is built for the boundary candidate set, and the connection relationship between segments, boundaries and paths is recorded as multi-dimensional index entries. An energy flow label is set for each entry to track the conduction path.

[0233] Perform convergence backtracking on the energy input and output of each connection in the index graph, remove connection entries whose energy balance deviation exceeds the set range, and obtain the boundary connection list of energy conservation.

[0234] Rearrange the path structure based on the boundary connection list and output the thermal response path optimization results that satisfy the energy balance constraint.

[0235] To further explain, the reconstruction of the thermal response structural boundary also includes:

[0236] Based on the boundary index diagram, the heat conduction path is divided into layers according to the node level. The interlayer intersection points in the multi-layer boundary structure are defined as coordination nodes, and an interlayer heat transfer coefficient is assigned to each coordination node to describe the energy transfer intensity.

[0237] Based on the heat transfer coefficient of the coordinating node and the phase difference of the corresponding temperature peak of each layer, an interlayer energy transfer link is established to generate an interlayer coupling matrix; a three-dimensional heat conduction link diagram is constructed based on the interlayer coupling matrix, the reverse chain of energy flow is identified and local topology rearrangement is performed to make the heat potential show a stable decreasing trend along the energy link direction, and the branch connection that does not meet this trend is deleted.

[0238] Energy consistency verification is performed on the rearranged heat conduction paths. Path groups with energy loss rates within the set range are retained, and the heat conduction path results after multi-layer coordination modeling are output for subsequent wear status judgment.

[0239] In addition, it should be noted that the thermal response path optimization results also include:

[0240] Within the region defined by the thermal response structure boundary, the energy flux is calculated based on the temperature gradient, contact bandwidth, and material thermal conductivity of each path segment, and an energy distribution table is generated.

[0241] By combining the energy distribution table, local heat capacity and path length, the energy compensation amount of the segment is calculated, and the segment energy compensation list is obtained;

[0242] The connection weights of the path segments are redistributed according to the energy compensation list, and the heat conduction directions are compared. Segment connections with opposite directions are deleted to obtain a weighted connection set with uniform heat conduction directions.

[0243] Time-series connectivity detection is performed on the weighted connection set. If a time break exists, the process reverts to the previous step and readjusts the weight distribution to obtain a time-continuous heat conduction path. Based on the time-continuous heat conduction path, an effective path structure corrected for energy balance is output for subsequent thermal behavior identification.

[0244] S104: Self-update the internal judgment order and feature weights of the wear state judgment path adjusted by the thermal response structural boundary; based on the updated judgment order, perform real-time feature alignment and state mapping based on the thermal response structural boundary, and output the current wear state of the tooth profile grinding wheel and its remaining life prediction results.

[0245] Wherein: the internal judgment order and feature weight update logic include:

[0246] Temperature, current and acoustic emission signals corresponding to the wear judgment path after thermal response structural boundary adjustment are collected, and statistical features are extracted according to a fixed time window to obtain a feature vector set;

[0247] Based on the feature vector set, the cross-correlation coefficient and covariance are calculated, and a feature correlation matrix is ​​constructed to measure the synchronicity of changes between different signals.

[0248] Using the difference between energy input and energy output as a penalty factor, the feature correlation matrix is ​​mapped to a feature weight matrix, and a weight revision table is generated.

[0249] The judgment order matrix is ​​reordered according to the weighted revision table to correct the bias in the wear state identification results;

[0250] Based on the corrected judgment order matrix, state mapping and life inference are performed on the feature vector set, and the current wear state and remaining life prediction results of the tooth profile grinding wheel are output.

[0251] The tooth profile grinding wheel thermal drift modeling and wear life prediction system provided in this embodiment is used to execute the tooth profile grinding wheel thermal drift modeling and wear life prediction methods disclosed in the above embodiments of the present invention. The system consists of multiple functional modules, each corresponding to a functional unit in the method steps, and achieves complete operation of the method flow through data interaction. Since the system's module design corresponds one-to-one with the method steps, the relevant methods and processes can be found in the detailed descriptions of the foregoing embodiments, and will not be repeated here.

[0252] The foregoing has only described certain exemplary embodiments of the present invention by way of illustration. Undoubtedly, those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the foregoing drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A method of thermal drift modeling and wear life prediction of a tooth profile grinding wheel, characterized in that, The method comprises the following steps: S101: synchronously collect temperature response sequences of multiple tooth surface regions during tooth profile grinding, and construct a thermal drift path network according to the cross correlation of temperature change trajectories of different regions, wherein the construction logic of the thermal drift path network comprises: cutting the temperature response trajectories of the multiple tooth surface regions into non-overlapping segments according to a relative time axis, and extracting drift direction difference values between adjacent segments; constructing a cross vector atlas of the drift direction difference values between the multiple segments, and merging cross points with associated rotation characteristics to form behavior nodes; clustering the behavior nodes according to dense intervals of trajectory segments, forming a thermal flow guide network prototype based on a node screening mechanism, realizing convergent reconstruction from discrete thermal response points to continuous heat conduction paths, and completing network convergence after eliminating path breakpoints; establishing a hierarchical index according to path intersection strength, and outputting the converged thermal flow guide network for thermal drift path network for trajectory evolution identification; S102: obtain a drift differentiation feature set by aggregating and reconstructing path evolution relationships of multiple time period paths in the thermal drift path network, and distinguish short-period thermal disturbances from trend drift disturbances based on the drift differentiation feature set; the generation logic of the drift differentiation feature set comprises: clustering the paths in the thermal drift path network according to node switching frequency and direction inversion number, and generating a multi-path combination cluster; mapping each path in the path combination cluster into a direction-gradient change two-dimensional vector and recording path disturbance intersection points; screening out a trajectory set with trend offset characteristics according to the co-occurrence mode of the disturbance intersection points between different time periods; outputting the set as the drift differentiation feature set for calling when the thermal response structure is fragmented and reorganized; S103: performing non-regular fragmentation and reorganization on the thermal drift path network according to the drift differentiation feature set; determining the thermal response structure boundary according to the intersection mode of the drift behavior trajectory of the reorganized path segment; and adjusting the wear state judgment path based on the thermal response structure boundary, to realize dynamic correction of the grinding thermal response behavior; S104: self-updating the internal judgment order and feature weight of the thermal response structure boundary adjusted wear state judgment path; performing real-time feature alignment and state mapping based on the thermal response structure boundary according to the updated judgment order, and outputting the current wear state of the tooth profile grinding wheel and the remaining life prediction result.

2. The method of thermal drift modeling and wear life prediction of a tooth profile grinding wheel of claim 1, wherein, The node screening mechanism comprises: collecting the order vector of all behavior nodes appearing in multiple time periods, and calculating the path direction changing span and adjacent coupling frequency thereof; combining the path direction changing span and the adjacent coupling frequency to generate a stability factor matrix, and marking the nodes with stability factor matrix values lower than a set threshold as boundary candidate nodes; jointly eliminating the candidate nodes according to the conduction direction consistency and position density, and retaining highly coincident behavior nodes, and marking the highly coincident behavior nodes as dominant nodes; reconnecting the screened dominant nodes into a path backbone graph, and using the path backbone graph as a thermal flow guide network prototype for dynamic behavior identification.

3. The method of thermal drift modeling and wear life prediction of a tooth profile grinding wheel of claim 1, wherein, The extraction method of the trend offset trajectory set comprises: dividing each path into equidistant segments on the time axis, and respectively calculating the total value of direction change within the segment and the number of direction changes; The total value of the direction change of each path and the number of direction changes form a trend coding vector, and the coding distance is clustered into groups; Filter out the path group with the characteristics of one-way accumulation of the offset direction in the trend coding group; Output the filtered path group as the trend offset path set, and mark the time period sequence for path differentiation modeling.

4. The method of thermal drift modeling and wear life prediction of a tooth profile grinding wheel of claim 1, wherein, The application logic of the thermal response structure boundary includes: Collect the temperature gradient field and stress gradient field of the path segment after recombination, and generate a coupling factor table that records the gradient amplitude, direction angle, and spatial position difference between each pair of path segments for subsequent boundary screening; Based on the coupling factor table and the path intersection intensity, simultaneously calculate the spatial direction consistency and the time interval overlap rate, and select the fragment pair set that is continuous in heat conduction and compatible in time span as the boundary candidate set; Establish a boundary index map for the boundary candidate set, record the connection relationship of the segment, boundary, and path as a multi-dimensional index entry, and set an energy flow direction label for each entry for tracking the conduction path; Perform convergence backtracking on the energy input and output of each connected entry in the index map, remove the connection entries with energy consumption deviation exceeding the set range, and obtain the boundary connection list that conserves energy; Rearrange the path structure according to the boundary connection list, and output the thermal response path optimization result that meets the energy balance constraint.

5. The method of thermal drift modeling and wear life prediction of a tooth profile grinding wheel of claim 4, wherein, The reconstruction of the thermal response structure boundary further includes: Based on the boundary index map, divide the heat conduction path into layers according to the node level, define the intersection points between the layers in the multi-layer boundary structure as coordination nodes, and assign an interlayer heat transfer coefficient to each coordination node for describing the energy transmission intensity; Based on the heat transfer coefficient of the coordination node and the phase difference of the corresponding temperature peak value of each layer, establish an interlayer energy transfer link to generate an interlayer coupling matrix; construct a three-dimensional heat conduction link diagram according to the interlayer coupling matrix, identify the reverse chain of energy flow direction, and perform local topology rearrangement to make the thermal potential show a stable decreasing trend along the energy link direction, and delete the branch connection that does not meet this trend; Perform energy consistency verification on the rearranged heat conduction path, retain the path group with energy loss rate within the set range, and output the heat conduction path result after multi-layer coordination modeling for subsequent wear state judgment.

6. The method of thermal drift modeling and wear life prediction of a tooth profile grinding wheel of claim 5, wherein, The thermal response path optimization result further includes: In the area defined by the thermal response structure boundary, calculate the energy flux according to the temperature gradient, contact bandwidth, and material thermal conductivity of each path segment, and generate an energy distribution table; Combine the energy distribution table, local heat capacity, and path length to calculate the energy compensation amount of the segment, and obtain the segment energy compensation list; Redistribute the connection weights of the path segments according to the energy compensation list, and compare the heat conduction directions, delete the segment connections with opposite directions, and obtain the weighted connection set with unified heat conduction direction; Perform time sequence connectivity detection on the weighted connection set, and if there is a time break, go back to the previous step to adjust the weight distribution, obtain the time-continuous heat conduction path, and output the effective path structure corrected by energy balance as the basis for subsequent thermal behavior identification.

7. The method of thermal drift modeling and wear life prediction of a tooth profile grinding wheel of claim 1, wherein, The update logic of the internal judgment order and feature weight includes: Collect the temperature signal, the current signal and the acoustic emission signal corresponding to the wear judgment path adjusted by the thermal response structure boundary, extract statistical features according to a fixed time window, and obtain a feature vector set; Based on the feature vector set, the cross-correlation coefficient and the covariance are calculated, the feature correlation matrix is constructed, and the change synchronization between different signals is measured; The difference between the energy input and the energy output is taken as the penalty factor, the feature correlation matrix is mapped to the feature weight matrix, and the weight revision table is generated; The judgment order matrix is reordered according to the weight revision table, and the deviation correction of the recognition result of the wear state is performed; Based on the corrected judgment order matrix, the state mapping and the life inference are performed on the feature vector set, and the current wear state and the remaining life prediction result of the tooth profile grinding wheel are output.

8. A system for modeling thermal drift of a profiled grinding wheel and predicting its wear life, based on the implementation of the method for modeling thermal drift of a profiled grinding wheel and predicting its wear life according to any one of claims 1-7, characterized by, It comprises a thermal response collection module, a dynamic behavior recognition module, a segment recombination module and a feedback updating module, and each module is connected through wired and / or wireless connection; The thermal response collection module is used for synchronously collecting temperature response sequences of multiple tooth surface areas during tooth profile grinding, and constructing a thermal drift path network based on the cross-correlation relationship of temperature change trajectories of different areas, which is used to represent the local conduction deviation trend in the thermal diffusion process; The dynamic behavior recognition module is used for obtaining a drift differentiation feature set by aggregating and reconstructing the path evolution relationship of multi-period paths in the thermal drift path network, and distinguishing short-period thermal disturbance and trend drift interference based on the drift differentiation feature set; The segment recombination module is used for irregularly segmenting and recombining the thermal drift path network according to the drift differentiation feature set; determining the thermal response structure boundary according to the interlaced mode of the drift behavior trajectory for the recombined path segment; and adjusting the wear state judgment path based on the thermal response structure boundary to realize dynamic correction of the grinding thermal response behavior; The feedback updating module is used for self-updating the internal judgment order and the feature weight of the wear state judgment path adjusted by the thermal response structure boundary; performing real-time feature alignment and state mapping based on the thermal response structure boundary according to the updated judgment order, and outputting the current wear state and the remaining life prediction result of the tooth profile grinding wheel.

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