Method for analyzing synchronous performance of mold clamping force and tapping

Abstract

The invention provides a mold clamping force and tapping synchronization performance analysis method which comprises the following steps: acquiring tool path data, and simulating a torque transmission process by combining a boundary condition of a narrow area in a mold to obtain torque distribution; tool root position coordinates are determined according to the torque distribution data, material attribute parameters are overlaid on the tool root position coordinates, and torque is optimized through a genetic algorithm; the optimized torque is input into the finite element grid model, stress concentration factor distribution is calculated from the finite element grid model, and the grid density is adjusted to obtain a refined stress diagram; acquiring peak stress data from the refining stress diagram, counting the number of stress cycles to determine a fatigue damage value, generating an adaptive control signal, and inputting the adaptive control signal into the simulated tapping cycle to obtain a tool running state; according to the tool operation state, three-dimensional space displacement data generated by the root of the lead screw under the torque effect are extracted and reflected by monitoring the axial and radial displacement data of the lead screw, and a stable torque path is confirmed.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of information technology, and in particular to a method for analyzing the synchronization performance of clamping force and tapping. BACKGROUND

[0002] In the field of mechanical processing and mold manufacturing, tapping technology as a key process to realize thread forming is self-evident. Especially in high-precision mold production, the quality of tapping is directly related to the connection reliability and service life of the product, and is the core link to ensure the quality of industrial manufacturing. However, as the mold design becomes more complex, the tapping process needs to be completed in an extremely small closed space, which poses higher challenges to technology and exposes the shortcomings of existing methods. At present, many solutions often have difficulty in balancing the relationship between processing quality and equipment durability when facing complex environments. Especially in the case of space limitation, the traditional tapping method lacks dynamic adaptability to the stress state of the tool, which is prone to irreversible damage to the tool under high load. This limitation is not simply a technical shortcoming, but because of the lack of in-depth attention to the stress changes and transmission mechanisms of the tool in extreme environments, the problem has not been effectively solved for a long time. Focusing on the specific technical difficulties, the torque transmission in the closed space becomes the primary bottleneck. Tapping requires sufficient torque to cut the material to form threads, but the narrow environment limits the selection of tool diameter and length, and a slender tap is usually used to enter deep holes or blind holes. This slender structure lacks rigidity when transmitting torque and is prone to bending deformation. All forces eventually converge at the connection point between the tool and the clamping end, i.e., the root area, which becomes the most stress-concentrated location, bearing complex torsional stress and bending stress, with local pressure rising sharply, which is prone to material fatigue, micro-crack propagation, and even sudden rupture. For example, when machining small blind hole threads in precision injection molds or die casting molds, in order to achieve the required thread depth and strength, it is often necessary to gradually increase the torque to overcome material resistance. However, the greater the tool insertion depth, the more obvious the leverage effect on the root, and the amplified torque leads to frequent root distortion. At the same time, the closed space also exacerbates the difficulty of chip removal and the poor flow of cooling liquid, further increasing tool load and accelerating fatigue damage. This not only affects the efficiency of single processing, but also shortens the tool life, increases mold repair costs and production interruption risks. Therefore, how to ensure sufficient torque in the closed space to improve thread forming quality while avoiding damage to the tool root due to stress concentration has become a key problem that needs to be overcome. SUMMARY

[0003] The present application provides a method for analyzing the synchronization performance of clamping force and tapping, mainly comprising: The tool path data is acquired, the torque distribution is obtained by simulating the torque transmission process in combination with the boundary conditions of the narrow area inside the mold, the tool root position coordinates are determined according to the torque distribution data, the material attribute parameters are superimposed on the tool root position coordinates, the torque is optimized through a genetic algorithm, the optimized torque is input into a finite element grid model, the stress concentration factor distribution is calculated from the finite element grid model, the grid density is adjusted to obtain a refined stress map, the peak stress data are acquired from the refined stress map, the fatigue damage value is determined by counting the stress cycle number, the adaptive control signal is generated and input into the simulated tapping cycle to obtain the tool running state, the three-dimensional space displacement data of the screw rod root generated under the action of the torque are extracted by monitoring the axial and radial displacement data of the screw rod according to the tool running state, the stable torque path is confirmed, the thread forming parameters are acquired from the stable torque path, the tapping quality index is determined, the clamping force is extracted by synchronously monitoring the pressure change in the clamping process, and the clamping force and tapping synchronization performance data are obtained based on the clamping force change and the tapping torque output. Further, the tool path data is acquired, the torque distribution is obtained by simulating the torque transmission process in combination with the boundary conditions of the narrow area inside the mold, including: The inner wall contour coordinate set of the closed space geometric model is acquired, the mold cavity topology network is constructed through the distance relationship of adjacent points in the coordinate set, the passable path set between the inlet position and the target thread hole position is extracted from the topology network, and the tool path data is determined according to the product of the path length and the curvature radius; the feeding depth value of the tool at each node is read according to the space coordinates of each node in the tool path data, the corresponding basic cutting resistance value is obtained by querying the material hardness table, and the initial torque value of each node is obtained by multiplying the basic cutting resistance value by the tool diameter; the initial torque value is used as a boundary condition to input the transmission path simulation, the vertical distance from each position point to the nearest wall surface is extracted from the mold cavity inner wall distance data, the corrected torque value is calculated according to the exponential relationship between the vertical distance and the torque attenuation, and the continuous torque distribution is obtained by numerical filling between all nodes of the tool path data through a bilinear interpolation method.

[0004] Further, the tool root position coordinates are determined according to the torque distribution data, the material attribute parameters are superimposed on the tool root position coordinates, and the torque is optimized through a genetic algorithm, including: extracting a region with a value exceeding a preset threshold from the torque distribution data, reversely tracking along a torque transmission main shaft direction to a tool and clamp device connection to obtain a tool root position coordinate, reading a pre-stored material yield strength at the tool root position coordinate, calculating a safety margin coefficient according to a ratio of the material yield strength and a current torque load, setting an upper limit of an optimization constraint by using the safety margin coefficient, constructing a three-dimensional parameter space including a torque amplitude, a main shaft rotating speed and a feed rate, randomly generating an initial population in the parameter space, selecting individuals with a high ranking in adaptability as parents by using a cumulative probability distribution function, and generating a child population by performing a single-point crossover operation on the parents.

[0005] Further, after simulating the torque transmission process to obtain the torque distribution in combination with a boundary condition of a narrow region inside a mold, the method further includes: determining a tool root position coordinate according to the torque distribution data, establishing a local cylindrical coordinate system at the tool root position coordinate, obtaining a complete description of a three-dimensional stress state of the root, performing root mechanical response analysis by superimposing material attribute parameters on the tool root position coordinate, identifying a critical stress value at which the material enters a plastic deformation stage as an optimization boundary condition, and optimizing the torque in combination with a geometric constraint condition of a closed space. Further, the method includes: establishing a local cylindrical coordinate system at the tool root position coordinate, decomposing the torque distribution data into a radial stress component, a tangential stress component and an axial stress component, and obtaining a three-dimensional stress state of the root by stress tensor transformation; identifying a critical stress value at which the material enters a plastic deformation stage as an optimization boundary condition, and optimizing the torque in combination with a geometric constraint condition of a closed space.

[0006] Further, the method includes inputting the optimized torque into a finite element grid model, calculating a stress concentration factor distribution from the finite element grid model, and adjusting a grid density to obtain a refined stress map. The optimized torque is used as the load input to establish a finite element grid, the geometric body at the root of the screw is discretized by tetrahedral elements, constraint conditions and torque loads are applied to the element nodes, the stiffness matrix is assembled to solve the node displacement, the stress components inside each element are calculated according to the displacement-strain relationship and the constitutive equation; the equivalent stress value of each element is extracted from the stress components, the high gradient region with a stress gradient change rate exceeding a preset threshold is identified, the ratio of the local peak stress in the region to the average stress of the same section is calculated as a stress concentration factor, and the continuous distribution of the stress concentration factor in the entire root space is obtained by cubic spline interpolation; according to the distribution of the stress concentration factor, a singular region with a numerical value greater than a preset critical value is identified, the grid size in the singular region is locally encrypted by halving, and the stress difference between adjacent nodes before and after encryption is calculated until the difference is less than the allowable error; the encrypted grid is used to perform finite element solving again, and the stress numerical matrix and gradient vector field are extracted from the solving results, the region position where the stress concentration factor exceeds the safety threshold is identified by color mapping, and the refined stress diagram containing the stress distribution cloud diagram and the concentration factor contour line is output.

[0007] Further, the peak stress data is obtained from the refined stress diagram, the stress cycle number is counted to determine the fatigue damage value, the adaptive control signal is generated and input into the simulated tapping cycle to obtain the tool running state, including: The region coordinates where the stress value exceeds the material fatigue limit are extracted from the refined stress diagram, the peak stress data and its spatial distribution in the region are read, the cycle number under different stress amplitudes is counted by the rain flow counting method, and the damage component value under each stress level is calculated according to the corresponding relationship between the cycle number and the material stress and life curve; the total fatigue damage value is obtained by superimposing the damage component values using the Miner linear cumulative damage criterion, the feed rate and spindle speed parameters are adjusted according to the total fatigue damage value, and the adaptive control signal containing the adjusted speed, feed rate and cutting depth is output; the input parameters of the tapping process simulation are set according to the adaptive control signal, the simulated tapping cycle calculation is performed, the position coordinates, stress state and vibration amplitude of the tool at each time node are recorded, and the tool running state data containing the wear grade and remaining life prediction value are output.

[0008] Further, according to the tool running state, the three-dimensional space displacement data reflecting the displacement of the screw root under the action of torque is extracted by monitoring the axial and radial displacement data of the screw, and the stable torque path is confirmed, including: According to the tool running state data, the axial displacement sequence and the radial deflection amplitude of the screw at each time point are read, the axial displacement, the radial deflection and the rotation angle of the screw are combined in coordinates, and the displacement vector of each node at the root of the screw in the three-dimensional space is obtained; the stress intensity at each node is calculated by using the displacement vector, the stress gradient between adjacent nodes is solved by using the finite difference method, and the stress flow lines are connected along the maximum gradient direction to form; the candidate paths with the transmission capacity value higher than the preset threshold value are screened from the stress flow lines, and the flow line with the minimum cumulative energy loss and the shortest path length is selected as the stable torque path.

[0009] Further, after obtaining the tool running state, the axial displacement time history data and the radial deflection amplitude sequence of the screw are read according to the tool running state, the two groups of signals are aligned by time stamp and combined in the cylindrical coordinate system, the three-dimensional displacement vector field of the nodes at the root of the screw under the action of torque is obtained, the displacement gradient tensor of each node is calculated from the displacement vector field by difference operation; the stress tensor is calculated according to the material constitutive relation through the displacement gradient tensor, the deformation energy density value of each microelement is obtained, and the main path of energy dissipation is formed by connecting from the high energy density area at the root of the screw to the low energy density area at the end of the tool along the direction in which the deformation energy density gradient decreases fastest; the region with gentle stiffness change is identified as the stable transmission area according to the material stiffness value of each point on the main path, the path segment with the deformation energy density lower than the preset safety threshold value is screened in the stable transmission area, and the candidate path set is obtained by accumulating the energy loss values of each microelement on the path; the ratio of input energy to output energy of each path is calculated as the transmission efficiency from the candidate path set, and the trajectory with the highest transmission efficiency and the shortest total path length is determined as the stable torque path.

[0010] Further, the thread forming parameters are obtained from the stable torque path, the tapping quality index is determined, the pressure change in the mold closing process is monitored synchronously to extract the mold closing force, and the mold closing force and tapping synchronization performance data are obtained based on the mold closing force change and the tapping torque output, including: The torque values and the rotation speed parameters of each node on the path are extracted from the stable torque path, the feed speed is calculated according to the product of the cutting speed and the pitch, the thread forming parameters are obtained by the ratio of the standard pitch value to the actual cutting depth, and the maximum depth and the thread profile integrity rate are determined as the tapping quality index by combining the geometric boundaries of the closed space; the sampling frequency of the pressure sensor is set by using the tapping quality index, the initial pressure value is recorded when the mold closing action starts, the pressure time history curve is obtained by continuous sampling, and the pressure change rate is obtained by calculating the ratio of the pressure difference value of adjacent sampling points to the time interval; the time difference is calculated according to the time when the pressure peak value appears and the time when the tapping torque peak value appears, the synchronization degree is evaluated by calculating the normalized product integral value of the mold closing force curve and the tapping torque curve, and the synchronization performance data including the phase deviation and the amplitude correlation coefficient are obtained.

[0011] The technical scheme provided by the embodiment of the present application can include the following beneficial effects: The application discloses a clamping force and tapping synchronization performance analysis method, and aims at solving the problems of uneven stress distribution at the root of a tool, unstable torque transmission path and difficult coordination of clamping force and tapping synchronization performance in a tapping process. BRIEF DESCRIPTION OF DRAWINGS

[0012] Figure 1 A flowchart of the clamping force and tapping synchronization performance analysis method of the present application. DETAILED DESCRIPTION

[0013] In order to further understand the present application, the present application will be described in detail in conjunction with the accompanying drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the related application, and not to limit the application. In addition, it should be noted that, for the convenience of description, only the parts related to the application are shown in the drawings.

[0014] As Figure 1 The clamping force and tapping synchronization performance analysis method of the present embodiment can specifically include: S101, tool path data is acquired, and a torque distribution is obtained by simulating a torque transmission process in combination with boundary conditions of narrow areas inside a mold.

[0015] An inner wall contour coordinate set of a closed space geometric model is acquired, a mold cavity topology network is constructed through a distance relationship of adjacent points in the coordinate set, a passable path set between an entrance position and a target thread hole position is extracted from the topology network, and optimal tool path data is determined according to a product of path length and curvature radius. According to space coordinates of each node in the tool path data, a feed depth value of the tool at each node is read, a corresponding basic cutting resistance value is obtained by querying a material hardness table, and an initial torque value of each node is calculated by using a formula ​Let r be the initial torque, d be the basic cutting resistance, f be the tool diameter, v be the depth of feed, v be the cutting speed, and m be the material property coefficient. The initial torque value is used as the boundary condition input for the transmission path simulation. This simulation is a finite element simulation of the torque along the tool path, with the initial torque and path data as inputs and the torque distribution as the output. Distance data between the inner walls of the mold cavity are calculated from the closed spatial geometric model. The vertical distance from each point to the nearest wall is extracted, based on the exponential relationship of torque decay. Calculate the corrected torque value, where To correct the torque, Let be the initial torque, k be the attenuation coefficient (set to 0.1), and distance be the vertical distance. A continuous torque distribution is obtained by numerically filling all nodes in the tool path data using spline interpolation.

[0016] In one implementation, the set of inner wall contour coordinates of the closed spatial geometric model is obtained through a laser rangefinder sensor array. The sensor scans the inner wall of the cavity at a sampling interval of 5 mm, and the obtained coordinate points are stored in a three-dimensional array according to their spatial position. The distance relationship between adjacent points includes not only Euclidean distance but also the angle between surface normal vectors. When the distance between two points is less than a preset threshold and the angle between the normal vectors is less than 15 degrees, the two points are considered to be connected, thereby constructing a complete cavity topology network.

[0017] Specifically, the topology network is represented by a graph structure, where nodes represent spatial coordinate points, edges represent walkable paths, and the weight of an edge is determined by the product of the path length and the minimum radius of curvature of that path segment.

[0018] For example, when processing deep-cavity threaded holes in precision injection molds, the entry point is typically located at the mold parting surface, while the target threaded hole is located deep within the cavity. Multiple accessible paths may exist between these two points. By traversing the topological network using Dijkstra's algorithm, the total weight value of each path is calculated. The weight is the path length divided by the minimum radius of curvature. The path with the smallest weight value is the optimal tool path data. This path ensures tool accessibility while reducing torque loss due to path detours.

[0019] In one possible implementation, the process of querying the material hardness table involves material type identification and hardness value matching.

[0020] Preferably, the corresponding Brinell hardness value is retrieved from a pre-established database based on the mold material grade, and then the Brinell hardness is converted into a cutting resistance coefficient using an empirical formula.

[0021] For example, for P20 mold steel, its Brinell hardness is about 290 HB, and the corresponding basic cutting resistance value is 0.35 Nm per millimeter of feed. This value will be dynamically adjusted according to the degree of tool wear.

[0022] Understandably, torque attenuation in the transmission path simulation follows an exponential decay law, with the attenuation coefficient inversely proportional to the vertical distance. The closer the tool is to the cavity wall, the more restricted the surrounding airflow becomes, leading to poorer heat dissipation. Difficult chip removal further increases the actual cutting resistance, thus reducing torque transmission efficiency. This exponential relationship is expressed as the corrected torque equal to the initial torque multiplied by the natural constant raised to the power of negative α times the vertical distance, where α is the material-dependent attenuation coefficient.

[0023] In one embodiment, the bilinear interpolation method establishes a continuous torque field between discrete nodes of the tool path. The torque value at any position is obtained by weighted averaging of the torque values ​​of four adjacent nodes. The weighting coefficient is determined by the normalized distance from the position to the four nodes, forming a continuous torque distribution map covering the entire tool path.

[0024] S102. Determine the tool root position coordinates based on the torque distribution data, superimpose material property parameters on the tool root position coordinates, and optimize the torque through a genetic algorithm.

[0025] Regions exceeding a preset threshold are extracted from the torque distribution data. The data is then traced backward along the tool axis to the connection point between the tool and the clamping device. The tracing path follows the direction of maximum torque gradient descent. This connection point represents the tool root position coordinates. Pre-stored material yield strength, elastic modulus, and Poisson's ratio values ​​are read at these coordinates. A safety margin coefficient is calculated based on the ratio of the yield strength to the current torque load. This safety margin coefficient is used to set the upper limit of optimization constraints, constructing a three-dimensional parameter space containing torque amplitude, spindle speed, and feed rate. An initial population is randomly generated within this parameter space, with each individual representing a set of parameter combinations. Individuals with high fitness rankings are selected as parents using a roulette wheel selection process. The probability of each individual is first calculated. ,in For individual fitness, The overall fitness of the population is used to select parents based on the cumulative probability distribution function, and a single-point crossover operation is performed on the parents to generate the offspring population. The equivalent stress value generated at the root position of the tool is calculated based on the parameter combination corresponding to each individual in the offspring population. If the equivalent stress value is lower than the material yield strength and the torque transmission efficiency is higher than a preset threshold, a higher fitness value is assigned. The evolutionary process terminates when the rate of change of the fitness value of the optimal individual is less than the convergence threshold within a preset number of iterations, and the optimized torque value obtained after decoding the optimal individual is output.

[0026] In one implementation, the torque distribution data is processed using a threshold segmentation method. The preset threshold is determined based on the fatigue strength of the mold material, typically 0.7 times the fatigue strength as the safety boundary. For P20 mold steel, its fatigue strength is 450 MPa, so the threshold is 315 MPa. The torque cloud map is scanned point by point. When the torque value in a certain area exceeds the threshold, the spatial coordinates of that area are recorded. The tracking path follows the direction of maximum torque gradient descent, until the mechanical interface between the tool and the clamping device is reached; this interface is the root position coordinate. The calculation of the safety margin coefficient involves a comprehensive consideration of multiple material parameters. At the root position coordinate, the yield strength of P20 mold steel is obtained from the material database as 830 MPa, the elastic modulus as 210 GPa, and the Poisson's ratio as 0.3. The equivalent stress under the current torque load is calculated according to the fourth strength theory. The ratio of the yield strength to the equivalent stress is the safety margin coefficient, which reflects the safety reserve of the tool under the current working conditions.

[0027] Preferably, during the construction of the three-dimensional parameter space, the torque amplitude range is set to 0.5 to 1.5 times the initial torque, the spindle speed range is 300 to 1200 rpm, and the feed rate range is 0.05 to 0.3 mm per rpm.

[0028] In one possible implementation, the initial population is uniformly distributed in the parameter space using the Latin hypercube sampling method. Each individual is encoded as a real-valued vector, with its three components corresponding to three optimization parameters. The cumulative probability distribution function is constructed based on the normalization of fitness values; the probability of an individual with high fitness being selected is proportional to its fitness value. A single-point crossover operation swaps the parameter values ​​of the parents at randomly selected gene loci.

[0029] For example, the equivalent stress value is calculated using the Von Mises stress criterion, which takes into account the combined effect of normal stress and shear stress.

[0030] Understandably, when a tool is tapping within a confined space, the root not only bears the shear stress generated by torsion but also the bending stress caused by spatial constraints, resulting in a combined stress state. The fitness function is designed as the product of the reciprocal of the difference between the equivalent stress and the yield strength and the torque transmission efficiency, ensuring both structural safety and processing efficiency.

[0031] For example, when machining blind hole threads with a depth of 80 mm, after a preset number of iterations, the optimal individual parameter combination is a torque of 12 Nm, a spindle speed of 450 rpm, and a feed rate of 0.12 mm per rpm. This combination ensures that the root equivalent stress is controlled within 85% of the material's yield strength, achieving a balance between safety and efficiency.

[0032] The tool root position coordinates are determined based on torque distribution data. A local cylindrical coordinate system is established at the tool root position coordinates to obtain a complete description of the three-dimensional stress state at the root. Material property parameters are superimposed on the tool root position coordinates to perform root mechanical response analysis. The critical stress value at which the material enters the plastic deformation stage is identified as the optimization boundary condition. The torque is optimized in combination with the closed space geometric constraint conditions.

[0033] The center coordinates of the peak region are extracted from the torque distribution data as the tool root position. A local cylindrical coordinate system is established at this position, with the tool axis as the z-axis, the radial direction as the r-axis, and the tangential direction as the θ-axis. The torque load in the Cartesian coordinate system is converted into three components—radial stress, tangential stress, and axial stress—in the cylindrical coordinate system using a coordinate transformation matrix. A third-order stress tensor matrix is ​​constructed based on these three stress components. By solving the eigenvalues ​​of the stress tensor matrix, the three principal stress values ​​and their corresponding principal direction vectors are obtained. The location of the section where the maximum shear stress occurs is determined using a circular graphical method. At this section location, the material's elastic modulus, yield strength, and Poisson's ratio parameters are superimposed to establish a stress-strain constitutive relationship. The equivalent stress value is calculated using the Von Mises yield criterion. If the equivalent stress exceeds the material's yield strength, the plastic flow law is determined based on the hardening modulus. The correspondence between stress increment and strain increment is used to track the turning point where the material transitions from the elastic stage to the plastic deformation stage, and the critical stress value corresponding to this turning point is recorded. The inner wall distance constraint of the enclosed space and the reachable angle range of the tool are obtained. An optimization objective function containing stress constraint terms and torque efficiency terms is established based on the critical stress values. Where T is the torque parameter, and w1 and w2 are the weights. For equivalent stress, Let η be the critical stress and η be the torque efficiency. The optimal combination of torque parameters is searched using a particle swarm optimization algorithm under geometric constraints. The input torque parameter space boundary is as follows: arrive The process includes initializing the particle swarm, iteratively updating particle velocity and position, evaluating the objective function and constraints until convergence, and outputting an optimized torque value that makes the root equivalent stress below the critical value and the torque transmission efficiency exceed 0.9.

[0034] In one implementation, the peak region extraction of torque distribution data is achieved using a sliding window method. The window size is set to a 5×5 grid cell, and the entire torque field is scanned point by point. When the average torque value within the window exceeds 1.5 times the average value of the entire field, the center of the window is marked as a candidate peak point.

[0035] Specifically, by comparing the torque magnitudes of adjacent candidate points, the local maximum value is retained as the center of the peak region, and the coordinates of this center are the location of the tool root. The local cylindrical coordinate system is established with the tool axis as the positive z-axis, and the direction perpendicular to the z-axis and pointing towards the nearest point on the cavity wall is selected as the radial r-axis. The tangential θ-axis direction is determined using the right-hand rule. The construction of the coordinate transformation matrix involves the direction cosine relationship between the basis vectors of the two coordinate systems. The torque load in the Cartesian coordinate system is represented as the distributed torque acting on the tool surface. By left-multiplying the load vector by the coordinate transformation matrix, the stress component expression in the cylindrical coordinate system is obtained. The radial stress reflects the tensile and compressive state of the material along the radial direction, the tangential stress reflects the shearing action in the circumferential direction, and the axial stress characterizes the normal stress distribution along the tool axis. These three components together describe the complete stress state at the root.

[0036] Preferably, the stress tensor matrix is ​​expressed in symmetric matrix form, with the main diagonal elements representing the three normal stress components and the off-diagonal elements representing the shear stress components.

[0037] In one possible implementation, three eigenvalues ​​are obtained by solving the characteristic equation, representing the numerical values ​​of the three principal stresses. These eigenvalues, arranged from largest to smallest, correspond to the first, second, and third principal stresses, respectively. The eigenvector corresponding to each eigenvalue represents the direction of that principal stress. These three eigenvectors are orthogonal to each other, forming an orthogonal basis for the principal stress space. The circular graphical method involves drawing a Mohr's circle in stress space. The diameter of the circle is equal to the difference between the maximum and minimum principal stresses, and the maximum shear stress is equal to the radius of the Mohr's circle. Its plane of action forms a 45-degree angle with the direction of the maximum principal stress. At this cross-sectional location, the material's elastic modulus determines the stress-strain ratio, Poisson's ratio reflects the ratio of transverse to longitudinal strain, and the yield strength marks the critical point where the material transitions from elastic to plastic deformation. These three parameters together constitute the constitutive framework describing the material's mechanical behavior.

[0038] For example, the physical meaning of the Von Mises yield criterion is that yielding begins when the distortion energy density within the material reaches a certain critical value. The calculation of equivalent stress comprehensively considers the contributions of the three principal stresses, obtaining a single value by taking the square root of the sum of the squares of the principal stress differences. This value is directly compared with the yield strength obtained from a uniaxial tensile test. When the equivalent stress exceeds the material's yield strength, the material enters the plastic deformation stage, at which point the stress-strain relationship is no longer linear. The hardening modulus describes the slope of the stress-strain curve in the plastic stage, reflecting the relationship between the stress increment required for further deformation and the resulting plastic strain increment.

[0039] It is understandable that plastic flow follows the law of positive alternating current, meaning the direction of the plastic strain increment is perpendicular to the yield surface. By establishing the yield surface equation in stress space and calculating the normal vector direction of the yield surface, this direction represents the direction of plastic flow. The correspondence between stress increment and strain increment is established using an elastoplastic constitutive matrix. When the material is in the elastic stage, the constitutive matrix is ​​an elastic matrix; after entering the plastic stage, the constitutive matrix needs to consider plasticity correction terms.

[0040] For example, when processing high-strength mold steel S136, whose yield strength is approximately 1100 MPa, the material approaches its yield state when the equivalent stress at the root reaches 0.9 times this value. At this point, by gradually increasing the torque load using a small incremental loading method, the slope of the stress-strain curve is monitored. When the slope abruptly changes from the elastic modulus to the hardening modulus, the corresponding stress value is the actual critical stress value. Furthermore, the inner wall distance constraint of the enclosed space is obtained by calculating the minimum clearance between the tool's outer contour and the inner wall of the mold cavity; this clearance value limits the maximum yaw rate of the tool. The reachable angle range of the tool is limited by the geometry of the inlet channel, determined by calculating the maximum deviation angle between the tool axis and the channel centerline.

[0041] In one embodiment, the optimization objective function is designed as a bi-objective form. The first term is a stress constraint term, which is expressed in the form of a penalty function. When the equivalent stress exceeds a critical value, a penalty value increases sharply. The second term is a torque efficiency term, which is defined as the ratio of the actual transmitted torque to the theoretically required torque.

[0042] Specifically, in the implementation of the particle swarm optimization algorithm, each particle represents a set of torque parameter combinations, including torque amplitude, loading rate, and pulse frequency. The particle's position in the parameter space is updated based on its own historical best position and the swarm's best position. The velocity update formula considers inertia weight, individual learning factor, and social learning factor. Through a preset number of iterative searches, when the objective function value of the swarm's optimal solution changes less than the convergence threshold over several consecutive generations, the torque parameter combination corresponding to that optimal solution is output, thus maximizing torque transmission efficiency while satisfying structural strength constraints.

[0043] S103. Using an optimized torque input finite element mesh model, the stress concentration factor distribution is calculated from the finite element mesh model, and the mesh density is adjusted to obtain a refined stress diagram.

[0044] A finite element mesh is established using optimized torque values ​​as load input. The geometry of the screw root is discretized using tetrahedral elements. Constraints and torque loads are applied to the element nodes, and the stiffness matrix is ​​assembled to solve for the nodal displacements. The stress components within each element are calculated based on the displacement-strain relationship and constitutive equations. The equivalent stress values ​​of each element are extracted from the stress components. High gradient regions where the rate of change of stress gradient exceeds a preset threshold are identified. The ratio of the local peak stress to the average stress of the same cross section within this region is calculated as the stress concentration factor. The continuous distribution of the stress concentration factor throughout the root space is obtained through cubic spline interpolation. Singular regions with values ​​greater than a preset critical value are identified based on the stress concentration factor distribution. In these singular regions, the mesh size is halved for local refinement. The stress difference between adjacent nodes before and after refinement is calculated. If the difference exceeds the allowable error, the mesh size is further reduced until the difference is below the allowable error. The finite element solution is re-executed using the refined mesh. The stress numerical matrix and gradient vector field are extracted from the solution results. The locations of regions where the stress concentration factor exceeds the safety threshold are marked by color mapping. A refined stress map containing stress distribution contour maps and concentration factor contour lines is output.

[0045] In one implementation, the finite element mesh creation process begins with importing the geometric model of the lead screw root, obtaining the outer contour coordinates of the root region by reading 3D CAD data. Tetrahedral elements are selected based on their adaptability to complex geometries; each tetrahedron consists of four nodes, with displacement interpolation relationships established between nodes using linear shape functions. Optimized torque values ​​are applied as boundary loads to the top section of the lead screw, while fixed constraints are applied to the bottom clamping end, restricting displacement and rotational degrees of freedom in all directions. The assembly of the stiffness matrix follows the standard finite element procedure: first, the element stiffness matrix is ​​calculated, then it is assembled into a global stiffness matrix according to the node numbering relationship. The nodal displacement vectors are obtained by solving the linear equations using Gaussian elimination or the conjugate gradient method. The calculation of stress components involves a transformation from the displacement field to the strain field and then to the stress field. According to the geometric equations, the strain tensor is equal to the symmetric part of the displacement gradient; within each element, the strain components are obtained by differentiating the nodal displacements using shape functions. The relationship between stress and strain is determined by the material constitutive equation. For isotropic elastic materials, a linear relationship between the two is established using the generalized Hooke's law. The elastic matrix includes the material's elastic modulus and Poisson's ratio parameters. The equivalent stress is extracted using the Von Mises criterion, which combines the six independent stress components into a single scalar value, facilitating the assessment of the material's stress state.

[0046] For example, the calculation of stress gradient requires numerical differentiation between adjacent elements.

[0047] In one possible implementation, the local stress field is fitted using the least squares method, and the gradient vector is obtained by differentiating the fitted function. When the gradient rate of change exceeds a preset threshold, it indicates that there is a sharp change in stress in that region, which is marked as a high-gradient region. The stress concentration factor is defined as the ratio of the local peak stress to the reference stress, where the reference stress is the arithmetic mean of the stresses at all nodes on the same cross-section. This definition can quantify the amplification of local stress relative to the overall stress level, providing a quantitative basis for subsequent safety assessment. The cubic spline interpolation method ensures the spatial continuity and smoothness of the stress concentration factor, guaranteeing the continuity of the first and second derivatives during interpolation and avoiding numerical oscillations. By performing interpolation calculations at regular grid points, a stress concentration factor field covering the entire root region is formed, with each spatial point corresponding to a specific concentration factor value.

[0048] Preferably, the identification of singular regions is based on the numerical magnitude and distribution characteristics of the stress concentration factor. When the stress concentration factor of a certain region exceeds 80% of the allowable value of the material, it is determined to be a singular region requiring special attention. Mesh refinement adopts an h-type adaptive method, that is, improving computational accuracy by reducing the element size.

[0049] Understandably, halving the mesh size involves a subdivision operation. For tetrahedral elements, a new node is inserted at the midpoint of each edge, subdividing the original tetrahedron into eight similar sub-tetrahedrons. The subdivided mesh maintains the original topological continuity, and the displacement of the newly added nodes is initially obtained from adjacent nodes through linear interpolation.

[0050] In one embodiment, the error estimation employs a posterior error estimation method based on the energy norm.

[0051] Specifically, the degree of stress discontinuity between adjacent elements is calculated. When the stress jump exceeds 10% of the average stress, the discretization error at that location is considered large. By comparing the stress solutions before and after refinement, if the relative error between the two calculations is less than 5%, the mesh is considered to have converged; otherwise, local refinement continues until the convergence condition is met. Furthermore, when re-executing the finite element solution, the refined mesh contains more nodes and elements, enabling more accurate capture of the detailed features of stress concentration regions.

[0052] For example, in the root analysis of deep hole tapping, the initial mesh contained approximately 5000 nodes. After two rounds of adaptive refinement, the number of nodes in the singular region increased to 20000, improving the stress calculation accuracy by an order of magnitude. The generation of the stress distribution contour map involves a mapping process from numerical values ​​to colors. Using a rainbow color spectrum, stress values ​​from small to large are mapped to a gradient from blue to red, making the spatial variation of stress distribution intuitively visible. Contour lines are drawn by tracing the spatial trajectory of the same stress concentration factor; the density of the contour lines reflects the gradient of the stress concentration factor.

[0053] For example, when machining the cooling water channel thread of a die-casting mold, the refining stress diagram shows that there are two obvious stress concentration areas at the root, located at the beginning of the thread and the transition of the root fillet, respectively, with stress concentration factors reaching 2.8 and 3.2. By adjusting the fillet radius and optimizing the thread lead angle, the stress concentration factor can be reduced to below 2.0, ensuring the safety of the tapping process.

[0054] S104. Obtain peak stress data from the refining stress diagram, determine fatigue damage value by counting the number of stress cycles, generate adaptive control signal, and input it into the simulated tapping cycle to obtain the tool running status.

[0055] The coordinates of regions where stress values ​​exceed the material fatigue limit are extracted from the refined stress diagram. The time-domain stress history data and peak distribution within this region are read using dynamic finite element simulation. The number of cycles at different stress amplitudes is counted using the rainflow counting method. Based on the correspondence between the number of cycles and the material stress-life curve, the damage component values ​​at each stress level are calculated. The Miner linear cumulative damage criterion is used to superimpose the damage component values ​​to obtain the total fatigue damage value. If this value exceeds a preset safety threshold, the feed rate and spindle speed parameters are reduced by a predetermined ratio; if it is below the threshold, the current parameter values ​​are maintained. An adaptive control signal containing the adjusted spindle speed, feed rate, and depth of cut is output. Based on the adaptive control signal, the input parameters of a predefined finite element simulation model of the tapping process are set, and simulated tapping cycle calculations are executed. The tool's position coordinates, stress state, and vibration amplitude are recorded at each time point. The degree of tool wear is determined by comparing the deviation between the actual trajectory and the theoretical trajectory. Tool operating status data containing wear level and remaining life prediction is output.

[0056] In one implementation, peak stress extraction from the refined stress map is achieved by scanning the entire stress field. The scanning step size is set to one-tenth of the grid size, and stress values ​​are compared point by point. When the stress value at a point is greater than the stress values ​​at the eight adjacent points, it is marked as a local peak point. The core of the rainflow counting method lies in identifying complete cycles in the stress time history. By tracking the peak-valley changes in the stress-time curve, the irregular stress history is decomposed into a series of full cycles and semi-cycles, each cycle corresponding to a specific stress amplitude and average stress.

[0057] Specifically, the material stress-life curve describes the number of cycles required for a material to fail under different stress levels. It is usually expressed in the form of a power function, and the slope of the curve reflects the fatigue sensitivity of the material.

[0058] Preferably, the damage component values ​​are calculated based on the linear damage assumption, that is, the damage caused by each stress cycle is inversely proportional to the fatigue life at that stress level, and the damage at each stress level can be linearly superimposed.

[0059] For example, the Miner linear cumulative damage criterion states that fatigue failure occurs when the total damage caused by stresses at each level reaches 1.

[0060] In one possible implementation, the safety threshold is set to 0.7, meaning that control parameters are adjusted when cumulative damage reaches 70%. The predetermined percentage is determined based on empirical data, typically by reducing the rotational speed by 15% to 25% and the feed rate by 20% to 30%, thereby extending tool life by reducing the cutting load.

[0061] For example, the simulation environment for simulating the tapping cycle includes a tool geometry model, material constitutive relations, and a cutting force model. The dynamic response of the tool is solved using the time-stepping method. The theoretical trajectory is determined by the kinematic equations under ideal cutting conditions, while the actual trajectory considers the deformation and vibration caused by the cutting force. The deviation between the two is obtained by calculating the Euclidean distance between the position coordinates at corresponding moments. Furthermore, the wear level is divided into three levels: slight wear, moderate wear, and severe wear, corresponding to trajectory deviations of less than 0.05 mm, 0.05 to 0.15 mm, and greater than 0.15 mm, respectively. Remaining life prediction is based on the linear extrapolation of the wear rate. The ratio of the current wear amount to the wear rate is used to estimate how long the tool can continue to work, providing a reference for maintenance decisions.

[0062] S105. Based on the tool's operating status, extract the three-dimensional spatial displacement data reflecting the torque generated at the root of the lead screw by monitoring the axial and radial displacement data of the lead screw, and confirm the stable torque path.

[0063] Based on the tool's operating status data, the axial displacement sequence and radial runout amplitude of the lead screw at various time points are read. By synthesizing the axial displacement, radial runout, and lead screw rotation angle using coordinates, the displacement vectors of each node at the root of the lead screw in three-dimensional space are obtained, constructing a spatial displacement field reflecting the effect of torque. Optionally, the stress intensity at each node is calculated using the spatial displacement field; the stress gradient between adjacent nodes is solved using the finite difference method; stress streamlines are formed by connecting along the direction of maximum gradient; and the transmission capacity value of the path is determined based on the product of the material stiffness and cross-sectional area at each point on the streamline. Candidate paths with transmission capacity values ​​higher than a preset threshold are selected from the stress streamlines. The cumulative energy loss from the root to the end of each candidate path is calculated, and the streamline with the minimum loss and shortest path length is selected as the stable torque path.

[0064] In one implementation, tool operating status data is acquired in real time via a sensor array. An axial displacement sensor is mounted on the bottom support of the lead screw, and a radial runout sensor is positioned in the middle of the lead screw. The coordinate synthesis process involves the fusion of three independent variables: axial displacement reflects the extension and contraction of the lead screw, radial runout reflects lateral vibration, and rotation angle is obtained through an encoder. These three variables are vector-synthesized in a cylindrical coordinate system to form the spatial position point at each sampling moment.

[0065] Specifically, the spatial displacement field is constructed using a gridding method, which divides the root region of the screw into several micro-elements. The displacement of the center point of each micro-element is obtained by interpolating the data from adjacent measuring points.

[0066] Preferably, the stress intensity is calculated based on the displacement-strain relationship. The strain tensor is obtained by taking the spatial derivative of the displacement field, and then converted into the stress tensor according to the material constitutive relation. The stress intensity is taken as the von Mises equivalent stress value. The finite difference method uses a central difference scheme to calculate the stress gradient, with the spacing between adjacent nodes equal to the mesh size, and the gradient vector pointing in the direction of the fastest stress growth.

[0067] For example, the formation process of stress streamlines is similar to streamline tracing in fluid mechanics, starting from a seed point in a high-stress region and gradually advancing along the local gradient direction with a step size of half the mesh size until reaching a low-stress region or the tool tip.

[0068] In one possible implementation, the transfer capacity value is defined as the minimum transfer capacity of each micro-segment along the path. The transfer capacity of each micro-segment is equal to the product of the material's elastic modulus, cross-sectional area, and shape factor at that location. The shape factor takes into account the influence of the cross-sectional shape on the torsional stiffness.

[0069] For example, when tapping an M8 threaded hole, three to five main stress flow lines are typically formed. These flow lines radiate from the stress concentration area at the root and extend along the screw helical groove to the cutting edge.

[0070] Understandably, the accumulated energy loss is obtained by line integral of the strain energy density at each point along the path, where the strain energy density is equal to half the scalar product of stress and strain. The path length is calculated using an arc-length parameterization method, ensuring accurate measurement of paths with different curvatures. Furthermore, the selection of the stable torque path follows the principle of minimum energy; while meeting the transmission capacity requirements, the path with the lowest energy loss is preferentially selected. Such paths typically have better stiffness distribution and lower stress concentration, ensuring the stability and reliability of torque transmission.

[0071] Based on the tool's operating status, the axial and radial displacement data of the lead screw are monitored to extract three-dimensional spatial displacement data reflecting the torque generated at the root of the lead screw. The main energy transfer path from the root of the lead screw to the end of the tool is traced, the stable transfer zone is determined, and the torque transfer path with a deformation energy density lower than the safety threshold and located in the stable transfer zone is identified as a set of candidate paths. The path with the highest energy transfer efficiency is selected from the set of candidate paths as the stable torque path.

[0072] The axial displacement time history data and radial yaw amplitude sequence of the lead screw are read based on the tool's operating status. These two sets of signals are aligned using timestamps and synthesized in cylindrical coordinates to obtain a three-dimensional displacement vector field at the root node of the lead screw under torque. The displacement gradient tensor of each node is calculated from this displacement vector field using differential operations. The stress tensor is calculated based on the material constitutive relation using the displacement gradient tensor, thus obtaining the deformation energy density value of each micro-element. The energy density gradient is traced point by point along the direction of the fastest decrease, connecting the high-energy-density region at the root of the lead screw to the low-energy-density region at the tool end, forming the main energy dissipation path. Regions with gradual stiffness changes are identified as stable transmission zones based on the material stiffness values ​​at each point on the main path. Within the stable transmission zone, path segments with deformation energy densities below a preset safety threshold are selected. The total loss is evaluated by accumulating the energy loss values ​​of each micro-element on the path, resulting in a candidate path set. The ratio of input energy to output energy for each path is calculated as the transmission efficiency from the candidate path set. The trajectory with the highest transmission efficiency and the shortest total path length is selected as the stable torque path.

[0073] In one implementation, high-precision displacement sensor arrays are used to acquire tool operating status data. The axial displacement sensor employs a laser interferometer with micrometer-level measurement accuracy, while the radial runout sensor uses an eddy current sensor with a response frequency of 10kHz. The timestamp alignment process involves the synchronous acquisition of two sets of signals. Hardware triggering ensures that both sets of sensors begin recording at the same time, with a sampling frequency set to 1000Hz. Each sampling point is marked with a precise time stamp. The cylindrical coordinate system is established with the lead screw axis as the z-axis and the center of the fixed end at the root of the lead screw as the origin. The radial direction (r) and circumferential direction (θ) form a polar coordinate plane. The three-dimensional displacement vector is synthesized by treating axial displacement as the z-component, radial runout as the r-component, and rotational angle change as the θ-component.

[0074] Specifically, the displacement gradient tensor is calculated using the central difference scheme. For any displacement vector u at any point in space, its gradient tensor is defined as the matrix of partial derivatives of the displacement components with respect to the spatial coordinates.

[0075] For example, on a discrete mesh, the spacing between adjacent nodes is set to 1 mm. The gradient components are obtained by calculating the difference in displacement between adjacent nodes and dividing by the node spacing. This nine-component tensor contains complete information about material deformation, with its symmetric part representing strain and its antisymmetric part representing rigid body rotation.

[0076] Preferably, the application of the material constitutive relation is based on the linear elastic assumption, under small deformation conditions, stress and strain have a linear relationship.

[0077] In one possible implementation, for isotropic materials, the constitutive relations are completely determined by two independent elastic constants: the elastic modulus and Poisson's ratio. The stress tensor is calculated by multiplying the strain tensor by the elastic stiffness matrix; for die steel, the typical elastic modulus is 210 GPa and the Poisson's ratio is 0.3. The strain energy density is defined as the elastic energy stored per unit volume, numerically equal to half the dot product of the stress and strain tensors; this scalar value reflects the energy storage state within the material.

[0078] Understandably, the tracking algorithm starts at the point of maximum deformation energy density at the root of the lead screw, calculates the energy density gradient vector at that point, and the negative direction of the gradient is the preferred direction of energy flow. It advances a small step along this direction, recalculates the gradient upon reaching a new position, and iterates until it reaches the tool tip. This point-to-point tracking method can accurately capture the energy transfer path in complex geometries. In actual tapping processes, due to the presence of helical grooves, the energy transfer path often presents a spiral shape rather than a straight line. By tracking multiple starting points, a main energy transfer path can be formed, and the spatial distribution of these paths reflects the main channels of torque transmission. Furthermore, the identification of the stable transfer zone is based on the spatial distribution characteristics of material stiffness.

[0079] For example, in the machining of cooling channel threads in die-casting molds, the stiffness varies in different regions due to the inhomogeneity of the mold material and differences in heat treatment. A criterion for a smooth stiffness change is that the stiffness difference between adjacent points is less than 5% of the average stiffness. Within such regions, the stress distribution is relatively uniform, and stress concentration is less likely to occur. In the stable transmission region, the safe threshold for deformation energy density is typically set at 70% of the energy density corresponding to the material's fatigue limit. This conservative value ensures safety under long-term cyclic loading.

[0080] In one embodiment, the formation of the candidate path set includes path discretization and cumulative calculation of energy loss. Each path is discretized into several micro-segments, and the energy loss of each micro-segment is estimated by multiplying the average deformation energy density within that segment by the segment length. The total energy loss is the sum of the losses of all micro-segments, which directly reflects the degree of energy dissipation of torque during transmission.

[0081] Specifically, calculating transmission efficiency involves the accurate measurement of input and output energy. Input energy is obtained by multiplying the root torque and the rotation angle, while output energy is obtained by multiplying the end cutting force and the cutting speed. Transmission efficiency is defined as the ratio of output energy to input energy; high efficiency means that more input energy is effectively converted into cutting work. The total path length is obtained by integrating the parameterized path; shorter paths typically have lower energy loss.

[0082] For example, when machining a blind hole thread with a depth of 100 mm, two to three main candidate paths are usually identified, with transmission efficiencies of 85%, 82% and 78%, respectively, and corresponding path lengths of 120 mm, 125 mm and 135 mm. Taking into account both efficiency and length, the first path is selected as the stable torque path. This path extends along the main helical groove of the lead screw, avoiding stress concentration areas and achieving stable torque transmission.

[0083] S106. Obtain thread forming parameters from the stable torque path, determine the tapping quality index, synchronously monitor the pressure change during the mold closing process to extract the mold closing force, and obtain the mold closing force and tapping synchronization performance data based on the mold closing force change and tapping torque output.

[0084] The torque values ​​and rotational speed parameters of each node on the stable torque path are extracted. The feed rate is calculated based on the product of the cutting speed and the pitch. The thread forming parameter P, i.e., the thread formation ratio, is obtained by the ratio of the standard pitch S to the actual cutting depth D. The maximum achievable depth and thread profile integrity rate are determined by combining the geometric boundary of the enclosed space as tapping quality indicators. Using the tapping quality indicators, the sampling frequency of the pressure sensor is set to a preset value. The initial pressure value is recorded when the mold closing action starts. The pressure time history curve is obtained by continuous sampling. The pressure change rate is obtained by calculating the ratio of the pressure difference between adjacent sampling points to the time interval. When the pressure reaches the preset mold closing force threshold, the corresponding timestamp and pressure peak value are recorded. The time difference is calculated based on the occurrence time of the pressure peak and the peak time of the tapping torque, where the peak time of the tapping torque is extracted from the torque time series curve. If the time difference exceeds the allowable range, the screw speed is increased or decreased proportionally to align the two peaks. The degree of synchronization is evaluated by calculating the normalized product integral value of the clamping force curve and the tapping torque curve. The normalized product integral, i.e., the cross-correlation value, represents the phase deviation and amplitude correlation coefficient, thus obtaining synchronization performance data that includes the phase deviation and amplitude correlation coefficient.

[0085] In one implementation, node data along the stable torque path is acquired using an equidistant sampling method. The sampling interval is set to the total path length divided by a preset number of sampling points. Each node records the torque value, rotational speed, and spatial coordinates. The product of the cutting speed and the pitch reflects the actual feed rate of the thread machining. The standard pitch value is obtained from a standard table based on the thread specification. The actual cutting depth is obtained by measuring the axial distance from the starting point to the ending point.

[0086] Specifically, the assessment of thread profile integrity involves three key parameters: crest width, root width, and flank angle. The degree of overlap between the actual machined thread profile and the standard thread profile is calculated as an indicator of integrity.

[0087] Preferably, the geometric boundary of the enclosed space is obtained through three-dimensional scanning, and the maximum achievable depth is equal to the shortest distance from the entrance to the obstacle minus the tool length.

[0088] For example, the sampling frequency setting of the pressure sensor needs to take into account the dynamic characteristics of the mold closing process, and is usually set to more than 20 times the mold closing action frequency to ensure that details of pressure changes can be captured.

[0089] In one possible implementation, the pressure change rate is linearly fitted to five consecutive sampling points using the least squares method, and the slope of the fitted line is the pressure change rate at that moment. When the pressure reaches the clamping force corresponding to the material's yield strength, the timestamp and pressure value at that moment are automatically recorded.

[0090] Understandably, the calculation of time difference requires a unified time reference, usually with the start of the mold closing action as the zero point.

[0091] For example, when machining M10 threads, the peak tapping torque occurs when the thread depth reaches 70%, while the peak clamping force occurs when the die is fully closed. The time difference between these two peaks reflects the process coordination. Furthermore, the screw speed is adjusted using a proportional control method. The adjustment amount equals the time difference multiplied by a preset adjustment coefficient. A positive time difference indicates that tapping is lagging and needs acceleration, while a negative time difference indicates that tapping is ahead and needs deceleration. The calculation of the normalized product integral value first normalizes the amplitudes of the two curves to the 0-1 interval, then calculates the product of the values ​​at corresponding moments, and finally integrates over the entire time interval. A larger integral value indicates better synchronization.

[0092] In one embodiment, the synchronization performance data includes three indicators: phase deviation, amplitude correlation coefficient, and peak time difference. These indicators together reflect the degree of coordination between mold closing and tapping actions.

[0093] The above are merely preferred embodiments of the present invention and do not limit the scope of the patent. Any equivalent structural or procedural transformations made based on the description and drawings of the present invention, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A method for analyzing the synchronous performance of clamping force and tapping, characterized in that, The method includes: Obtain tool path data and combine it with boundary conditions of a narrow area inside the mold to simulate the torque transmission process and obtain torque distribution; The tool root position coordinates are determined based on torque distribution data, material property parameters are superimposed on the tool root position coordinates, and the torque is optimized through a genetic algorithm. An optimized torque input finite element mesh model is used to calculate the stress concentration factor distribution from the finite element mesh model, and the mesh density is adjusted to obtain a refined stress map. Peak stress data is obtained from the refining stress diagram, fatigue damage value is determined by counting the number of stress cycles, adaptive control signal is generated and input into the simulated tapping cycle to obtain the tool running status; Based on the tool's operating status, the three-dimensional spatial displacement data reflecting the torque generated at the root of the lead screw is extracted by monitoring the axial and radial displacement data of the lead screw, thus confirming the stable torque path. Thread forming parameters are obtained from the stable torque path to determine the tapping quality index. The pressure change during the mold closing process is monitored synchronously to extract the mold closing force. Based on the change of mold closing force and the tapping torque output, the synchronous performance data of mold closing force and tapping are obtained.

2. The method for analyzing the synchronous performance of clamping force and tapping according to claim 1, characterized in that, The acquisition of tool path data, combined with the simulation of torque transmission process in the narrow area inside the mold to obtain torque distribution, includes: Obtain the set of inner wall contour coordinates of the closed spatial geometric model. Construct a mold cavity topology network based on the distance relationship between adjacent points in the coordinate set. Extract a set of passable paths between the inlet position and the target threaded hole position from the topology network. Determine the tool path data based on the product of the path length and the radius of curvature. Read the feed depth value of the tool at each node based on the spatial coordinates of each node in the tool path data. Obtain the corresponding basic cutting resistance value by querying the material hardness table. Multiply the basic cutting resistance value by the tool diameter to obtain the initial torque value of each node. Use the initial torque value as the boundary condition input to transfer the path simulation. Extract the vertical distance from each position point to the nearest wall from the inner wall distance data of the mold cavity. Calculate the corrected torque value based on the exponential relationship between the vertical distance and torque attenuation. Fill the values ​​between all nodes of the tool path data using bilinear interpolation to obtain a continuous torque distribution.

3. The method for analyzing the synchronous performance of clamping force and tapping according to claim 1, characterized in that, The process of determining the tool root position coordinates based on torque distribution data, superimposing material property parameters onto the tool root position coordinates, and optimizing the torque using a genetic algorithm includes: The region where the value exceeds the preset threshold is extracted from the torque distribution data. The tool root position coordinates are obtained by tracing back along the torque transmission spindle direction to the connection between the tool and the clamping device. The pre-stored material yield strength is read at the tool root position coordinates. The safety margin coefficient is calculated based on the ratio of the material yield strength to the current torque load. The safety margin coefficient is used to set the upper limit of the optimization constraint. A three-dimensional parameter space containing torque amplitude, spindle speed, and feed rate is constructed. An initial population is randomly generated in the parameter space. The individual with the highest fitness ranking is selected as the parent through the cumulative probability distribution function. A single-point crossover operation is performed on the parent to generate the offspring population. The equivalent stress value generated at the tool root position is calculated based on the parameter combination corresponding to each individual in the offspring population. The optimized torque that makes the equivalent stress value lower than the material yield strength and the torque transmission efficiency higher than the preset threshold is output.

4. The method for analyzing the synchronous performance of clamping force and tapping according to claim 1, characterized in that, After simulating the torque transmission process by combining the boundary conditions of the narrow area inside the mold to obtain the torque distribution, the process also includes: determining the coordinates of the tool root position based on the torque distribution data, establishing a local cylindrical coordinate system at the tool root position coordinates, obtaining a complete description of the three-dimensional stress state at the root, superimposing material property parameters on the tool root position coordinates to perform root mechanical response analysis, identifying the critical stress value of the material entering the plastic deformation stage as the optimization boundary condition, and optimizing the torque by combining the geometric constraints of the closed space.

5. The method for analyzing the synchronous performance of clamping force and tapping according to claim 4, characterized in that, The tool root position coordinates are determined based on torque distribution data. A local cylindrical coordinate system is established at the tool root position coordinates to obtain a complete description of the three-dimensional stress state at the root. Material property parameters are superimposed on the tool root position coordinates to perform root mechanical response analysis. The critical stress value at which the material enters the plastic deformation stage is identified as the optimization boundary condition. The torque is optimized in combination with the geometric constraints of the closed space, specifically including: A local cylindrical coordinate system is established at the root position coordinates of the tool. The torque distribution data is decomposed into radial stress components, tangential stress components, and axial stress components. The three-dimensional stress state at the root is obtained through stress tensor transformation. The critical stress value at which the material enters the plastic deformation stage is identified as the optimization boundary condition. The torque is optimized in combination with the geometric constraints of the closed space.

6. The method for analyzing the synchronous performance of clamping force and tapping according to claim 1, characterized in that, The process of employing an optimized torque input finite element mesh model, calculating the stress concentration factor distribution from the finite element mesh model, and adjusting the mesh density to obtain a refined stress map includes: A finite element mesh is established using optimized torque as the load input. The geometry of the screw root is discretized using tetrahedral elements. Constraints and torque loads are applied to the element nodes, and the stiffness matrix is ​​assembled to solve for the nodal displacements. The stress components within each element are calculated based on the displacement-strain relationship and constitutive equations. The equivalent stress values ​​of each element are extracted from the stress components. High gradient regions where the rate of change of stress gradient exceeds a preset threshold are identified. The ratio of the local peak stress to the average stress of the same cross section within this region is calculated as the stress concentration factor. The continuous distribution of the stress concentration factor throughout the root space is obtained through cubic spline interpolation. Singular regions with values ​​greater than a preset critical value are identified based on the stress concentration factor distribution. Local refinement is performed in these singular regions by halving the mesh size. The stress difference between adjacent nodes before and after refinement is calculated until the difference is lower than the allowable error. The finite element solution is re-executed using the refined mesh. The stress numerical matrix and gradient vector field are extracted from the solution results. The locations of regions where the stress concentration factor exceeds the safety threshold are marked by color mapping. A refined stress map containing stress distribution contour maps and concentration factor contour lines is output.

7. The method for analyzing the synchronous performance of clamping force and tapping according to claim 1, characterized in that, The process of obtaining peak stress data from the refining stress diagram, determining fatigue damage values ​​by counting stress cycles, generating adaptive control signals, and inputting them into the simulated tapping cycle to obtain the tool operating status includes: The coordinates of the region where the stress value exceeds the material fatigue limit are extracted from the refined stress diagram. The peak stress data and its spatial distribution within this region are read. The number of cycles under different stress amplitudes is counted using the rainflow counting method. The damage component value at each stress level is calculated based on the correspondence between the number of cycles and the material stress-life curve. The damage component values ​​are superimposed using the Miner linear cumulative damage criterion to obtain the total fatigue damage value. The feed rate and spindle speed parameters are adjusted based on the total fatigue damage value, and an adaptive control signal containing the adjusted speed, feed rate, and depth of cut is output. The input parameters for the tapping process simulation are set based on the adaptive control signal, and the simulated tapping cycle calculation is executed. The tool's position coordinates, stress state, and vibration amplitude at each time node are recorded, and tool operating status data containing wear level and remaining life prediction value is output.

8. The method for analyzing the synchronous performance of clamping force and tapping according to claim 1, characterized in that, The step of extracting three-dimensional spatial displacement data reflecting the root of the lead screw under torque by monitoring the axial and radial displacement data of the lead screw based on the tool's operating status, and confirming the stable torque path, includes: Based on the tool's operating status data, the axial displacement sequence and radial runout amplitude of the lead screw at each time point are read. By synthesizing the axial displacement, radial runout, and lead screw rotation angle into coordinates, the displacement vectors of each node at the root of the lead screw in three-dimensional space are obtained. The stress intensity at each node is calculated using the displacement vectors, and the stress gradient between adjacent nodes is solved using the finite difference method. Stress streamlines are formed by connecting them along the direction of maximum gradient. Candidate paths with transmission capacity values ​​higher than a preset threshold are selected from the stress streamlines, and the streamline with the minimum cumulative energy loss and the shortest path length is selected as the stable torque path.

9. The method for analyzing the synchronous performance of clamping force and tapping according to claim 1, characterized in that, After obtaining the tool's operating status, the process further includes: reading the axial displacement time history data and radial yaw amplitude sequence of the lead screw based on the tool's operating status; aligning the two sets of signals using timestamps and synthesizing them in cylindrical coordinates to obtain a three-dimensional displacement vector field of the lead screw root node under torque; calculating the displacement gradient tensor of each node from the displacement vector field using differential operations; calculating the stress tensor based on the material constitutive relation using the displacement gradient tensor to obtain the deformation energy density value of each micro-element; tracing point by point along the direction of the fastest decrease in deformation energy density gradient, connecting the high energy density region at the lead screw root to the low energy density region at the tool end to form the main path of energy dissipation; identifying regions with gentle stiffness changes as stable transmission zones based on the material stiffness values ​​at each point on the main path; selecting path segments with deformation energy densities lower than a preset safety threshold within the stable transmission zone; obtaining a candidate path set by accumulating the energy loss values ​​of each micro-element on the path; calculating the ratio of input energy to output energy for each path from the candidate path set as the transmission efficiency; and selecting the trajectory with the highest transmission efficiency and the shortest total path length as the stable torque path.

10. The method for analyzing the synchronous performance of clamping force and tapping according to claim 1, characterized in that, The process involves obtaining thread forming parameters from a stable torque path, determining tapping quality indicators, simultaneously monitoring pressure changes during mold closing to extract mold closing force, and obtaining mold closing force and tapping synchronization performance data based on mold closing force changes and tapping torque output, including: The torque values ​​and rotational speed parameters of each node on the stable torque path are extracted. The feed rate is calculated based on the product of the cutting speed and the pitch. The thread forming parameters are obtained by the ratio of the standard pitch value to the actual cutting depth. The maximum achievable depth and thread profile integrity rate are determined by combining the geometric boundary of the enclosed space as tapping quality indicators. The sampling frequency of the pressure sensor is set using the tapping quality indicators. The initial pressure value is recorded when the mold closing action starts. The pressure time history curve is obtained by continuous sampling. The pressure change rate is obtained by calculating the ratio of the pressure difference between adjacent sampling points to the time interval. The time difference is calculated based on the time of the pressure peak and the time of the tapping torque peak. The synchronization degree is evaluated by calculating the normalized product integral value of the mold closing force curve and the tapping torque curve, and the synchronization performance data including phase deviation and amplitude correlation coefficient is obtained.

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