A comb blade parameter adaptive optimization method and system

Abstract

The application relates to the technical field of machining and computer-aided engineering, and discloses a comb-shaped blade parameter adaptive optimization method and system, which comprises the following steps: acquiring comb-shaped blade reference constraint data, constructing an initial tooth array parameter vector population, extracting adjacent comb tooth space shielding and shared contact data to generate inter-tooth contact topology tensors; acquiring shear resistance of each comb tooth, comprehensive stress of a tooth root and inter-tooth retained contact area; extracting a load transmission coefficient matrix, calculating a coupling fitness and a load balance penalty term, and constructing a fitness function for evaluation; selecting parent individuals, performing cross operation according to a preset geometric proportion constraint to obtain topological feasible offspring; calculating multi-physical field partial derivatives to determine parameter sensitivity, adaptively distributing mutation probability to generate a mutation population and selecting a candidate optimal parameter combination; and performing forming rule verification on the optimal parameters to generate a manufacturing model. The application improves the convergence precision of the optimization algorithm in a nonlinear solution space and the success rate of landing of a blade manufacturing entity.

Description

Technical Field

[0001] This application relates to the fields of machining and computer-aided engineering technology, and in particular to an adaptive optimization method and system for comb-shaped blade parameters. Background Technology

[0002] Comb-shaped cutting tools, as core working components in high-end cutting and crushing equipment, are widely used in high-load industrial scenarios such as scrap metal shredding, hard engineering plastic crushing, and complex profile milling. The geometry, spacing ratio, and root morphology of the comb teeth directly determine the tool's resistance to bending and breakage, as well as the smoothness of chip removal. In the traditional design and parameter optimization of comb-shaped cutting tools, engineers' long-term experience is usually highly relied upon, using static lookup tables or simplified theoretical empirical formulas to determine the various dimensional parameters of the cutting tools. However, under actual high-speed cutting conditions, the material shearing process is an extremely nonlinear dynamic process accompanied by large deformation, high friction, and thermo-mechanical coupling. Traditional static design methods often treat each comb tooth as an isolated force unit, ignoring the stress concentration and transmission effect caused by the close spatial array between adjacent comb teeth, as well as the chain compression interference caused by the obstruction of material flow in the narrow inter-tooth channels. This local design, which deviates from the actual physical processing state, can easily lead to serious accidents such as tool breakage due to excessive local stress or blockage of the chip removal groove under complex working conditions.

[0003] Furthermore, with the introduction of computer intelligent algorithms, some studies have begun to attempt to use genetic algorithms or particle swarm optimization algorithms to globally optimize blade parameters. However, existing conventional evolutionary algorithms, due to a lack of deep integration with the laws of physical space interference, exhibit severe blindness when performing crossover and mutation operations. This leads to the generation of a large number of distorted and invalid solutions during the iteration process, where the ratio of adjacent comb tooth spacing to comb tooth height is severely imbalanced or the root fillets of the teeth overlap and interfere with each other. This not only wastes a huge amount of simulation computing power but also easily destroys the excellent bending resistance genes that have been painstakingly inherited during random mutation, making the algorithm prone to getting trapped in local optima and unable to extricate itself.

[0004] Furthermore, most purely mathematical optimization solutions currently used in the industry are severely disconnected from the actual physical manufacturing processes in downstream workshops. The so-called globally optimal parameters, painstakingly calculated by intelligent algorithms, often exceed the physical machining limits of real CNC machine tools. For example, the calculated chip flute width may be smaller than the diameter of the smallest milling cutter in the workshop, or the tooth root fillet may be smaller than the minimum chamfer limit of the grinding wheel. As a result, theoretically perfect cutting tools cannot be machined in reality. The data barrier between the design and manufacturing ends has not been broken down, lengthening the trial-and-error cycle of high-end special cutting tool development and resulting in high sunk costs. Summary of the Invention

[0005] To address the aforementioned technical issues, this application provides an adaptive optimization method and system for comb-shaped cutting tool parameters. This method automatically optimizes and outputs a solid cutting tool manufacturing model that combines global load balance and smooth chip removal, while meeting the underlying physical machining limits of CNC machine tools. This is achieved by integrating dynamic multiphysics feedback and boundary constraint-type nonlinear evolution mechanisms.

[0006] In a first aspect, this application provides an adaptive optimization method for comb-shaped blade parameters, the method comprising: S1. Obtain the baseline constraint data of the comb blade, construct the initial tooth row parameter vector population representing the comb blade, divide the comb tooth surface for each individual in the initial tooth row parameter vector population, extract the spatial occlusion and shared contact data between adjacent comb teeth, and generate the tooth contact topology tensor corresponding to each individual. S2. Perform shear simulation on each individual in the initial tooth row parameter vector population to obtain the shear resistance, root stress and inter-tooth contact area of ​​each comb tooth. S3. Extract the load transfer coefficient matrix from the inter-tooth contact topology tensor of each individual, calculate the coupling fitness of each comb tooth by combining the shear resistance, root stress and inter-tooth retention contact area of ​​each comb tooth, use the distribution variance of the coupling fitness of all comb teeth as the inter-tooth load balance penalty term, construct the fitness function and evaluate each individual in the initial tooth row parameter vector population. S4. Based on the evaluation results, select two parent individuals from the initial tooth row parameter vector population, and perform genetic crossover on the two parent individuals according to the preset geometric ratio constraint to obtain topologically feasible offspring. S5. Calculate the partial derivatives of the combined stress at the tooth root and the inter-tooth contact area with respect to each parameter dimension of the topologically feasible offspring to determine the parameter sensitivity. Adaptively allocate the mutation probability based on the parameter sensitivity and perform mutation on the topologically feasible offspring to generate a mutant population. Use the fitness function to evaluate and select candidate optimal parameter combinations from the mutant population. S6. Perform preset forming rule verification on the candidate optimal parameter combination, and generate the manufacturing model of the comb blade based on the verification results.

[0007] Secondly, this application provides an adaptive optimization system for comb-shaped blade parameters, the system comprising: The baseline population module is used to obtain baseline constraint data of the comb blade, construct an initial tooth row parameter vector population that characterizes the comb blade, divide the comb tooth surface for each individual in the initial tooth row parameter vector population, extract the spatial occlusion and shared contact data between adjacent comb teeth, and generate the tooth contact topology tensor corresponding to each individual. The shear simulation module is used to perform shear simulation on each individual in the initial tooth row parameter vector population to obtain the shear resistance, root stress and inter-tooth contact area of ​​each comb tooth. The equilibrium evaluation module is used to extract the load transfer coefficient matrix from the inter-tooth contact topology tensor of each individual, calculate the coupling fitness of each comb tooth by combining the shear resistance, root stress and inter-tooth retention contact area of ​​each comb tooth, use the distribution variance of the coupling fitness of all comb teeth as the inter-tooth load equilibrium penalty term, construct the fitness function and evaluate each individual in the initial tooth row parameter vector population. The geometric crossover module is used to select two parent individuals from the initial tooth row parameter vector population based on the evaluation results, and perform genetic crossover on the two parent individuals according to the preset geometric ratio constraints to obtain topologically feasible offspring. The sensitive mutation module is used to calculate the partial derivatives of the tooth root integrated stress and the inter-tooth retained contact area with respect to each parameter dimension of the topologically feasible offspring to determine the parameter sensitivity. Based on the parameter sensitivity, the mutation probability is adaptively allocated and mutation is performed on the topologically feasible offspring to generate a mutation population. The fitness function is used to evaluate and select candidate optimal parameter combinations from the mutation population. The forming verification module is used to perform preset forming rule verification on the candidate optimal parameter combination and generate a manufacturing model of the comb blade based on the verification results.

[0008] Compared with the prior art, the beneficial effects of the present invention are at least as follows: 1. This application constructs a precise evaluation system that integrates digital twin and multiphysics coupling effects. By reconstructing the three-dimensional surface from the dimensionality-reduced parameters and extracting the spatial occlusion and shared contact data between adjacent comb teeth, the inter-tooth contact topology tensor is generated. Combined with the shear resistance, comprehensive stress and contact area obtained from elastoplastic dynamics simulation, the traditional static and isolated force analysis mode is abandoned. On this basis, a load transfer coefficient matrix and a distribution variance penalty term are introduced to accurately quantify the deterioration and contagion effect of local stress concentration and chip accumulation spreading to the surrounding area. This forces the evaluation system to focus on the load balance of the entire tool, providing a high-fidelity and mathematically rigorous quantitative judgment base for the performance evaluation of complex multi-tooth tools under real cutting conditions.

[0009] 2. This application proposes an intelligent evolution mechanism based on strong constraints of physical laws and sensitivity perception of partial derivatives, which solves the problems of wasted computing power and local optimum traps caused by blind iteration in conventional genetic algorithms. In the crossover stage, an adaptive shrinkage adjustment strategy is used to perform reverse multiplication to force correction of out-of-bounds parameters by utilizing the geometric ratio of adjacent comb tooth spacing and comb tooth height, eliminating the physical interference and breakage risks between comb teeth. In the mutation stage, a breakthrough is made by using the numerical difference principle to solve the partial derivatives of physical performance indicators with respect to each parameter dimension, establishing a negative exponential mapping barrier between sensitivity and mutation probability. This directional mutation strategy of high sensitivity and heavy protection, and low sensitivity and heavy exploration, maximizes the release of evolutionary vitality of non-sensitive parameters while stabilizing the excellent mechanical genes of the genetic blades, significantly improving the global convergence quality of the algorithm in complex nonlinear spaces.

[0010] 3. This application breaks down the manufacturing barriers in the entire closed-loop process from the pure mathematical black box of intelligent algorithms to the physical entity processing in the workshop. By introducing a low-level hard threshold verification for the root fillet radius and minimum tooth clearance at the end of the evolutionary optimization process, it eliminates theoretically perfect but unmanufacturable defective designs by using insurmountable manufacturing red lines. When the optimal parameter combination successfully passes the machining limit collision comparison, the system can directly drive the three-dimensional low-level engine to automatically construct the geometric entity and assign material tolerance properties, seamlessly exporting a standard structured model for computer-aided manufacturing systems. This mechanism avoids high downstream trial and error costs and achieves a one-time successful implementation of special cutting tools from performance adaptive optimization to automatic manufacturability verification and engineering drawing delivery, thus advancing the intelligent and automated process of industrial tool design. Attached Figure Description

[0011] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a flowchart illustrating the steps of an adaptive optimization method for comb-shaped blade parameters in an embodiment of this application. Figure 2 This is a schematic diagram illustrating the construction of the initial tooth row parameter vector population characterizing the comb-shaped blade in an embodiment of this application; Figure 3 This is a structural diagram of a comb-shaped blade parameter adaptive optimization system according to an embodiment of this application. Detailed Implementation

[0013] This application provides a method and system for adaptive optimization of comb-shaped blade parameters. The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0014] Example 1: For ease of understanding, the specific process of the embodiments of this application is described below, such as... Figure 1 The adaptive optimization method for comb-shaped blade parameters shown in the embodiment of this application includes: S1. Obtain the baseline constraint data of the comb blade, construct the initial tooth row parameter vector population representing the comb blade, divide the comb tooth surface for each individual in the initial tooth row parameter vector population, extract the spatial occlusion and shared contact data between adjacent comb teeth, and generate the tooth contact topology tensor corresponding to each individual.

[0015] S1 contains a population of initial tooth row parameter vectors representing the comb-shaped blade, including: such as Figure 2 The schematic diagram shows how the outline dimensions and material manufacturing constraints are extracted from the baseline constraint data; the initial values ​​of comb tooth spacing, comb tooth height, comb tooth inclination angle, tooth root fillet radius, and blade thickness are determined based on the outline dimensions and material manufacturing constraints; the initial values ​​are arranged in a preset dimension order to generate a baseline tooth row parameter vector, and random perturbation is introduced into the baseline tooth row parameter vector at a preset scale to generate an initial tooth row parameter vector population.

[0016] Specifically, in the conventional design and manufacturing process of comb-shaped cutting tools, there is a lack of systematic mathematical abstraction of the physical characteristics of complex cutting tools, which makes it difficult to perform subsequent automated optimization when facing multiple working conditions, and easily leads to insufficient sample diversity in the optimization algorithm during cold start. In order to solve the technical problems of high-fidelity conversion of physical entity structure to digital optimization space and construction of optimization base sample, this application achieves this by obtaining the benchmark constraint data of comb-shaped cutting tools and constructing a population of initial tooth row parameter vectors representing comb-shaped cutting tools. Among them, the benchmark constraint data refers to the set of basic limiting conditions existing in machine tool design drawings or process specification documents. The population is a core concept in genetic evolution and heuristic optimization algorithms. In this application, it refers to a set containing multiple alternative comb-shaped cutting tool design schemes. Each alternative scheme in the population is called an individual, and each individual is uniquely determined by a parameter vector in the form of a one-dimensional mathematical array.

[0017] In the specific calculation process of constructing the initial tooth row parameter vector population, the outline dimensions and material manufacturing constraint parameters are first extracted from the baseline constraint data. The outline dimensions limit the maximum three-dimensional spatial envelope volume of the overall length, width, and height of the comb-shaped blade. The material manufacturing constraint parameters cover the minimum machining tool radius, material yield strength thickness, and other physical baseline data of the machine tool and material. Then, based on the extracted outline dimensions and material manufacturing constraint parameters, the initial values ​​of comb tooth spacing, comb tooth height, comb tooth inclination angle, tooth root fillet radius, and blade thickness are determined. The specific calculation process is as follows: a constant is subtracted from the estimated default total number of comb teeth. 1. Obtain the number of arrangement span segments, then divide the maximum usable working length in the outer contour dimensions by the number of arrangement span segments to accurately express the true geometric span of the center points of adjacent comb teeth in the case of linear arrangement with teeth at the ends, thereby calculating the initial value of the comb tooth spacing; extract the minimum machining tool radius in the material manufacturing constraint parameters, and add the preset safety process tolerance to the radius value to calculate the initial value of the tooth root fillet radius; similarly, subtract the assembly reserved clearance from the height limit and thickness limit of the outer contour dimensions to obtain the initial values ​​of the comb tooth height and the blade thickness, respectively, and set the initial value of the comb tooth tilt angle to a zero-degree vertical state.

[0018] After obtaining the physical starting values ​​for all dimensions, the initial values ​​are arranged in a preset dimensional order to generate a baseline tooth row parameter vector. Since each dimension in the parameter vector strictly corresponds to a specific geometric feature dimension, this ordered arrangement constitutes a one-dimensional data structure, allowing the complex three-dimensional entity to be reduced in dimensionality and abstracted into a linear algebraic expression that can be efficiently read by a computer. Subsequently, random perturbations are introduced into the baseline tooth row parameter vector at a preset size to generate an initial tooth row parameter vector population. The preset size refers to the upper limit of the total number of individuals in the population. The introduction of random perturbations aims to give the optimization algorithm diversity in the starting point of the global search. The specific calculation process is as follows: for each parameter dimension in the baseline tooth row parameter vector, the corresponding outer contour dimensions and material manufacturing constraints are used to calculate the value of that dimension. Legal physical fluctuation upper and lower limits; call a pseudo-random number generator to generate corresponding random deviation values ​​within the legal physical fluctuation upper and lower limit range without changing the original physical dimensions of this dimension; directly sum the random deviation values ​​with the initial values ​​of the corresponding dimension of the reference tooth row parameter vector; after summing, perform boundary check judgment. If the summing result exceeds the legal physical fluctuation upper and lower limits, the value is forcibly truncated to the closest valid boundary value, thereby generating a physically absolutely feasible and characteristically different variant individual. Repeat the above-mentioned dimensional random perturbation, summing calculation and boundary truncation process until the number of generated variant individuals reaches the preset scale, and finally combine to generate a population containing multiple initial tooth row parameter vectors with differentiated parameter configurations.

[0019] The above content rigorously reduces the physical geometry of the blade to a mathematical vector that the algorithm can deeply analyze, and establishes a legal design sample library with multidimensional feature diversity that fully conforms to the underlying engineering layout logic. By introducing a strict "working length / (number of teeth - 1)" span layout calculation logic, the systematic geometric deviation caused by average distribution is eliminated from the source, ensuring that the extracted tooth pitch truly reflects the center distance between adjacent teeth. At the same time, by introducing in-situ dimensional random perturbation strictly constrained by physical boundaries, the algorithm's optimization breadth during cold start is broadened under the premise of absolutely ensuring that each initial blade is machined. This avoids the risk of getting trapped in local optima due to the homogeneity of initial samples, laying a solid and computationally friendly digital foundation for subsequent high-precision finite element mechanical simulation evaluation and genetic cross-iteration.

[0020] In S1, spatial occlusion and shared contact data between adjacent comb teeth are extracted to generate inter-tooth contact topology tensors for each individual. This includes: constructing corresponding three-dimensional surfaces of comb teeth according to the parameters contained in each individual, and dividing each three-dimensional surface of comb teeth into contact area, sliding area and bearing area according to preset shear limits; projecting the adjacent comb teeth along the shear direction, extracting the overlapping area of ​​the projection surface as shared contact data, and extracting the included angle of non-overlapping edges as spatial occlusion data; assembling the shared contact data and spatial occlusion data into a multi-dimensional array according to the physical arrangement order of the comb teeth to generate inter-tooth contact topology tensors.

[0021] Specifically, after generating the basic parameters of a single digitized individual, since the physical comb-shaped cutting tool has a spatially close array between adjacent comb teeth in actual processing, the simple independent dimension parameters cannot effectively express the physical coupling interference effect of adjacent comb teeth when cutting the same local material, nor can they reflect the spatial dynamic constraint of the chip removal channel. In order to solve the technical problem of accurately capturing the spatial interference correlation between adjacent comb teeth and constructing structured features that can be used for subsequent global evaluation, this application extracts the spatial occlusion and shared contact data between adjacent comb teeth to generate the tooth contact topology tensor corresponding to each individual.

[0022] Specifically, based on the parameters contained in each individual component, a corresponding three-dimensional comb surface is constructed. This comb surface is a digital, continuous geometric shell describing the outer contour of the cutting tool. Since the values ​​of comb tooth spacing, height, and tilt angle in the individual parameter vector are one-dimensional macroscopic geometric scalars and cannot directly drive surface generation, a local three-dimensional spatial coordinate system is pre-established with the end of the blade base as the origin. Using preset geometric triangulation rules, the aforementioned comb tooth spacing, height, and tilt angle values ​​are calculated and converted into three-dimensional spatial coordinates of each comb tooth's feature boundaries, such as the tooth tip, tooth flank contour, and the center of the tooth root transition arc. Specifically, the lower left corner of the blade base is taken as the origin O of the local three-dimensional coordinate system. The blade length direction is defined as the positive X-axis, the comb tooth height direction as the positive Y-axis, and the blade thickness direction as the positive Z-axis. Let the tooth pitch parameter of the i-th comb tooth be... The comb tooth height parameter is The comb tooth tilt angle parameter is The radius of the tooth root fillet is First, calculate the coordinates of the center position of the comb tooth root: , , ,in, This represents the initial coordinates of the center of the first comb tooth root in the X direction; subsequently, based on the comb tooth height... and comb tooth angle Calculate the coordinates of the tooth tip: , , Furthermore, the coordinates of the center of the tooth root arc are calculated based on the tooth root fillet radius R_i: , , Subsequently, using the center of the tooth root arc, the center of the tooth root, and the tooth tip as control points, the tooth side profile curve is obtained through a combination of preset straight line segments and arc segments; the tooth side profiles on both sides are constructed symmetrically about the central axis of the comb tooth; after completing the two-dimensional profile construction, the comb tooth three-dimensional solid model is generated by stretching along the Z-axis using the blade thickness parameter T; further, the coordinates of all vertices and mesh nodes of the three-dimensional solid model are extracted to form the spatial position coordinate data of the corresponding three-dimensional curved surface of the comb tooth; for multiple comb teeth, according to the corresponding... Each comb tooth is arranged sequentially into a three-dimensional solid form, which is then combined to form a complete three-dimensional curved surface model of the comb blade. In this embodiment, the above-mentioned geometric triangulation mapping rule adopts a combination of trigonometric function coordinate transformation and parametric solid modeling. The spatial coordinates of each feature point are calculated step by step according to the comb tooth spacing, comb tooth height, comb tooth tilt angle and tooth root fillet radius. A two-dimensional contour is constructed based on the calculated control points. Then, the solid is stretched along the thickness direction in combination with the blade thickness parameters, and finally a three-dimensional geometric model of the comb blade corresponding one-to-one with the parameter vector is generated. Then, these calculated three-dimensional spatial position coordinates are used as spatial control point mesh, and together with the preset node vector and local weight matrix, they are input into the non-uniform rational B-spline modeling algorithm to fit and generate three-dimensional spatial vertex and surface normal data consistent with the actual physical blade shape, thereby obtaining a three-dimensional curved surface of each comb tooth containing a complete shape. The non-uniform rational B-spline modeling algorithm is an existing technology and will not be described in detail here.

[0023] After constructing the three-dimensional surface, each comb tooth's three-dimensional surface is divided into contact zone, sliding zone, and bearing zone according to preset shear limits. The preset shear limits refer to the set of physical height classification benchmarks constructed based on the cutting depth and chip removal friction depth pre-set by the machine tool process, specifically including the first cutting depth threshold and the second friction depth threshold. Traversing each spatial vertex on the three-dimensional surface, the single axial coordinate component of each vertex along the comb tooth height direction, i.e., the tool cutting into the material depth direction, is extracted in the pre-built local three-dimensional spatial coordinate system and defined as the depth coordinate value of that vertex. Subsequently, a rigorous threshold boundary classification calculation is performed based on this depth coordinate value: vertices with depth coordinate values ​​greater than the first cutting depth threshold and their connected mesh surfaces are classified as contact zones that directly participate in the peeling and stripping of the target material; vertices and mesh surfaces with depth coordinate values ​​less than or equal to the first cutting depth threshold and greater than the second friction depth threshold are classified as sliding zones used to guide the chips outward; and the remaining mesh surfaces with depth coordinate values ​​less than or equal to the second friction depth threshold are classified as bearing zones that only provide physical support and bending stiffness.

[0024] After the division is completed, the adjacent comb teeth are projected along the shearing direction, which is the feed motion vector direction of the blade relative to the workpiece machining surface extracted in advance. A two-dimensional orthogonal projection plane perpendicular to the shearing direction is constructed, and the spatial vertex coordinates of the three-dimensional curved surfaces of the two adjacent comb teeth are mapped to the two-dimensional orthogonal projection plane by applying an orthogonal transformation matrix, generating two adjacent two-dimensional polygonal contours. Then, the overlapping area of ​​the projection plane is extracted as shared contact data, and the included angle of the non-overlapping edges is extracted as spatial occlusion data. In the specific calculation process, the polygon Boolean intersection algorithm is used to calculate the vertex coordinates of the closed region of the intersection of the two two-dimensional polygonal contours, and the specific area value of the closed region is obtained by applying the polygon vertex area calculation formula, which is used as shared contact data to characterize the degree of material extrusion coupling between the teeth. At the same time, the system obtains the independent edge contour segments of the non-overlapping polygons through Boolean difference, performs a straight line fitting on the independent edge contour segments using the least squares method to obtain their respective principal direction vectors, and calculates the included angle between these principal direction vectors using the vector dot product formula, which is used as spatial occlusion data to characterize the degree of physical space restriction when the chips curl and flow out.

[0025] Finally, the shared contact data and spatial occlusion data are assembled into a multidimensional array according to the physical arrangement of the comb teeth to generate the inter-tooth contact topology tensor. The inter-tooth contact topology tensor is a high-order matrix data structure used to characterize the spatial adjacency interference state of the entire blade. Since the dimension of the shared contact data is physical area and the dimension of the spatial occlusion data is physical angle, in order to prevent the significant difference in magnitude from causing computational distortion or gradient anomalies in the subsequent algorithm, the acquired shared contact data and spatial occlusion data are normalized by division mapping according to the set maximum theoretical area limit and maximum theoretical angle limit, so that their values ​​are uniformly transformed into the dimensionless real number range of 0 to 1. Then, the physical array sequence number of the adjacent comb teeth on the blade substrate is used as the row and column two-dimensional index coordinates of the tensor, and the normalized data feature type is used as the depth channel dimension of the tensor. The processed values ​​are filled into the corresponding coordinate index positions of the multidimensional array, and finally the structured generation of the inter-tooth contact topology tensor containing all local inter-tooth interference relationships of the entire individual is completed.

[0026] The above content transforms discrete blade parameters into a topological matrix that accurately maps the physical arrangement of comb teeth and cutting forces, constructing a standardized mathematical foundation for quantifying the spatial interference between solid teeth and chip removal resistance. By reconstructing a real three-dimensional surface based on the basic parameters and using rigorous high and low thresholds to delineate different physical force functional areas, the computational interference of non-cutting redundant surfaces is eliminated, improving the physical focus of the subsequent feature extraction process under real working conditions. Orthogonal projection and Boolean operations along the shear feed direction break through the observation blind spots of conventional two-dimensional planes, extracting the complex stress superposition and overlap areas and chip removal geometric resistance angles between adjacent teeth in a high-fidelity form, accurately reflecting the dynamic boundary friction morphology of compact blades during actual material removal.

[0027] S2. Perform shear simulation on each individual in the initial tooth row parameter vector population to obtain the shear resistance, root stress and inter-tooth contact area of ​​each comb tooth.

[0028] S2 includes: introducing the shearing material model into a simulation environment containing the comb blades corresponding to each individual, and setting the relative kinematic parameters and contact boundary conditions between the shearing material model and the comb blades; calling the finite element solver to perform dynamic calculations, generating dynamic response data of each individual during the shearing process, extracting the reaction force of each comb tooth contact interface from the dynamic response data as shear resistance, and extracting the peak equivalent stress of each comb tooth root mesh node as the tooth root comprehensive stress; identifying the retained material distributed in the gap between adjacent comb teeth based on the dynamic response data, and calculating the mesh surface area of ​​the retained material in contact with the tooth sidewall as the tooth retention contact area.

[0029] Specifically, after completing the structured extraction of the static spatial geometric topological relationship between the comb-shaped blade teeth, since the simple static topological data cannot directly reflect the dynamic mechanical response of the blade and the spatial flow state of the material chips in the actual machining scenario, in order to solve the technical problem of accurately evaluating the actual stress load and chip removal smoothness of individual blades with different structural parameters in the actual cutting process, this application achieves this by performing shear simulation on each individual in the initial tooth row parameter vector population to obtain the shear resistance, tooth root comprehensive stress and inter-tooth contact area of ​​each comb tooth.

[0030] Specifically, a shearing material model is introduced into a simulation environment containing individual comb-shaped blades. The relative kinematic parameters and contact boundary conditions between the shearing material model and the comb-shaped blades are set. The shearing material model is a three-dimensional finite element meshed physical calculation model based on continuum mechanics and elastoplastic constitutive equations. Since it is essentially a rigorous physical mechanics derivation system rather than a data-driven AI model, it does not require sample iterative training. Its internal algorithm structure directly establishes the stiffness matrix mapping relationship between stress and strain through a set constitutive mathematical formula. The input data of this model are the real physical property parameters of the target material, specifically including material density, elastic modulus, Poisson's ratio, yield strength, and damage evolution fracture threshold. The constitutive mathematical formula describes how a specific material changes internally under stress. The mathematical expression of the shape's characteristics is used as input. Under this input, the model can output data simulating the plastic flow, chip separation, and strain field distribution of real materials under compression through internal iteration. When constructing the simulation environment, based on the machining process settings of the real machine tool, the preset feed rate and cutting depth are converted into relative kinematic parameters and applied to the three-dimensional centroid reference point of the comb-shaped blade in the simulation environment, driving the blade to dynamically cut into the material model along a specified trajectory. At the same time, the contact boundary conditions between the two are set. A contact penalty algorithm based on Coulomb's friction law is defined between the blade surface and the material mesh interface to give a set surface friction coefficient. An adaptive mesh separation criterion is set to allow the mesh cells in the material model to be physically deleted after reaching the set damage fracture threshold to simulate the physical peeling process of real chips.

[0031] Subsequently, the finite element solver is invoked to perform dynamic calculations, generating dynamic response data for each individual component during the shearing process. The reaction force at the contact interface of each comb tooth is extracted from the dynamic response data as shear resistance, and the peak equivalent stress of the mesh nodes at the root of each comb tooth is extracted as the comprehensive stress at the tooth root. The finite element solver is a numerical simulation program based on an explicit time integration algorithm. It discretizes the continuous simulation time domain into small time steps and uses Newton's second law of motion to iteratively solve the displacement, velocity, and acceleration of all mesh nodes in the space step by step, summarizing and generating dynamic response data that includes the time-series changes of the coordinate displacement and internal stress-strain field of each mesh node. When obtaining shear resistance, the dynamic response data within a single calculation cycle is traversed to locate the contact interface between the blade rake face and the comb tooth sidewall in physical contact. Specifically, when establishing the finite element model of the comb-shaped blade, each surface element is pre-numbered according to the blade geometry and topology. The surface that first contacts the workpiece material along the tool feed direction is defined as the rake face region, and the surfaces located on both sides of each comb tooth and parallel to the tool thickness direction are defined as the comb tooth sidewall regions, and corresponding region identifiers are assigned to them. During the finite element solution process, each calculation increment outputs the contact element state variable; all surface elements belonging to the rake face region and comb tooth sidewall region are traversed. When the contact state variable of the corresponding surface element indicates that the element has effective contact with the material element and the contact pressure is greater than the preset contact pressure threshold, the surface element is determined to be in physical contact state; further, all surface elements that meet the above conditions are extracted to form the blade rake face contact interface and comb tooth sidewall contact interface at the current moment, and are used as the subsequent reaction force statistical area; the dynamic reaction force component values ​​of all force mesh nodes distributed on the above contact surface in the tool feed direction are extracted; firstly, all the above component values ​​at a specific time sampling point are spatially accumulated to obtain the total cutting reaction force in that instantaneous state; then, since the cutting process is accompanied by high-frequency oscillation, in order to obtain a stable evaluation index, the total cutting reaction force at each discrete time point within a single calculation cycle is calculated by time domain integration; in this embodiment, the single calculation cycle refers to the complete time integration interval corresponding to two adjacent structural state updates during the finite element dynamic solution process. In explicit dynamics solutions, the overall cutting process is discretized into multiple consecutive computational cycles. Each computational cycle includes several time integration steps, and each time integration step corresponds to a fixed time increment Δt. Let the k-th computational cycle contain N consecutive time integration steps, then the total duration of this computational cycle is: Within this calculation cycle, the instantaneous cutting reaction forces corresponding to all time integration steps are cumulatively integrated: ,in, This represents the instantaneous total reaction force at the blade contact interface during the j-th time integration step; subsequently, the cumulative integration result is divided by the duration of the calculation cycle. The average shear resistance corresponding to this calculation period is obtained: The average shear resistance obtained from multiple consecutive calculation cycles can be further averaged as the shear resistance evaluation index corresponding to the current blade structure. Finally, in order to restore the calculation result from the impulse dimension of Newton-second to a resistance parameter that conforms to the mechanical definition, the time domain integral result is divided by the total length of the time window of a single-step calculation cycle, thereby calculating the average shear resistance value used to characterize the macroscopic mechanical load intensity during the cutting stage, with the dimension remaining in Newton. When obtaining the tooth root comprehensive stress, each tooth root mesh node in the smooth transition area between the comb geometry and the blade matrix is ​​located. Based on the three-dimensional multi-directional principal stress tensor components of each node in the dynamic response data, the corresponding equivalent stress scalar value is calculated using the classical Von Mises yield criterion formula. This equivalent stress is a characteristic quantity that transforms a complex three-dimensional spatial stress state into a single scalar value, used to comprehensively evaluate whether the stressed material has reached the yield failure limit. The equivalent stress scalar values ​​of all mesh nodes in the tooth root area are extracted and compared one by one to select the equivalent stress point with the largest value as the tooth root comprehensive stress of the comb, thereby quantitatively characterizing the upper limit of the maximum tooth breakage failure risk of the current blade structure during cutting.

[0032] Furthermore, based on dynamic response data, the trapped material distributed in the gap between adjacent comb teeth is identified, and the mesh surface area where the trapped material adheres to the sidewall of the tooth is calculated as the trapped contact area between the teeth. During the cutting process, poor chip removal can lead to secondary extrusion friction or even tooth jamming and tool breakage. Therefore, a judgment algorithm combining spatial coordinate system transformation and speed verification is used to accurately quantify the trapped state. Through coordinate range matching, material mesh cells that fall completely or partially within the coordinate boundary of the spatial gap enclosed by the three-dimensional sidewalls and base surfaces of two adjacent comb teeth are extracted. Then, the global velocity vector of the material mesh cells in these specific gap areas is extracted and projected onto the local coordinate system of the cutting tool itself to calculate the relative sliding velocity of each mesh cell. The calculated relative sliding velocity is then compared with the preset maximum... A strict size comparison and classification is performed on the small flow velocity threshold. Grid cells with a relative sliding velocity greater than or equal to the threshold are judged as chips that flow out smoothly and are removed. Grid cells with a relative sliding velocity less than the threshold are accurately identified and marked as stagnant material that cannot flow out of the chip removal channel smoothly. For the external surface grid patches marked as stagnant material, it is determined whether their three-dimensional spatial coordinate point set has geometric collision interference with the grid on the side wall surface of the comb tooth gap. For grid patches with actual contact and adhesion, the physical surface area value of each contact patch is calculated using the three-dimensional polygon area calculation formula. The surface area values ​​of all contact patches in the same adjacent comb tooth gap are algebraically summed to output the inter-tooth stagnant contact area, which represents the severity of chip removal congestion in the local physical channel.

[0033] The above content constructs a physical quantification and computational mechanism that transforms static geometric entities into dynamic cutting mechanical responses, providing a high-dimensional and realistic dynamic data foundation for accurately evaluating and optimizing the overall service performance of cutting tools. By introducing a physical shear material model with embedded elastoplastic constitutive equations and setting strict kinematic driving and frictional separation contact boundary conditions, the nonlinear dynamic cutting process under real machine tool processing environment is highly reproduced, ensuring that the extracted force and flow field characteristics perfectly match the actual working conditions. Using an explicit finite element solver, precise extraction and integration of the time-domain dynamic response data at the micro-node level are performed, accurately capturing not only the transient state of the macroscopic contact interface. Shear resistance can also be used to directly pinpoint the maximum fatigue yield risk extreme point in the local area of ​​the tooth root by converting and calculating equivalent stress, eliminating the blind spots in the assessment of complex stress states by traditional static empirical formulas. At the same time, a mechanism combining grid coordinate space boundary matching and relative slip velocity classification is adopted to achieve accurate identification of trapped materials without dead angles, and further calculate the positive value of the actual contact surface between the material and the tooth sidewall. The dynamic obstruction degree of the chip removal channel is physically mapped with intuitive and rigorous numerical indicators, providing strong dynamic mechanical verification and chip removal flow field state support for subsequent highly targeted parameter adaptive optimization structure correction.

[0034] S3. Extract the load transfer coefficient matrix from the inter-tooth contact topology tensor of each individual, calculate the coupling fitness of each comb tooth by combining the shear resistance, root stress and inter-tooth retention contact area of ​​each comb tooth, use the distribution variance of the coupling fitness of all comb teeth as the inter-tooth load balancing penalty term, construct the fitness function and evaluate each individual in the initial tooth row parameter vector population.

[0035] S3 includes: calculating the mechanical transmission ratio between adjacent comb teeth based on the shared contact data and spatial occlusion data contained in the inter-tooth contact topology tensor, and constructing a load transfer coefficient matrix according to the comb tooth arrangement dimension; assigning preset performance weight coefficients to shear resistance, tooth root comprehensive stress, and inter-tooth retained contact area respectively for normalized weighted calculation, and introducing the load transfer coefficient matrix to perform adjacent comb tooth state coupling correction to obtain the coupling fitness of each comb tooth; calculating the numerical distribution variance of the coupling fitness of all comb teeth, defining the numerical distribution variance as the inter-tooth load balance penalty term, calculating the total average value of the coupling fitness of all comb teeth, and subtracting the inter-tooth load balance penalty term scaled by a preset ratio from the total average value to construct the fitness function.

[0036] Specifically, after obtaining the shear resistance, root stress, and inter-tooth contact area of ​​each comb tooth, since the comb-shaped blade does not perform cutting tasks in isolation in real cutting scenarios, there will be significant mechanical transmission and state coupling effects between adjacent comb teeth through material extrusion in the chip removal space and elastic deformation of the blade matrix. Moreover, the overall wear life and breakage risk of the blade often depend on the weakest local area with the most uneven stress. To solve the technical problems of how to accurately quantify the physical coupling transmission effect between adjacent comb teeth and how to comprehensively evaluate the overall load distribution balance of the blade to accurately guide the adaptive optimization of blade parameters, this application extracts the load transfer coefficient matrix from the inter-tooth contact topology tensor of each individual, calculates the coupling fitness of each comb tooth by combining the shear resistance, root stress, and inter-tooth contact area of ​​each comb tooth, uses the distribution variance of the coupling fitness of all comb teeth as the inter-tooth load balance penalty term, constructs the fitness function, and evaluates each individual in the initial tooth row parameter vector population.

[0037] In specific implementation, firstly, based on the shared contact data and spatial occlusion data contained in the inter-tooth contact topology tensor, the mechanical transmission ratio between adjacent comb teeth is calculated, and a load transfer coefficient matrix is ​​constructed according to the comb tooth arrangement dimension. The inter-tooth contact topology tensor is a high-dimensional data structure constructed in the previous steps to characterize the three-dimensional spatial arrangement and geometric topological interference relationship of the comb teeth. Shared contact data representing the area of ​​the parallel, directly opposite regions within a preset projection height between the sidewalls of two adjacent teeth, and spatial occlusion data representing the degree of narrowness of the chip flow direction in adjacent chip removal channels are extracted from it. In the calculation step, the obtained shared contact area is first divided by the preset standard sidewall area of ​​a single tooth for dimensionless processing to obtain the area ratio. Further, to ensure that the shared contact data and spatial occlusion data have a unified dimensionless representation, normalization processing is performed on both data items respectively. Let the shared contact area corresponding to adjacent comb teeth be... The preset standard lateral area of ​​a single tooth is then directly calculated based on the current insert parameters, and its calculation expression is: ,in: This represents the standard lateral surface area of ​​a single tooth. This represents the current comb tooth height. The blade thickness is given; the standard side area of ​​a single tooth represents the theoretically effective force-bearing area of ​​a single comb tooth sidewall under conditions of no geometric obstruction, therefore it does not need to be pre-defined, but is calculated in real time based on the geometric parameters corresponding to the current topologically feasible offspring; the normalized calculation of the shared contact area is as follows: ,when At that time, the normalization result is limited to 1; simultaneously, the previously extracted spatial occlusion data, i.e., the angle of non-overlapping edges, is retrieved and divided by the preset maximum theoretical interference angle threshold to calculate the percentage of blocked space between 0 and 1; furthermore, the spatial occlusion angle corresponding to adjacent comb teeth is denoted as... The preset maximum theoretical interference angle threshold is determined based on the maximum spatial occlusion state allowed by the blade, and its calculation method uses the maximum allowable angle of the blade design as the theoretical upper limit: Or it can be expressed in radians. In actual calculations, the same angular units as the spatial occlusion data are used; therefore, the normalized calculation of spatial occlusion is as follows: The results obtained satisfy When the actual included angle exceeds the theoretical maximum value, the normalization result is limited to 1.

[0038] Subsequently, the dimensionless area ratio is mathematically added to the percentage of obstructed space, and then mapped to a mechanical transmission ratio between 0 and 1 using a preset exponential decay function with a natural constant base. This ratio objectively quantifies the probability and intensity of stress concentration transfer and chip congestion between adjacent comb teeth. Furthermore, to comprehensively reflect the combined influence of shared contact degree and spatial obstruction degree on the load transfer capability between adjacent comb teeth, this application uses an exponential decay function to establish a nonlinear mapping relationship between the two and the load transfer coefficient; let the normalized shared contact area be... The normalized spatial occlusion is The load transfer coefficient between adjacent comb teeth is then calculated as follows: ,in: Indicates the first The comb teeth are directed towards the first... Load transfer coefficient of each comb tooth; This is the exponential decay adjustment coefficient; This represents an exponential function with the natural constant e as its base; the exponential decay adjustment coefficient is preset based on the dynamic range of the load transfer coefficient, and its value satisfies... By adjusting the exponential decay adjustment coefficient, the rate at which the shared contact area and spatial occlusion affect load transfer capability can be controlled. When it is necessary to enhance the impact of local geometric changes on load transfer capability, the exponential decay adjustment coefficient is increased; when it is necessary to improve the robustness of the load transfer coefficient to local geometric changes, the exponential decay adjustment coefficient is decreased. The load transfer coefficients between all adjacent comb teeth are calculated using the above expressions, and filled into the corresponding positions of the load transfer coefficient matrix according to the actual arrangement order of the comb teeth. The main diagonal elements of the matrix are fixed at 1, indicating that each comb tooth always maintains its own load transfer capability. There is no direct load transfer relationship between non-adjacent comb teeth, and their corresponding matrix elements are assigned a value of 0, thereby constructing a complete load transfer coefficient matrix.

[0039] Subsequently, a square matrix is ​​constructed according to the actual physical arrangement of the comb teeth on the blade substrate from left to right. The intrinsic transmission coefficient of each comb tooth is fixed as a constant of 1 and placed on the main diagonal of the square matrix. Here, the intrinsic transmission coefficient refers to the basic autocorrelation weight of a single comb tooth bearing its own assigned cutting load. Its physical meaning is that the specific comb tooth itself must bear 100% of the independent force reference directly applied to its surface, without including the additional force transmitted from the outside. Then, the mechanical transmission ratio between adjacent comb teeth calculated above is placed in the corresponding non-diagonal adjacent position in the matrix, that is, the secondary diagonal position on both sides of the main diagonal. For other comb tooth nodes that are not physically directly adjacent, it is determined that they have no direct contagion effect, and their corresponding positions in the matrix are assigned a value of 0, thereby constructing the final load transmission coefficient matrix. This matrix is ​​essentially an algebraic mapping relationship table describing the physical deterioration state between adjacent spatial nodes inside the system, such as sudden changes in local cutting force and chip blockage contagion intensity.

[0040] Next, pre-defined performance weighting coefficients were assigned to shear resistance, tooth root stress, and inter-tooth contact area for normalized weighted calculation. A load transfer coefficient matrix was then introduced to correct the coupling between adjacent comb teeth, yielding the coupling fitness of each comb tooth. Since shear resistance is measured in Newtons, tooth root stress in megapascals, and inter-tooth contact area in square millimeters, their physical properties are drastically different and their dimensions are completely inconsistent. Direct calculation would lead to numerical inconsistencies. Furthermore, all three indicators are negative performance indicators where larger values ​​indicate more severe stress or congestion. Therefore, a minimax normalization calculation was employed. The method involves extracting the historical maximum and minimum values ​​of the three characteristics mentioned above for all individuals in the current population. The extracted characteristic value of the current comb tooth is then subtracted from the historical minimum value and divided by the range, transforming all three into a dimensionless deterioration index between 0 and 1. Based on the engineering emphasis of the current cutting process on mechanical load, tooth breakage risk, and chip removal capability, a performance weighting coefficient with a sum of 1 is pre-set. The dimensionless deterioration indices are multiplied by their corresponding performance weighting coefficients and summed to obtain a comprehensive load scalar characterizing the severity of independent stress on each comb tooth. Specifically, the performance weighting coefficients include a shear resistance weighting coefficient. Tooth root comprehensive stress weighting coefficient and interdental contact area weighting coefficient ,satisfy: All weighting coefficients are greater than 0. The weighting coefficients are allocated based on the importance of cutting efficiency, structural strength, and chip removal capability according to the actual application conditions of the cutting insert. When the cutting insert is mainly used in high-intensity continuous cutting conditions, the weighting coefficient corresponding to the combined stress at the tooth root can be appropriately increased to reduce the risk of insert breakage. When the cutting insert is mainly used in high-chip removal machining conditions, the weighting coefficient corresponding to the inter-tooth contact area can be appropriately increased. When the cutting insert is mainly used in high-speed cutting conditions, the weighting coefficient corresponding to the shear resistance can be appropriately increased. As a preferred embodiment, this example adopts: , , Among them, the root stress directly determines the risk of tooth breakage and fatigue failure of the cutting tool, and therefore is given the highest weight; shear resistance directly affects the cutting load and machining energy consumption, and therefore is given the second highest weight; the inter-tooth contact area mainly affects the smoothness of chip removal, and is given a relatively low weight under the premise of ensuring the structural safety of the cutting tool; furthermore, in other embodiments, the above weight coefficients can be readjusted according to different machining objects, but all of them satisfy: ; ; And always satisfy: The aforementioned weighting coefficients can be determined based on the cutting tool design objectives, existing cutting test data, finite element simulation results, or engineering experience. When the overall adaptability corresponding to different weight combinations reaches its maximum, the performance weighting coefficients corresponding to the current machining conditions are determined.

[0041] To accurately represent the physical contagion effect, a linear algebraic matrix multiplication operation is performed on the column vector composed of the comprehensive load scalar of each comb tooth and the load transfer coefficient matrix constructed above. Under the action of matrix multiplication, the comprehensive load of the current comb tooth not only includes its own original load, but also absorbs the load components transmitted from the adjacent comb teeth according to the mechanical transmission ratio, completing the state coupling correction and outputting the true coupling load value. Finally, the coupling load value is subtracted from the preset standard maximum full score value to perform a direction reversal mapping, which is transformed into a positive score that the larger the value, the better the comprehensive service performance, and is defined as the coupling fitness of each comb tooth.

[0042] Based on this, the numerical distribution variance of the coupling fitness of all comb teeth is calculated. This numerical distribution variance is defined as the inter-tooth load balancing penalty term, and a fitness function is constructed accordingly. The numerical distribution variance is a statistical algorithm that measures the degree of dispersion of a set of discrete data from its mathematical expectation, i.e., the average value. In the specific calculation, the algebraic sum of the coupling fitness of all comb teeth on the current blade individual is first calculated and divided by the total number of comb teeth to obtain the overall average value that reflects the overall average performance level of the blade. Then, the coupling fitness of each comb tooth is extracted, and the square of its difference from this overall average value is calculated. Finally, the sum of the squared differences of all comb teeth is obtained and divided by the total number of comb teeth. The resulting variance value is strictly defined as the inter-tooth load balancing penalty term. The larger the penalty value, the more significant the difference in stress and chip removal performance between the individual comb teeth, indicating a very high risk of local overload or single-tooth chip breakage. Next, the calculated inter-tooth load balance penalty is multiplied by a pre-set scaling factor to adjust its influence on the overall evaluation. This scaled inter-tooth load balance penalty is then subtracted from the overall average value. The resulting difference forms the global fitness function for evaluating the individual blade. Using this fitness function, a unique quantitative evaluation score is calculated for each individual in the initial tooth row parameter vector population, providing a rigorous mathematical criterion for the survival of the fittest and the direction of parameter evolution in subsequent optimization algorithms.

[0043] The above content constructs a comprehensive evaluation mathematical model that conforms to the laws of mechanical contagion and integrates global load balance constraints, solving the core problem of lacking reliable quantitative fitness evaluation standards for complex multi-tooth cutting tools in multi-parameter optimization. By extracting spatial interference data to construct a load transfer coefficient matrix, the isolated single-tooth feature evaluation is upgraded to a multi-tooth coupled evaluation that integrates adjacent physical transmission. Matrix multiplication is used to accurately quantify the deteriorating contagion effect of local stress concentration and chip accumulation spreading to the surrounding area, making the evaluation model highly consistent with the physical truth of nonlinear mechanical transmission under real cutting conditions. In the process of multi-feature fusion, a standardized normalization method is adopted. The method eliminates the computational barriers between different physical dimensions. At the same time, through clever load superposition and direction reversal logic, it ensures the rigor of the evaluation system in mathematical reasoning and the self-consistency of engineering logic. Furthermore, it introduces the variance of the numerical distribution, which represents the degree of dispersion, as a penalty term into the construction of the fitness function. This accurately captures the local non-uniformity of the overall force on the blade, effectively preventing the survival of abnormal parameter combinations with excellent local tooth performance but severe overall force unevenness in the optimization population. From the mathematical bottom layer, it forces the subsequent adaptive evolution algorithm to converge efficiently towards the global optimal solution with overall load balance and smooth local chip removal.

[0044] S4. Based on the evaluation results, select two parent individuals from the initial tooth row parameter vector population, and perform genetic crossover on the two parent individuals according to the preset geometric ratio constraints to obtain topologically feasible offspring.

[0045] S4 includes: using a preset selection strategy based on the evaluation results of the fitness function to select two parent individuals from the initial tooth row parameter vector population; exchanging and recombining the tooth pitch and tooth profile components contained in the two parent individuals to generate initial offspring individuals; calculating the ratio of the adjacent comb tooth spacing to the comb tooth height corresponding to the initial offspring individuals as the geometric ratio, and determining whether the geometric ratio falls within the permissible range defined by the preset geometric ratio constraint; performing adaptive shrinkage adjustment on the numerical boundary of the initial offspring individuals that do not fall within the permissible range to eliminate physical interference defects between comb teeth, and generating topologically feasible offspring.

[0046] Specifically, after the above steps are used to quantitatively evaluate each individual in the initial tooth row parameter vector population using the fitness function, although the merits of the current parameter combination can be objectively distinguished based on the score, the initial population often cannot directly cover the global optimal solution. In order to drive the parameters to evolve towards a better direction and solve the technical problem that traditional unconstrained genetic algorithms generate invalid and useless solutions with physical overlap of comb teeth, machining interference, or easy breakage due to proportional imbalance during crossover and mutation, this application selects two parent individuals from the initial tooth row parameter vector population based on the evaluation results and performs genetic crossover on the two parent individuals according to the preset geometric proportion constraints to obtain topologically feasible offspring.

[0047] In specific implementation, based on the evaluation results of the fitness function, a preset selection strategy is first used to select two parent individuals from the initial tooth row parameter vector population. The tooth pitch and tooth profile components of the two parent individuals are then exchanged and recombinated to generate the initial offspring individuals. The preset selection strategy here adopts the tournament selection algorithm, which is implemented by simulating local biological competition to select individuals with superior genes. During execution, a preset number of individuals are randomly selected from the current population to form a competition subset. The fitness scores of each individual in this subset are retrieved and compared, and the individual with the highest score is directly extracted and retained as the first parent individual. Following this... The process of random sampling and local comparison is repeated to select the second parent individual. Then, the tooth row parameter vectors of the two parent individuals are extracted, and the tooth pitch component representing the span of adjacent comb teeth and the tooth shape component representing the geometric shape of comb teeth are located. Using a multi-point crossover algorithm, crossover nodes at the same position are randomly generated in the data segments of the above two components, and the parameter segments between the corresponding crossover nodes of the two parent individuals are forcibly interchanged. Through this calculation action, this application mathematically fuses the chip removal distance feature of one parent individual with the resistance tooth shape feature of another parent individual, and initially outputs the initial offspring individual carrying the recombinant features of the two parents.

[0048] To ensure that the generated initial offspring are physically manufacturable and possess reasonable mechanical load-bearing capacity, the ratio of adjacent comb tooth spacing to comb tooth height corresponding to the initial offspring is calculated as the geometric ratio. It is then determined whether this geometric ratio falls within the permissible range defined by the preset geometric ratio constraint. Adjacent tooth spacing values ​​are extracted from the tooth spacing component of the parameter vector of the initial offspring, and divided by the comb tooth height value included in the tooth profile component to calculate the dimensionless geometric ratio. The preset geometric ratio constraint is pre-set based on the mechanical strength limit of the blade matrix material and the minimum chip removal groove width in CNC machining. It consists of a clear lower and upper threshold values ​​forming a closed permissible range. Furthermore, to ensure that the offspring generated by genetic crossover simultaneously meet the mechanical strength requirements of the comb teeth and the chip removal channel requirements, the preset geometric ratio constraint uses the ratio of comb tooth spacing to comb tooth height as the constraint index. Its calculation expression is as follows: Where R is the geometric ratio, P is the center-to-center distance between adjacent comb teeth, and H is the comb tooth height; the minimum geometric ratio that meets the mechanical strength requirements of the tooth root is calculated based on the allowable bending stress corresponding to the blade material. The maximum geometric proportion that meets the chip removal requirements is calculated based on the minimum chip removal groove width specified in the processing technology. The preset geometric ratio allowable range is expressed as: in, In the formula, This indicates the minimum allowable spacing between comb teeth while meeting the mechanical strength requirements of the tooth root; simultaneously, In the formula, Determined by the minimum chip removal groove width requirement, when the comb tooth thickness is T, the minimum chip removal groove width specified by the machining process is... Sometimes, Therefore, the preset geometric scale allowable range can be expressed as: After obtaining the initial offspring through genetic crossover, the corresponding geometric ratio R is calculated. If R is within the aforementioned permissible range, it is determined that the geometric ratio constraint is met. If it exceeds the permissible range, the corresponding parameters are adjusted to the boundary of the permissible range according to the principle of closest boundary, so that the corrected offspring meet the requirements of no physical interference between comb teeth and having chip removal space. The calculated geometric ratio is compared with the upper and lower limits of the permissible range. If the ratio is lower than the lower limit threshold, it indicates that the comb tooth spacing is too narrow or the tooth height is too long, which poses a risk of chip removal interference and single tooth bending breakage. If the ratio is higher than the upper limit threshold, it indicates that the tooth spacing is too wide or the tooth height is too short, which will seriously weaken the cutting efficiency of the cutting tool.

[0049] When it is determined that the geometric proportion does not fall within the permissible range, an adaptive shrinkage adjustment is performed on the numerical boundary of the initial offspring individuals that do not fall within the permissible range to eliminate physical interference defects between the comb teeth, generating topologically feasible offspring. In the calculation of the adaptive shrinkage adjustment, the geometric proportion that currently exceeds the limit is first extracted, and the nearest permissible range boundary threshold is determined. That is, the target calibration value of individuals below the lower limit is set as the lower limit threshold, and the target calibration value of individuals above the upper limit is set as the upper limit threshold. Then, the determined boundary threshold is divided by the current out-of-limit geometric proportion to calculate the shrinkage correction coefficient. The value of the tooth pitch component in the initial offspring individual that causes the out-of-limit movement is directly multiplied by the calculated shrinkage correction coefficient, forcing the out-of-limit movement of the tooth pitch component. Individuals whose values ​​exceed the permissible range due to gene recombination are proportionally pulled back to the safe numerical boundary of the preset permissible range. This contraction adjustment of the numerical boundary ensures that the ratio of the adjacent comb tooth spacing to the comb tooth height of the corrected offspring individuals falls exactly at the critical threshold of the permissible boundary, fundamentally eliminating spatial interference defects and brittle fracture risks between comb teeth. Subsequently, individuals that pass the adjustment are preserved and output as topologically feasible offspring for constructing the next generation of evolutionary populations. Furthermore, to avoid the geometric ratio deviating further from the permissible range due to a uniform contraction method for different crossover directions, this application adopts different boundary correction strategies based on the crossover direction of the geometric ratio. Let the initial geometric ratio of the offspring obtained by topological crossover be... ,in, The distance between adjacent comb teeth. For the comb tooth height, a preset geometric ratio allowable range is satisfied. ,when If the tooth spacing is too large or the tooth height is too small, it indicates that the geometric proportions are too close to the permissible range. Therefore, a shrinkage correction factor is calculated. ,in By using a shrinkage correction factor to proportionally reduce the tooth pitch parameter or to inversely amplify the tooth height parameter, the corrected geometric proportions are satisfied. ,when If the tooth spacing is too narrow or the tooth height is too high, this indicates that the tooth spacing is too narrow or the tooth height is too high. To avoid further reducing the tooth spacing and causing physical interference between the teeth, this application does not use shrinkage correction, but instead uses expansion correction strategy, and calculates the expansion correction coefficient. ,in According to the preset parameter correction rules, the tooth pitch parameter is enlarged proportionally, or the tooth height parameter is reduced proportionally, so that the corrected geometric proportions meet the requirements. Among them, tooth pitch enlargement and tooth height reduction can be performed by either option, or the two parameters can be adjusted simultaneously according to preset weights to ensure that the correction meets the allowable range requirements and avoids new geometric interference. After the correction is completed, the minimum gap between adjacent comb teeth is recalculated. When the minimum gap is greater than the preset safe gap threshold, the corresponding offspring is determined to be a topologically feasible offspring. Otherwise, the above boundary correction process is repeated until the geometric constraint requirements are met.

[0050] The above content addresses the technical problem of traditional genetic optimization easily generating a large number of unmanufacturable invalid solutions and causing algorithm divergence by introducing a constrained crossover evolution mechanism that integrates physical space exclusivity and mechanical proportionality laws. Through the combination of tournament selection and multi-point crossover algorithms, it accurately realizes the directional inheritance and gene recombination of superior comb tooth structural features, ensuring the evolutionary dynamics of the population towards higher fitness. More importantly, immediately after gene segment crossover, a geometric proportional constraint based on the ratio of adjacent comb tooth spacing to comb tooth height is introduced, strictly defining a real-world constraint for parameter optimization in purely mathematical operations. The mechanical and processing boundaries of the physical world are considered. For the initial offspring individuals whose proportions exceed the limits after recombination, instead of an inefficient direct elimination strategy, an adaptive shrinkage adjustment mechanism is introduced. The calculated shrinkage correction coefficient is used to perform reverse multiplication correction on the out-of-bounds parameter components. This flexible numerical boundary pull-back strategy not only eliminates the risk of comb tooth interference and breakage, but also preserves the excellent gene fragments accumulated after cross-recombination to the greatest extent. This improves the global search efficiency and convergence quality of the optimization algorithm in complex physical constraint space, ensuring that the final optimized output comb blade parameters are absolutely safe and feasible in industrial production.

[0051] S5. Calculate the partial derivatives of the combined stress at the tooth root and the inter-tooth contact area with respect to each parameter dimension of the topologically feasible offspring to determine the parameter sensitivity. Adaptively allocate the mutation probability based on the parameter sensitivity and perform mutation on the topologically feasible offspring to generate a mutant population. Use the fitness function to evaluate and select candidate optimal parameter combinations from the mutant population.

[0052] In S5, the partial derivatives of the tooth root stress and inter-tooth retention contact area with respect to each parameter dimension of the topologically feasible offspring are calculated to determine the parameter sensitivity. This includes: introducing a preset perturbation step size for each parameter dimension of the topologically feasible offspring, generating a one-dimensional perturbation offspring corresponding to each parameter dimension, calculating the tooth root stress and inter-tooth retention contact area for the topologically feasible offspring without perturbation and the one-dimensional perturbation offspring respectively; calculating the difference in tooth root stress between the one-dimensional perturbation offspring and the topologically feasible offspring, and then... Divide the stress difference by the preset perturbation step size to obtain the first partial derivative of the tooth root comprehensive stress with respect to each parameter dimension. Calculate the difference in inter-tooth retention contact area between the single-dimensional perturbation offspring and the topologically feasible offspring. Divide the difference in inter-tooth retention contact area by the preset perturbation step size to obtain the second partial derivative of the inter-tooth retention contact area with respect to each parameter dimension. Assign preset sensitivity weights to the absolute values ​​of the first and second partial derivatives respectively, perform weighted summation, and calculate the parameter sensitivity of each parameter dimension of the topologically feasible offspring.

[0053] In step S5, mutation probabilities are adaptively allocated based on parameter sensitivity, and mutation is performed on topologically feasible offspring to generate a mutant population. A fitness function is used to evaluate and select candidate optimal parameter combinations from the mutant population. This includes: establishing a nonlinear mapping function where mutation probability and parameter sensitivity decrease inversely; inputting the parameter sensitivity of each parameter dimension of the topologically feasible offspring into the nonlinear mapping function to calculate the mutation probability of each parameter dimension; generating corresponding random distribution values ​​for each parameter dimension of the topologically feasible offspring, comparing the random distribution values ​​with the mutation probabilities of each parameter dimension, and superimposing Gaussian perturbation values ​​on parameter dimensions with random distribution values ​​less than the mutation probability to generate mutant individuals; repeatedly performing the perturbation operation according to a preset population size to generate a mutant population; calculating the fitness value corresponding to each mutant individual in the mutant population based on the fitness function; selecting mutant individuals whose fitness values ​​meet preset optimization extreme value conditions from the mutant population; and extracting the parameters contained in the selected mutant individuals as candidate optimal parameter combinations.

[0054] Specifically, after obtaining topologically feasible offspring that ensures no spatial interference in the physical structure through the above steps, if the traditional fixed global mutation probability is used to perform genetic mutation operations, it will be impossible to objectively distinguish the differences in the impact of each parameter dimension of the comb-shaped blade on mechanical and chip removal performance. This can easily lead to the destruction of excellent gene segments that are extremely sensitive to performance in blind random perturbations, while the algorithm will be trapped in local optima due to insufficient exploration of insensitive parameters. In order to solve the technical problem of how to accurately quantify the performance impact weight of each parameter dimension and perform differentiated protection and targeted mutation exploration accordingly, this application determines the parameter sensitivity by calculating the partial derivatives of the tooth root comprehensive stress and the inter-tooth retention contact area with respect to each parameter dimension of the topologically feasible offspring, adaptively allocating the mutation probability according to the parameter sensitivity, performing mutation on the topologically feasible offspring to generate a mutation population, and using the fitness function to evaluate and select candidate optimal parameter combinations from the mutation population.

[0055] In practical implementation, a preset perturbation step size is introduced for each parameter dimension of the topologically feasible offspring, generating a single-dimensional perturbation offspring corresponding to each parameter dimension. Here, the preset perturbation step size refers to a very small parameter increment value pre-set in the numerical difference algorithm, used to simulate the system state response when a certain parameter experiences a small drift. The system locks each specific dimension in the parameter vector of the topologically feasible offspring one by one, increasing the preset perturbation step size only on the current dimension parameter each time, while forcibly keeping other dimension parameters fixed, thereby generating a batch of single-dimensional perturbation offspring with only a single-dimensional difference. Then, based on the pre-constructed physical analysis environment, the numerical values ​​of the combined root stress and inter-tooth contact area corresponding to the topologically feasible offspring without perturbation and the generated single-dimensional perturbed offspring are calculated respectively. Furthermore, since the various parameter dimensions included in the topologically feasible offspring correspond to different physical quantities such as comb tooth spacing, comb tooth height, comb tooth inclination angle, root fillet radius, and blade thickness, and each parameter has different dimensions and numerical magnitudes, to ensure that the partial derivatives obtained from the finite difference calculation have uniform numerical stability, a relative perturbation method is used to determine the corresponding preset perturbation step size for each parameter dimension; let the first... The current parameter value corresponding to each parameter dimension is The corresponding preset perturbation step size is expressed as: ,in, For the first The perturbation step size corresponding to each parameter dimension; The preset relative disturbance ratio coefficient; The current parameter value; This is the minimum absolute disturbance value allowed for the corresponding parameter. When the parameter value is large, a certain proportion of the current parameter value is used as the disturbance step size to ensure that parameters of different orders of magnitude maintain a consistent relative disturbance amplitude. When the parameter value is small, to avoid the finite difference calculation being affected by numerical rounding errors due to an excessively small disturbance step size, the minimum absolute disturbance value allowed for the corresponding parameter is used as the disturbance step size. The minimum absolute disturbance value for different parameter dimensions is determined based on the manufacturing precision of the corresponding parameter. Specifically, the minimum absolute disturbance value corresponding to the comb tooth spacing is taken as the minimum positioning resolution allowed by the processing equipment. The minimum absolute perturbation value corresponding to the comb tooth height is taken as the height machining allowable error; the minimum absolute perturbation value corresponding to the tooth root fillet radius is taken as the minimum fillet machining accuracy; the minimum absolute perturbation value corresponding to the blade thickness is taken as the thickness machining tolerance; the minimum absolute perturbation value corresponding to the comb tooth tilt angle is taken as the angle machining resolution; after determining the perturbation step size, only the current parameter dimension is increased by the corresponding perturbation step size, while the other parameters remain unchanged, generating the corresponding one-dimensional perturbation offspring, and using the finite difference method to calculate the performance change rate corresponding to the parameter dimension to obtain the partial derivative of the corresponding parameter dimension; furthermore, for the th The partial derivatives of the parameters are calculated using forward finite difference: ,in, These represent the performance indicators corresponding to the combined stress at the tooth root or the retained contact area between teeth.

[0056] To accurately capture the direct impact of parameter changes on physical performance, the difference in tooth root stress between the one-dimensional perturbation offspring and the topologically feasible offspring is calculated. This difference is then divided by a preset perturbation step size, and the first partial derivative of the tooth root stress with respect to each parameter dimension is estimated using the numerical difference principle. Similarly, the difference in inter-tooth retention contact area between the one-dimensional perturbation offspring and the topologically feasible offspring is calculated. This difference is then divided by a preset perturbation step size, yielding the second partial derivative of the inter-tooth retention contact area with respect to each parameter dimension. Since the first partial derivative originates from the stress dimension characterizing the mechanical load, the second partial derivative... Originating from the area dimension representing spatial congestion, the two have drastically different dimensions and their values ​​often differ by orders of magnitude. Direct fusion calculation would cause a severe numerical flooding effect. Therefore, the absolute values ​​of the first and second partial derivatives are first extracted, and then mapped to the dimensionless standard interval of 0 to 1 using a minimax normalization algorithm to achieve dimensional unification. Furthermore, to ensure the comparability of the first and second partial derivatives and to eliminate the influence of different physical dimensions on the parameter sensitivity calculation results, this application performs normalization processing on the absolute values ​​of the first and second partial derivatives respectively; let the first... The absolute value of the first partial derivative for each parameter dimension is The absolute value of the second partial derivative is ,in, This indicates the combined stress at the tooth root; Indicates the area of ​​contact retained between teeth; Indicates the first Each parameter; calculate the set of absolute values ​​of the first partial derivative for each parameter dimension of the current topological feasible offspring. and the set of absolute values ​​of the second partial derivatives The maximum and minimum values ​​in the set are taken as the maximum and minimum values, respectively, that is: , , , Then, the calculations were performed using maximum and minimum normalization: as well as When the maximum value in the corresponding set is equal to the minimum value, in order to avoid the denominator being zero, all normalized results in the set are uniformly set to a preset constant of 1, indicating that each parameter dimension has a consistent sensitivity to the corresponding performance index.

[0057] Subsequently, based on the emphasis on tool fracture resistance and chip removal smoothness in engineering applications, a weighted sum of 1 is assigned to the absolute values ​​of the normalized first and second partial derivatives, respectively, for weighted calculation. This yields a comprehensive and dimensionless evaluation index for each parameter dimension of the topologically feasible offspring, namely, parameter sensitivity. Furthermore, to comprehensively reflect the influence of each parameter dimension on tool fracture resistance and chip removal performance, this application determines the sensitivity weights based on the contribution ratio of the two performance indicators to the comprehensive optimization objective function; let the weight corresponding to the first partial derivative be... The second partial derivative corresponds to the weight. satisfy Among them, two weights are determined synchronously based on the performance weights used for the corresponding performance indicators in the fitness function, that is: , ,in, The performance weights corresponding to the combined stress at the tooth root in the fitness function; The performance weights corresponding to the inter-tooth contact area in the fitness function are defined as follows: Since the two performance weights are pre-set based on specific tool design goals, the sensitivity weights automatically inherit the same engineering focus, ensuring consistency between parameter sensitivity evaluation and overall fitness evaluation, and avoiding deviations in parameter optimization direction caused by inconsistent evaluation standards. Finally, the... The parameter sensitivity for each parameter dimension is calculated as follows: The obtained parameter sensitivity is used for subsequent nonlinear mutation probability calculation.

[0058] After obtaining the influence weights of each dimension, a nonlinear mapping function is established in which the mutation probability and parameter sensitivity have an inverse decreasing relationship. Specifically, this nonlinear mapping function can be a negative exponential decay function with the natural constant as its base. The logic is as follows: when the sensitivity of a parameter dimension is extremely high, it must be assigned an extremely low mutation probability to protect the already established excellent cutting features from damage; conversely, when the sensitivity of a parameter dimension is low, it indicates that there is still a huge performance exploration space in that dimension, so it is assigned a higher mutation probability to stimulate evolutionary vitality. The parameter sensitivity of each parameter dimension of the topologically feasible offspring is input into this nonlinear mapping function to calculate the mutation probability specific to each parameter dimension of the topologically feasible offspring. Furthermore, to achieve a nonlinear inverse mapping between parameter sensitivity and mutation probability, so that parameter dimensions with higher parameter sensitivity have lower mutation probabilities, and parameter dimensions with lower parameter sensitivity have higher mutation probabilities, this application uses an exponential decay mapping function to calculate the mutation probability corresponding to each parameter dimension; let the th parameter dimension be... The parameter sensitivity corresponding to each parameter dimension is: ,in Then the mutation probability of the corresponding parameter dimension is calculated as follows: ,in: For the first The mutation probability corresponding to each parameter dimension; The maximum mutation probability is preset. Preset minimum mutation probability; This is a non-linear adjustment coefficient used to control the decay rate of the mutation probability as the parameter sensitivity increases; to ensure that the obtained mutation probability always remains within the allowable range, it is preset. Therefore, for any parameter dimension, it satisfies As parameter sensitivity gradually increases, the exponential decay term... As the parameter sensitivity decreases, the corresponding mutation probability gradually decreases. As the parameter sensitivity decreases, the exponential decay term gradually increases, and the corresponding mutation probability gradually approaches the preset maximum mutation probability, thus increasing the search capability for low-sensitivity parameter dimensions. To further adapt to different optimization stages, the preset maximum mutation probability, preset minimum mutation probability, and nonlinear adjustment coefficient remain unchanged during each genetic iteration. Only the parameter sensitivity corresponding to each parameter dimension is recalculated based on the current topologically feasible offspring, and the mutation probability corresponding to each parameter dimension is updated in real time according to the above mapping relationship, so that the mutation probability can automatically adjust with changes in parameter sensitivity. Subsequently, for the... Generates random numbers with one parameter dimension that follow a uniform distribution within the interval [0, 1]. ,when If the parameter dimension changes, a Gaussian perturbation is applied; otherwise, the parameter dimension remains unchanged, thus determining whether the parameter dimension has changed.

[0059] The mutation executor is then activated, generating a random distribution value between 0 and 1 for each parameter dimension of the topologically feasible offspring. This random distribution value is compared with the mutation probability of each parameter dimension. For parameter dimensions where the random distribution value is less than the mutation probability, a mutation operation is performed. Specifically, a Gaussian perturbation value is randomly generated using the current parameter value as the baseline mean and superimposed on the original parameter value to generate a mutated individual. For dimensions where the random distribution value is greater than or equal to the mutation probability, the original value remains unchanged. This perturbation operation is repeated continuously according to a preset population size, thereby generating a mutated population consisting of a large number of individuals that have undergone local mutations.

[0060] After the population evolution is completed, the fitness values ​​of each mutant individual in the mutant population are calculated based on the fitness function constructed above, and these values ​​are globally ranked and evaluated. The mutant individuals whose fitness values ​​meet the preset optimization extreme value conditions, that is, the highest fitness score and the algorithm converges after reaching the preset maximum number of iterations, are selected from the mutant population. Finally, the various size parameters contained in the selected optimal mutant individuals are completely extracted and output as the final candidate optimal parameter combination of the comb blade.

[0061] The above content proposes a nonlinear mutation mechanism based on multi-physics partial derivative sensitivity analysis, solving the technical bottleneck of blind mutation leading to the destruction of excellent characteristics and easy getting trapped in local optima in multi-dimensional parameter optimization. By introducing a preset perturbation step size and the differential calculation principle to solve the partial derivatives of stress and contact area, the local sensitivity of each parameter dimension of the comb-shaped blade to mechanical stability and chip removal smoothness is objectively and accurately quantified. In the sensitivity fusion calculation, an absolute value extraction and normalization mechanism is adopted to eliminate the calculation interference caused by different physical dimensions and their huge numerical differences, ensuring the rigorous weighted consistency of multi-objective influence factors at the mathematical level. Furthermore, it utilizes... By using a nonlinear mapping function with reverse decreasing values ​​to independently configure the mutation probability of each parameter, a highly sensitive and heavily protected, and a low-sensitivity and heavily exploratory intelligent evolutionary barrier is constructed. This parameter-level adaptive mutation strategy, combined with Gaussian perturbation, stabilizes the excellent mechanical genes of the genetic cutting tool while maximizing the release of the exploration space of insensitive parameters. This significantly improves the algorithm's global optimization capability in the solution space of complex nonlinear parameters. Finally, by using the extreme value screening of the fitness function, it is ensured that the extracted candidate optimal parameter combination achieves the best dynamic balance between structural resistance and chip removal efficiency in physical reality, thereby improving the reliability and automation level of industrial cutting tool parameter optimization.

[0062] S6. Perform preset forming rule verification on the candidate optimal parameter combination, and generate the manufacturing model of the comb blade based on the verification results.

[0063] S6 includes: parsing multi-dimensional geometric parameters from the candidate optimal parameter combination, including the root fillet radius and the minimum inter-tooth clearance; comparing the root fillet radius with the preset minimum machining fillet radius and the minimum inter-tooth clearance with the preset machining tool limit dimension to obtain a verification result characterizing the machining feasibility; if the verification result meets the machining requirements, constructing the three-dimensional geometric profile of the comb-shaped insert based on the parameters included in the candidate optimal parameter combination; assigning preset machining tolerances and material property information to the three-dimensional geometric profile to derive the manufacturing model of the corresponding comb-shaped insert.

[0064] Specifically, after selecting candidate optimal parameter combinations with the best theoretical mechanical state and chip removal performance from the mutant population through the above steps using the fitness function, since the parameter combinations are generated entirely by pure mathematical evolution algorithms in the continuous solution space, they often do not fully consider the physical size and rigidity limitations of CNC machine tools and cutting tools in actual production workshops. This can easily lead to the optimization results with excellent theoretical performance being impossible to process in reality, resulting in a technical problem of disconnect between theory and actual manufacturing process. In order to break down the final barrier from algorithmic mathematical optimization to physical entity processing, this application performs a preset forming rule verification on the candidate optimal parameter combinations and generates a manufacturing model of comb-shaped blades based on the verification results.

[0065] In practice, the multidimensional geometric parameters are first analyzed from the selected candidate optimal parameter combinations. Since the parameter vector directly records the independent underlying design variables, the direct vector components such as the root fillet radius, the center distance of the comb teeth, and the maximum width of the comb teeth are extracted. Then, the minimum inter-tooth clearance is calculated by subtracting the maximum width of the comb teeth from the extracted center distance value. Here, the root fillet radius represents the arc surface size of the transition area at the bottom of the adjacent comb teeth of the blade, and the minimum inter-tooth clearance represents the width value of the narrowest point of the spatial distance between two adjacent comb teeth. Subsequently, the pre-entered underlying machine tool processing constraint data is retrieved, namely the preset minimum machining fillet radius and the preset machining tool limit size. The preset minimum machining fillet radius refers to the minimum concave angle size that the grinding wheel or milling cutter used to process the comb-shaped blade can cut under its own geometric and physical constraints. The preset machining tool limit size refers to the minimum spatial channel width that allows the cutting tool to smoothly enter and safely exit.

[0066] Next, the underlying threshold verification logic is executed to obtain verification results characterizing the processing feasibility. The parsed root fillet radius is compared with the preset minimum processing fillet radius, and the parsed minimum inter-tooth clearance is compared with the preset machining tool limit size. If the comparison results show that the parsed root fillet radius is greater than or equal to the preset minimum processing fillet radius, and the parsed minimum inter-tooth clearance is greater than or equal to the preset machining tool limit size, then a verification result that meets the processing requirements is generated. If any of the above dimensions is less than the corresponding preset process limit value, then it is determined that the processing requirements are not met and the parameter combination is discarded. When the verification result meets the processing requirements, based on the parameters such as tooth height, tooth pitch, and root fillet radius included in the candidate optimal parameter combination, the underlying parametric 3D modeling engine is called. Through actions such as stretching, sweeping, and Boolean operations in computer graphics, a closed and accurate 3D geometric contour of the comb-shaped cutting tool is constructed.

[0067] After generating the three-dimensional geometric contour, preset machining tolerances and material property information are assigned to the three-dimensional geometric contour, and the manufacturing model of the corresponding comb-shaped insert is exported. The preset machining tolerances are used to define the legally permissible range of dimensional fluctuations to guide subsequent CNC machining and quality inspection. The material property information includes engineering data such as the density and elastic modulus of the insert matrix material, such as cemented carbide. It should be clarified that the manufacturing model mentioned in this application is an industrial three-dimensional digital entity model for computer-aided manufacturing, rather than a machine learning model that relies on massive historical data for network weight iteration. Therefore, the manufacturing model does not have a neural network structure, nor does it have training data or a model training process. The input data of the manufacturing model is the aforementioned constructed three-dimensional geometric contour, preset machining tolerances, and material property information. Through a specific industrial data exchange protocol, the above input data is structured, encoded, and semantically encapsulated to obtain the output data of the manufacturing model, which is a CAD / CAM standard format file containing complete geometric and manufacturing attributes. This output data can be directly read by downstream CNC machine tool systems and used to generate machining toolpath codes.

[0068] The above content proposes a physical dimension hard verification and automated modeling mechanism oriented towards the actual workshop process boundary, solving the technical problem that theoretical optimization parameters cannot be implemented in manufacturing due to deviation from the machining limits of machine tools. By comparing the analyzed tooth root fillet radius with the minimum machining fillet radius, and by strictly comparing the minimum tooth clearance with the limit size of the machining tool, an insurmountable manufacturing red line verification mechanism is established. This bottom-line verification eliminates the invalid design that is theoretically perfect but cannot be machined in reality during the mathematical optimization process, avoiding high downstream trial and error and scrap costs from the source. At the same time, after the verification is passed, the three-dimensional geometric contour is directly constructed using parameter combination, and machining tolerances and material properties are automatically integrated to derive a structured manufacturing model that can be directly identified by the production end. This series of coherent data comparison and encapsulation operations breaks down the digital barrier from the intelligent algorithm black box to the CNC machining in the workshop, realizing the seamless connection of the entire chain from performance adaptive optimization, automatic manufacturability verification to engineering model output for comb-shaped inserts, greatly shortening the R&D cycle of high-end special-shaped tools and improving the implementation efficiency and automation level of industrial production.

[0069] Through the coordination of steps S1 to S6 above, this application improves the convergence accuracy of the optimization algorithm in the nonlinear solution space and the success rate of the actual blade manufacturing.

[0070] Example 2: The above describes an adaptive optimization method for comb-shaped blade parameters in embodiments of this application. The following describes an adaptive optimization system for comb-shaped blade parameters in embodiments of this application, such as... Figure 3 As shown, an adaptive optimization system for comb-shaped blade parameters in an embodiment of this application includes: The baseline population module is used to obtain baseline constraint data of the comb blade, construct an initial tooth row parameter vector population representing the comb blade, divide the comb tooth surface for each individual in the initial tooth row parameter vector population, extract the spatial occlusion and shared contact data between adjacent comb teeth, and generate the inter-tooth contact topology tensor corresponding to each individual.

[0071] The shear simulation module is used to perform shear simulation on each individual in the initial tooth row parameter vector population to obtain the shear resistance, root stress and inter-tooth contact area of ​​each comb tooth.

[0072] The equilibrium evaluation module is used to extract the load transfer coefficient matrix from the inter-tooth contact topology tensor of each individual, calculate the coupling fitness of each comb tooth by combining the shear resistance, root stress and inter-tooth retention contact area of ​​each comb tooth, use the distribution variance of the coupling fitness of all comb teeth as the inter-tooth load equilibrium penalty term, construct the fitness function and evaluate each individual in the initial tooth row parameter vector population.

[0073] The geometric crossover module is used to select two parent individuals from the initial tooth row parameter vector population based on the evaluation results, and perform genetic crossover on the two parent individuals according to the preset geometric ratio constraints to obtain topologically feasible offspring.

[0074] The sensitive mutation module is used to calculate the partial derivatives of the combined stress at the tooth root and the inter-tooth contact area with respect to each parameter dimension of the topologically feasible offspring to determine the parameter sensitivity. Based on the parameter sensitivity, the mutation probability is adaptively allocated and mutation is performed on the topologically feasible offspring to generate a mutation population. The fitness function is used to evaluate and select candidate optimal parameter combinations from the mutation population.

[0075] The forming verification module is used to perform preset forming rule verification on the candidate optimal parameter combination and generate a manufacturing model of the comb blade based on the verification results.

[0076] Through the synergistic cooperation of the above components, this application further improves the convergence accuracy of the optimization algorithm in the nonlinear solution space and the success rate of the actual implementation of the blade manufacturing entity.

[0077] In summary, this application discloses an adaptive optimization method and system for comb-shaped cutting tool parameters. By deeply integrating multidimensional spatial topology analysis, nonlinear dynamic simulation, and adaptive genetic algorithm, this application not only constructs the inter-tooth contact topology tensor and load transfer coefficient matrix, accurately reproducing the local stress contagion and chip congestion effects of complex multi-tooth cutting tools under real cutting conditions, but also, in the core evolutionary optimization stage, employs a forced cross-correction mechanism based on the physical geometric proportion allowable range and a sensitivity nonlinear adaptive mutation strategy based on the calculation of physical field differential partial derivatives. This effectively avoids the destruction of excellent genes and the generation of useless solutions caused by blind mutation from the algorithm's underlying layer. Finally, by introducing machine tool-level physical constraint verification, a three-dimensional digital manufacturing entity model that meets industrial precision standards is directly output. This application establishes a complete data link from digital twin state assessment and intelligent evolutionary qualitative optimization to mistake-proof implementation in the physical workshop, significantly improving the computational efficiency, mechanical structural safety, and one-time success rate of physical machining and manufacturing in the development of high-end special-shaped cutting tools, and possesses extremely high industrial application value.

[0078] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the system and unit described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0079] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0080] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for adaptive optimization of comb-shaped blade parameters, characterized in that, The method includes: S1. Obtain the baseline constraint data of the comb blade, construct the initial tooth row parameter vector population representing the comb blade, divide the comb tooth surface for each individual in the initial tooth row parameter vector population, extract the spatial occlusion and shared contact data between adjacent comb teeth, and generate the tooth contact topology tensor corresponding to each individual. S2. Perform shear simulation on each individual in the initial tooth row parameter vector population to obtain the shear resistance, root stress and inter-tooth contact area of ​​each comb tooth. S3. Extract the load transfer coefficient matrix from the inter-tooth contact topology tensor of each individual, calculate the coupling fitness of each comb tooth by combining the shear resistance, root stress and inter-tooth retention contact area of ​​each comb tooth, use the distribution variance of the coupling fitness of all comb teeth as the inter-tooth load balance penalty term, construct the fitness function and evaluate each individual in the initial tooth row parameter vector population. S4. Based on the evaluation results, select two parent individuals from the initial tooth row parameter vector population, and perform genetic crossover on the two parent individuals according to the preset geometric ratio constraint to obtain topologically feasible offspring. S5. Calculate the partial derivatives of the combined stress at the tooth root and the inter-tooth contact area with respect to each parameter dimension of the topologically feasible offspring to determine the parameter sensitivity. Adaptively allocate the mutation probability based on the parameter sensitivity and perform mutation on the topologically feasible offspring to generate a mutant population. Use the fitness function to evaluate and select candidate optimal parameter combinations from the mutant population. S6. Perform preset forming rule verification on the candidate optimal parameter combination, and generate the manufacturing model of the comb blade based on the verification results.

2. The adaptive optimization method for comb-shaped blade parameters according to claim 1, characterized in that, S1 constructs a population of initial tooth row parameter vectors representing the comb-shaped blades, including: Extract the external profile dimensions and material manufacturing constraints from the baseline constraint data; The initial values ​​for comb tooth spacing, comb tooth height, comb tooth inclination angle, tooth root fillet radius, and blade thickness are determined based on the external outline dimensions and material manufacturing constraints. The initial values ​​are arranged in a preset dimension order to generate a reference tooth row parameter vector, and random perturbation is introduced into the reference tooth row parameter vector according to a preset scale to generate an initial tooth row parameter vector population.

3. The adaptive optimization method for comb-shaped blade parameters according to claim 1, characterized in that, S1 extracts spatial occlusion and shared contact data between adjacent comb teeth, generating the inter-tooth contact topology tensor for each individual, including: Based on the parameters contained in each individual, the corresponding three-dimensional surface of the comb tooth is constructed, and the three-dimensional surface of each comb tooth is divided into contact area, sliding area and bearing area according to the preset shear limit; Projecting adjacent comb teeth along the shear direction, the overlapping area of ​​the projection surface is extracted as shared contact data, and the included angle of non-overlapping edges is extracted as spatial occlusion data. The shared contact data and spatial occlusion data are assembled into a multidimensional array according to the physical arrangement of the comb teeth to generate the inter-tooth contact topology tensor.

4. The adaptive optimization method for comb-shaped blade parameters according to claim 1, characterized in that, S2 include: The shearing material model is introduced into a simulation environment containing the comb blades corresponding to each individual, and the relative kinematic parameters and contact boundary conditions between the shearing material model and the comb blades are set. The finite element solver is called to perform dynamic calculations, generating dynamic response data of each individual in the shear process. The reaction force of each comb tooth contact interface is extracted from the dynamic response data as shear resistance, and the equivalent stress peak value of each comb tooth root mesh node is extracted as tooth root comprehensive stress. Based on dynamic response data, the retained material distributed in the gaps between adjacent comb teeth is identified, and the grid surface area where the retained material adheres to the sidewall of the tooth is calculated as the retention contact area between the teeth.

5. The adaptive optimization method for comb-shaped blade parameters according to claim 1, characterized in that, S3 includes: Based on the shared contact data and spatial occlusion data contained in the inter-tooth contact topology tensor, the mechanical transmission ratio between adjacent comb teeth is calculated, and a load transfer coefficient matrix is ​​constructed according to the comb tooth arrangement dimension. Preset performance weighting coefficients are assigned to shear resistance, tooth root stress and inter-tooth residual contact area respectively for normalized weighted calculation, and load transfer coefficient matrix is ​​introduced to correct the state coupling of adjacent comb teeth to obtain the coupling fitness of each comb tooth. Calculate the numerical distribution variance of the coupling fitness of all comb teeth, define the numerical distribution variance as the inter-tooth load balancing penalty term, calculate the total average value of the coupling fitness of all comb teeth, subtract the inter-tooth load balancing penalty term scaled by a preset ratio from the total average value, and construct the fitness function.

6. The adaptive optimization method for comb-shaped blade parameters according to claim 1, characterized in that, S4 includes: Based on the evaluation results of the fitness function, a preset selection strategy is used to select two parent individuals from the initial tooth row parameter vector population. The tooth pitch component and tooth profile component contained in the two parent individuals are exchanged and recombined to generate the initial offspring individuals. The ratio of the adjacent comb tooth spacing to the comb tooth height corresponding to the initial offspring individual is calculated as the geometric ratio. It is then determined whether the geometric ratio falls within the permissible range defined by the preset geometric ratio constraint. For the initial offspring individuals that do not fall within the permissible range, an adaptive shrinkage adjustment is performed on the numerical boundary to eliminate physical interference defects between comb teeth, thereby generating topologically feasible offspring.

7. The adaptive optimization method for comb-shaped blade parameters according to claim 1, characterized in that, In S5, the partial derivatives of the combined stress at the tooth root and the inter-tooth retained contact area with respect to each parameter dimension of the topologically feasible offspring are calculated to determine the parameter sensitivity, including: For each parameter dimension of the topologically feasible offspring, a preset perturbation step size is introduced to generate a one-dimensional perturbation offspring corresponding to each parameter dimension. The root stress and inter-tooth contact area corresponding to the topologically feasible offspring without perturbation and the one-dimensional perturbation offspring are calculated respectively. Calculate the difference in tooth root stress between the one-dimensional perturbation offspring and the topologically feasible offspring. Divide the difference in tooth root stress by the preset perturbation step size to obtain the first partial derivative of the tooth root stress with respect to each parameter dimension. Calculate the difference in inter-tooth retention contact area between the one-dimensional perturbation offspring and the topologically feasible offspring. Divide the difference in inter-tooth retention contact area by the preset perturbation step size to obtain the second partial derivative of the inter-tooth retention contact area with respect to each parameter dimension. By assigning preset sensitivity weights to the absolute values ​​of the first and second partial derivatives respectively, and performing weighted summation, the parameter sensitivity of each parameter dimension of the topologically feasible offspring is calculated.

8. The adaptive optimization method for comb-shaped blade parameters according to claim 7, characterized in that, In S5, mutation probabilities are adaptively allocated based on parameter sensitivity, and mutation is performed on topologically feasible offspring to generate a mutant population. A fitness function is then used to evaluate and select candidate optimal parameter combinations from the mutant population, including: A nonlinear mapping function is established in which the mutation probability and parameter sensitivity decrease inversely. The parameter sensitivity of each parameter dimension of the topologically feasible offspring is input into the nonlinear mapping function to calculate the mutation probability of each parameter dimension of the topologically feasible offspring. For each parameter dimension of the topologically feasible offspring, a corresponding random distribution value is generated, and the random distribution value is compared with the mutation probability of each parameter dimension. For parameter dimensions where the random distribution value is less than the mutation probability, a Gaussian perturbation value is superimposed to generate mutated individuals. The perturbation operation is repeated according to the preset population size to combine and generate mutated populations. The fitness value of each mutant individual in the mutant population is calculated based on the fitness function. Mutants whose fitness values ​​meet the preset optimization extreme value conditions are selected from the mutant population, and the parameters contained in the selected mutant individuals are extracted as candidate optimal parameter combinations.

9. The adaptive optimization method for comb-shaped blade parameters according to claim 1, characterized in that, S6 include: Multidimensional geometric parameters are extracted from the candidate optimal parameter combinations. These multidimensional geometric parameters include the root fillet radius and the minimum inter-tooth clearance. The root fillet radius is numerically compared with the preset minimum machining fillet radius, and the minimum tooth clearance is numerically compared with the preset machining tool limit size to obtain the verification result characterizing the machining feasibility. If the verification result meets the machining requirements, the three-dimensional geometric profile of the comb-shaped blade is constructed based on the parameters included in the candidate optimal parameter combination. Assign preset machining tolerances and material property information to the three-dimensional geometric contour, and export the manufacturing model of the corresponding comb-shaped blade.

10. A comb-shaped blade parameter adaptive optimization system, used to implement the comb-shaped blade parameter adaptive optimization method as described in any one of claims 1-9, characterized in that, The system includes: The baseline population module is used to obtain baseline constraint data of the comb blade, construct an initial tooth row parameter vector population that characterizes the comb blade, divide the comb tooth surface for each individual in the initial tooth row parameter vector population, extract the spatial occlusion and shared contact data between adjacent comb teeth, and generate the tooth contact topology tensor corresponding to each individual. The shear simulation module is used to perform shear simulation on each individual in the initial tooth row parameter vector population to obtain the shear resistance, root stress and inter-tooth contact area of ​​each comb tooth. The equilibrium evaluation module is used to extract the load transfer coefficient matrix from the inter-tooth contact topology tensor of each individual, calculate the coupling fitness of each comb tooth by combining the shear resistance, root stress and inter-tooth retention contact area of ​​each comb tooth, use the distribution variance of the coupling fitness of all comb teeth as the inter-tooth load equilibrium penalty term, construct the fitness function and evaluate each individual in the initial tooth row parameter vector population. The geometric crossover module is used to select two parent individuals from the initial tooth row parameter vector population based on the evaluation results, and perform genetic crossover on the two parent individuals according to the preset geometric ratio constraints to obtain topologically feasible offspring. The sensitive mutation module is used to calculate the partial derivatives of the tooth root integrated stress and the inter-tooth retained contact area with respect to each parameter dimension of the topologically feasible offspring to determine the parameter sensitivity. Based on the parameter sensitivity, the mutation probability is adaptively allocated and mutation is performed on the topologically feasible offspring to generate a mutation population. The fitness function is used to evaluate and select candidate optimal parameter combinations from the mutation population. The forming verification module is used to perform preset forming rule verification on the candidate optimal parameter combination and generate a manufacturing model of the comb blade based on the verification results.

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