Discrete point-based cutting force prediction method supporting any cutting edge shape

Abstract

The invention discloses a discrete point-based cutting force prediction method supporting any cutting edge shape, and relates to the technical field of milling machining.The discrete point-based cutting force prediction method comprises the steps that firstly, a workpiece and a tool are both expressed in a discrete model, a milling track is defined as a series of linear segments through NC codes, and a tool and cutting edge model and a Tri-Dexel workpiece model are built; secondly, a tool swept volume is obtained, and material removal is calculated; then subdividing the tool motion into smaller analysis steps to obtain the cutting condition of each turn, determining the cutting meshing area of each analysis step and blade elements participating in cutting, and calculating the nominal instantaneous undeformed chip thickness of each blade element based on the actual feeding direction, the normal vector and the compensation coefficient; then, discretizing the cutting condition into a plurality of orthogonal cutting units, and predicting the cutting force of each participating blade element by adopting a neural network trained based on simulation data; and finally, integrating the cutting forces of all participating blade elements to obtain a synthetic cutting force field of each analysis step. According to the method provided by the invention, the force field prediction capability in a variable geometry processing scene is effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of milling machining, and particularly relates to a discrete point-based cutting force prediction method supporting any cutting edge shape. Background Art

[0002] In the field of precision machining, as the core physical quantity of the dynamic interaction between the cutting tool and the workpiece, the cutting force directly determines the machining efficiency, tool life, and workpiece surface quality. The sudden change of the cutting force will not only cause tool chatter and lead to a sharp drop in machining accuracy, but also may cause catastrophic failures such as tool chipping. Especially in the machining of high-value parts such as aeroengine blades, blisks, and casings, such problems will cause the production cost to increase exponentially. Constructing a high-precision cutting force prediction model is not only the core prerequisite for realizing advanced processes such as intelligent matching of cutting parameters and dynamic optimization of tool paths, but also the key enabling technology for eliminating chatter risks and ensuring the stability of the machining process.

[0003] In the current mainstream modeling methods, although the finite element method (FEM) can obtain the accurate force field distribution through multi-physics field coupling simulation, its huge computational cost is difficult to cope with complex tool paths and workpiece geometric features; the analytical method based on the mechanical model relies on empirical formulas and simplified assumptions, and is prone to systematic deviations under non-uniform tool geometric conditions; the data-driven method based on machine learning shows prediction advantages under specific working conditions, but its generalization ability is significantly limited because the input parameters cannot fully characterize the three-dimensional dynamic meshing state; although the hybrid modeling method attempts to combine the above advantages, there are still bottlenecks in the analysis of the non-uniform geometric features of the cutter-workpiece engagement (CWE). Especially when dealing with non-symmetric cutting edge structures such as non-uniform helix angles and variable pitch cutters, the traditional uniform grid modeling system is difficult to accurately describe the microscopic topography changes and dynamic meshing characteristics of the cutting edge, resulting in distorted prediction of the contact stress distribution, which severely restricts the engineering applicability of the model in complex machining scenarios. Summary of the Invention

[0004] The object of the present invention is to provide a discrete point-based cutting force prediction method supporting any cutting edge shape, which solves the problems that in the existing discrete cutting force prediction methods in milling machining, when the cutting edge of the tool presents a non-symmetric helix angle distribution, special pitch or special geometric features, the uniform grid discretization method cannot accurately describe the spatial topological characteristics of the cutting edge, and in complex trajectory machining scenarios, the traditional model has systematic deviations in the calculation of the dynamic contact domain and the cutting force prediction accuracy decreases.

[0005] To achieve the above object, the present invention provides a discrete point-based cutting force prediction method supporting any cutting edge shape, including the following steps:

[0006] Step 1: Represent both the workpiece and the cutting tool in a discrete model. Define the milling trajectory as a series of linear segments through NC code, and build the cutting tool and cutting edge models as well as the Tri-Dexel workpiece model. Each linear segment includes the target coordinates, the cutting tool's axial attitude, the feed rate, and the spindle speed.

[0007] Step 2: Obtain the cutting tool swept volume and calculate the material removal. Update the Tri-Dexel workpiece model based on the completed NC operation steps and calculate the removed material.

[0008] Step 3: Extract the cutting zone engagement (CWE) and calculate the nominal instantaneous undeformed chip thickness of each cutting edge element. Subdivide the cutting tool movement into smaller analysis steps to obtain the cutting conditions per revolution, determine the cutting zone engagement area and the cutting edge elements involved in cutting for each analysis step, and calculate the nominal instantaneous undeformed chip thickness (IUCT) of each cutting edge element based on the actual feed direction, normal vector, and compensation coefficient.

[0009] Step 4: Discretize the cutting conditions into multiple orthogonal cutting elements and use a neural network trained based on simulation and experimental data to predict the cutting forces of each participating cutting edge element.

[0010] Step 5: Integrate the cutting forces of all participating cutting edge elements to obtain the resultant cutting force field for each analysis step.

[0011] Preferably, the construction of the cutting tool and cutting edge models in Step 1 includes the construction of the cutting tool and the cutting edge. The cutting tool adopts a dual-modal modeling strategy: the rotating body part is constructed by triangular meshes for calculating the cutting tool swept volume and dynamic engagement analysis; the cutting edge part adopts a high-density point cloud topology, and each discrete point corresponds to an orthogonal cutting element. The specific construction process is as follows: the rotating body is generated by rotating a two-dimensional contour around an axis to create triangular meshes. The data structure of the triangular meshes consists of three parts, which are a 3×N point array storing the point coordinates on the contour, and two 3×N surface arrays storing the indices of the points forming the triangular faces and the normal vectors of the triangular faces respectively; the multi-dimensional geometric parameters of the cutting edge point cloud are independently stored in a cache in the form of arrays, including spatial coordinates (3×N edge ), tangent / normal / axial unit vectors (3×3×N edge ), rotation radius (1×N edge ), and rake / relief angles (2×N edge ) attributes. Here, N point represents the number of grid points of the cutting tool rotating body, N surface represents the number of triangular faces of the cutting tool rotating body, and N edge represents the number of cutting edge elements after discretization of the cutting edge.

[0012] Preferably, in the construction of the cutting edge, a compensation coefficient k is introduced for each cutting edge element i , to eliminate the influence of the spatial distribution of the cutting edge and obtain an accurate chip thickness. The expression of the compensation coefficient k i is as follows:

[0013]

[0014] In the formula, α nominal represents the nominal proportion of each cutting edge element in a single revolution. N flute is the nominal number of tool edges. For example, in a four-edge tool, N flute = 4, α i represents the actual proportion of each cutting edge element.

[0015] Preferably, the Tri-Dexel workpiece model is used for three-dimensional digital reconstruction by the Tri-Dexel model. The Tri-Dexel model is discretized along the orthogonal coordinate axes, and the workpiece geometric structure is decomposed into a set of parallel line segments on a regular grid. The data structure is "matrix + linked list", where the matrix is used to store the header nodes of the linked list, including the address of the next section of the linked list and the two coordinates (a, b) corresponding to the parallel lines; the linked list nodes store the address of the next section of the linked list and the line segment information; each line segment is precisely anchored to the workpiece surface by two endpoints, and the endpoint coordinates t1, t2 (t1 < t2) and the corresponding normal vector information are integrated and stored; for the irregular blank geometry, it is initialized by constructing an over-boundary Tri-Dexel model and performing a Boolean intersection operation with the original blank; the model sampling accuracy is determined by the grid density, and its value is quantified by the sampling spacing, and the corresponding spacing is proportional to the geometric detail restoration degree.

[0016] Preferably, the process of obtaining the tool swept volume is as follows: According to the coordinate vectors of the starting and ending positions of each NC step and the tool axis vector, equidistant interpolation is performed on the tool triangular mesh to obtain the tool swept volume.

[0017] Preferably, the process of material removal is the change of the workpiece geometry as the tool feeds along the milling trajectory. By calculating the intersection points of each grid and the workpiece Tri-Dexel rays and the corresponding normals, the meshing area is detected to obtain the corresponding removed material; among them, the convex algorithm is used to obtain the corresponding intersection points, and the normal at the intersection points is obtained through the cross product calculation. The specific calculation process is as follows:

[0018] Denote the triangular mesh grid point as (x i , y i , z i ), i = 1, 2, 3. The points within the triangular mesh are expressed as:

[0019]

[0020] Among them, m, n, and (1 - m - n) respectively represent the centroid coordinates of the point (x, y, z) in the triangle with vertices (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3). Given any two of x, y, and z, m and n are solved through the above formula, and it is determined whether the point is within the grid, thereby obtaining the intersection point. Through cross product calculation, the normal vector at the intersection point is obtained simultaneously, and the expression is as follows:

[0021]

[0022] Preferably, the process of extracting the cutting engagement area in step 3 is as follows: The improved empty ball determination algorithm (Any EmptyBall, AEB) is used to determine the engagement state of the cutting micro-elements: With the cutting micro-element as the center, two characteristic spheres are constructed in combination with adjacent engagement points: The centers of the spheres are coplanar with the cutting element and the engagement points, and the four points form a rhombus topological structure on the normal vector plane. When there are no other engagement points within the sphere domain, it is determined as an empty ball. All engagement points within a radius of 2R are traversed to generate spheres. If any empty ball exists, it is determined that the cutting micro-element is out of the engagement area and does not participate in cutting. Otherwise, the cutting micro-element is within the engagement area and participates in cutting.

[0023] Preferably, the calculation expression of the nominal instantaneous undeformed chip thickness of each cutting edge element in step 3 is as follows:

[0024]

[0025] In the formula, h i represents the nominal instantaneous undeformed chip thickness of each cutting edge element; represents the feed vector; represents the normal vector; k i represents the compensation coefficient.

[0026] Preferably, the process of predicting the cutting forces of each participating cutting edge element using a neural network trained based on simulation data in step 4 is as follows: Meshing analysis decouples the instantaneous cutting process into a series of orthogonal cutting element sets. Each unit is compiled into a structured input vector containing cutting width, chip thickness, and velocity vector, which is used as the input of the neural network to establish a non-linear mapping of cutting parameters - acting forces, and outputs the tangential, radial, and axial three-component force vectors; among them, the neural network adopts a hybrid training strategy, specifically: Finite element simulation generates multi-physical field coupling data, including cutting width, chip thickness, and velocity vector, and an orthogonal cutting test bench obtains the measured data of tool - material cutting, including the three-way average cutting force vector, to train the neural network. Finally, the cutting forces of each participating cutting edge element are predicted through the trained neural network.

[0027] Preferably, the expression of the synthesized cutting force field F in step 5 is as follows:

[0028]

[0029] Wherein, represents the radial force of each cutting edge element; represents the tangential force of each cutting edge element; represents the axial force of each cutting edge element; represents the x-axis component of the cutting force of each cutting edge element; represents the y-axis component of the cutting force of each cutting edge element; represents the z-axis component of the cutting force of each cutting edge element; R i represents the rotation matrix of the coordinate system of each cutting edge element with respect to the workpiece coordinate system; F i represents the cutting force vector of each cutting edge element in the cutting edge element coordinate system; represents the coordinates of the radial unit vector of the cutting edge element coordinate system in the workpiece coordinate system; represents the coordinates of the tangential unit vector of the cutting edge element coordinate system in the workpiece coordinate system; represents the coordinates of the axial unit vector of the cutting edge element coordinate system in the workpiece coordinate system.

[0030] Therefore, the present invention adopts the above-mentioned discrete point-based cutting force prediction method that supports arbitrary cutting edge shapes, and has the following beneficial effects:

[0031] (1) A dual-module modeling method is proposed: the tool rotating body is described by a triangular mesh, and the discrete point cloud represents an arbitrary edge shape;

[0032] (2) An enhanced point-based CWE extraction algorithm is developed: the machining process is discretized into explicit orthogonal cutting units to accurately calculate the instantaneous contact parameters;

[0033] (3) A neural network prediction model trained with a hybrid dataset is constructed: integrating physical simulation and measured data to improve the prediction robustness under variable geometric conditions.

[0034] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Description of the Drawings

[0035] Figure 1 is the overall flowchart of a discrete point-based cutting force prediction method that supports arbitrary cutting edge shapes according to the present invention;

[0036] Figure 2 is the dual-modal modeling strategy diagram of the embodiment of the present invention;

[0037] Figure 3 is the schematic diagram of correcting the feed per tooth and chip thickness according to the compensation coefficient in the embodiment of the present invention, wherein, (a) is the compensation coefficient distribution diagram of the tool with uneven cutting edge helix angle; (b) is the compensation coefficient distribution diagram of the tool with uneven number of cutting edges;

[0038] Figure 4 Schematic diagram of decomposing the geometric structure of the workpiece in the embodiment of the present invention into a set of parallel line segments on a regular grid;

[0039] Figure 5 Schematic diagram of material removal in the embodiment of the present invention;

[0040] Figure 6 Schematic diagram of accurately analyzing the transient tool-workpiece contact area through point cloud interference detection in the embodiment of the present invention;

[0041] Figure 7 Schematic diagram of using an improved empty sphere determination algorithm to discriminate the meshing state of cutting micro-elements in the embodiment of the present invention;

[0042] Figure 8 Graph of constructing a micro-element cutting force model based on a neural network in the embodiment of the present invention. Detailed implementation manners

[0043] The following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention.

[0044] Please refer to Figures 1 - 8 , a discrete point-based cutting force prediction method supporting arbitrary cutting edge shapes, comprising the following steps:

[0045] Step 1: Represent both the workpiece and the tool in a discrete model, define the milling trajectory as a series of linear segments through NC code, and build a tool and cutting edge model and a Tri-Dexel workpiece model; wherein, each linear segment includes target coordinates, tool axial attitude, feed rate, and spindle speed; wherein, the construction of the tool and cutting edge model includes the construction of the cutting tool and the cutting edge; wherein, the cutting tool adopts a dual-modal modeling strategy, as Figure 2 shown: The rotating body part is constructed by triangular meshes for tool swept volume calculation and dynamic meshing analysis; the cutting edge part adopts a high-density point cloud topology, and each discrete point corresponds to an orthogonal cutting element; the specific construction process is as follows: The rotating body is generated by rotating a two-dimensional contour around an axis to form triangular meshes. The data structure of the triangular meshes consists of three parts, namely a 3×N point array to store the point coordinates on the contour, and two 3×N surface respectively store the indices of the points forming the triangular faces and the normal vectors of the triangular faces; the multi-dimensional geometric parameters of the cutting edge point cloud are independently stored in a cache in the form of an array, including spatial coordinates (3×N edge ), tangent / normal / axial unit vectors (3×3×Nedge )、 Rotation radius (1×N edge ) and front / rear angle (2×N edge ) attributes, where N point represents the number of grid points of the tool rotating body, N surface represents the number of triangular faces of the tool rotating body, N edge represents the number of cutting edge elements after discretization of the cutting edge; This decoupled modeling supports the accurate characterization of complex cutting edge configurations such as asymmetric helix angles and non-uniform pitches, and allows different sampling strategies for the rotating body and the cutting edge - the rotating body accuracy matches the macroscopic geometric constraints of the tool, and the sampling density of the cutting edge is optimized for the microscopic meshing state. In the construction of the cutting edge, by introducing a compensation coefficient k i for each cutting edge element, the influence of the spatial distribution of the cutting edge is eliminated and the accurate chip thickness is obtained. In addition, through this coefficient, the feed per tooth and chip thickness of each cutting edge element are independently corrected according to their actual proportion in a single revolution. As Figure 3 shown in the compensation coefficient distribution diagrams in different cases, (a) is the compensation coefficient distribution of a tool with non-uniform helix angle, and (b) is the compensation coefficient distribution of a tool with non-uniform number of cutting edges. The expression of the compensation coefficient k i is as follows:

[0046]

[0047] In the formula, α nominal represents the nominal proportion of each cutting edge element in a single revolution, N flute is the nominal number of cutting edges of the tool. For example, in a four-edge tool, N flute = 4, α i represents the actual proportion of each cutting edge element.

[0048] The Tri-Dexel workpiece model uses the Tri-Dexel model for three-dimensional digital reconstruction. The Tri-Dexel model decomposes the workpiece geometric structure into a set of parallel line segments on a regular grid by discretization along the orthogonal coordinate axes. As Figure 4As shown, the data structure is "matrix + linked list", where the matrix is used to store the header nodes of the linked list, including the address of the next section of the linked list and the two coordinates (a, b) corresponding to the parallel lines; the linked list nodes store the address of the next section of the linked list and the line segment information; each line segment is precisely anchored to the workpiece surface by two endpoints, and the endpoint coordinates t1, t2 (t1 < t2) and the corresponding normal vector information are integrated and stored; for example, for the Dexel in the z direction, a linked list node represents a straight line at x = a, y = b, where z = t1 and z = t2 are two points on the workpiece surface, and the space between the two points is filled with workpiece material. For irregular blank geometries, initialization is achieved by constructing an over-boundary Tri-Dexel model and performing a Boolean intersection operation with the original blank; the model sampling accuracy is determined by the grid density, and its value is quantified by the sampling spacing, and the corresponding spacing is proportional to the geometric detail restoration degree. In practical applications, the grid density is dynamically adjusted according to the minimum feature size of the workpiece to achieve an optimal balance between millimeter-level detail capture and computational efficiency.

[0049] Step 2: Obtain the tool swept volume and calculate the material removal; update the Tri-Dexel workpiece model based on the completed NC process steps and calculate the removed material; among them, the process of obtaining the tool swept volume is as follows: according to the coordinate vectors of the starting and ending positions of each NC step and the tool axis vector, perform equidistant interpolation on the tool triangular mesh to obtain the tool swept volume. The process of material removal is the change of the workpiece geometry as the tool feeds along the milling trajectory. By calculating the intersection points of each grid and the workpiece Tri-Dexel ray and the corresponding normal vectors, the meshing area is detected to obtain the corresponding removed material; the material removal is essentially a Boolean operation on the tool swept volume and the three-way ray model, as Figure 5 shown; among them, a convex algorithm is used to obtain the corresponding intersection points, and the normal vectors at the intersection points are obtained through cross product calculation. The specific calculation process is as follows:

[0050] Denote the triangular mesh grid point as (x i , y i , z i ), i = 1, 2, 3, and represent the points inside the triangular mesh as:

[0051]

[0052] Among them, m, n, and (1 - m - n) respectively represent the barycentric coordinates of the point (x, y, z) in the triangle with (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) as vertices. Given any two of x, y, z, solve for m and n through the above formula and determine whether the point is inside the grid to obtain the intersection points; through cross product calculation, the normal vectors at the intersection points are obtained simultaneously, and the expression is as follows:

[0053]

[0054] Step 3: Extract the cutting engagement zone (CWE) and calculate the nominal instantaneous undeformed chip thickness of each cutting edge element; Subdivide the tool movement into smaller analysis steps to obtain the cutting conditions per revolution, determine the cutting engagement area and the cutting edge elements participating in cutting for each analysis step, and simultaneously calculate the nominal instantaneous undeformed chip thickness (IUCT) of each cutting edge element based on the actual feed direction, normal vector, and compensation coefficient; Among them, the process of extracting the cutting engagement zone is as follows: The CWE during the machining process is accurately analyzed through point cloud interference detection, as Figure 6 shown. Intersect the material removal area obtained based on Boolean subtraction with the tool mesh, filter the valid engagement points where the included angle between the feed direction and the normal vector is acute, and form a high-density point cloud set distributed on the tool surface. The characterization accuracy of this point cloud is strictly synchronized with the Tri-Dexel workpiece model to ensure the millimeter-level restoration of the three-dimensional engagement state; Use an improved empty ball determination algorithm (Any Empty Ball, AEB) to determine the engagement state of cutting micro-elements, as Figure 7 shown: Taking the cutting micro-element as the center, construct two characteristic spheres in combination with adjacent engagement points: The center of the sphere is coplanar with the cutting element and the engagement point, and the four points form a rhombus topological structure on the normal vector plane (the side length R is taken as 1.5 - 2 times the sampling interval). When there are no other engagement points within the sphere domain, it is determined as an empty ball. Traverse all the engagement points within a radius of 2R to generate spheres. If any empty ball exists, it is determined that the cutting micro-element is out of the engagement area and does not participate in cutting. Otherwise, the cutting micro-element is within the engagement area and participates in cutting. This algorithm replaces the global boundary reconstruction through local point cloud traversal, significantly reducing the computational complexity while ensuring the sub-millimeter-level detection accuracy.

[0055] The calculation expression for the nominal instantaneous undeformed chip thickness of each cutting edge element is as follows:

[0056]

[0057] In the formula, h i represents the nominal instantaneous undeformed chip thickness of each cutting edge element; represents the feed vector; represents the normal vector; k i represents the compensation coefficient.

[0058] Step 4: Discretize the cutting conditions into multiple orthogonal cutting units, and use a neural network trained based on simulation and experimental data to predict the cutting forces of each participating cutting edge element; The specific process is as follows: Engagement analysis decouples the instantaneous cutting process into a set of series orthogonal cutting elements. Each unit is compiled into a structured input vector containing the cutting width, chip thickness, and velocity vector, which is used as the input of the neural network to establish a non-linear mapping of cutting parameters - force, and outputs the tangential, radial, and axial three-component force vectors, as Figure 8As shown in the figure; among them, the neural network adopts a hybrid training strategy, specifically: the finite element simulation generates multi-physical field coupling data, including cutting width, chip thickness, and velocity vector, and the orthogonal cutting test bench obtains the measured data of tool-material cutting, including the three-way average cutting force vector, and uses this to train the neural network. Finally, the cutting force of each participating cutting edge element is predicted through the trained neural network.

[0059] Step 5: Integrate the cutting forces of all participating cutting edge elements to obtain the synthetic cutting force field for each analysis step; among them, the expression of the synthetic cutting force field F is as follows:

[0060]

[0061] In the formula, represents the radial force of each cutting edge element; represents the tangential force of each cutting edge element; represents the axial force of each cutting edge element; represents the x-axis component of the cutting force of each cutting edge element; represents the y-axis component of the cutting force of each cutting edge element; represents the z-axis component of the cutting force of each cutting edge element; R i represents the rotation matrix of each cutting edge element coordinate system with respect to the workpiece coordinate system; F i represents the cutting force vector of each cutting edge element in the cutting edge element coordinate system; represents the coordinate of the radial unit vector of the cutting edge element coordinate system in the workpiece coordinate system; represents the coordinate of the tangential unit vector of the cutting edge element coordinate system in the workpiece coordinate system; represents the coordinate of the axial unit vector of the cutting edge element coordinate system in the workpiece coordinate system.

[0062] Therefore, the present invention adopts the above-mentioned discrete point-based cutting force prediction method that supports any cutting edge shape, independently separates the cutting edge from the rotational body mesh, uses the point cloud characterization technology to accurately describe the edge line characteristics of any geometric shape, and combines the dynamic interference detection algorithm to real-time analyze the cutting contact area; by constructing a hybrid-driven cutting force prediction model, it effectively improves the force field prediction ability in variable geometry machining scenarios and provides theoretical support for the process optimization of complex tools in multi-axis linkage machining.

[0063] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that: they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A discrete point-based cutting force prediction method supporting any cutting edge shape, characterized in that It includes the following steps: Step 1: Represent both the workpiece and the tool as discrete models. Define the milling trajectory as a series of linear segments through NC code, and build the tool and cutting edge models and the Tri-Dexel workpiece model. Among them, each linear segment contains the target coordinates, the tool axial attitude, the feed rate, and the spindle speed. Step 2: Obtain the tool swept volume and calculate the material removal. Update the Tri-Dexel workpiece model based on the completed NC operation step, and calculate the removed material. Step 3: Extract the cutting engagement zone and calculate the nominal instantaneous undeformed chip thickness of each cutting edge element. Subdivide the tool movement into smaller analysis steps to obtain the cutting conditions per revolution, determine the cutting engagement area and the cutting edge elements participating in cutting for each analysis step, and calculate the nominal instantaneous undeformed chip thickness of each cutting edge element based on the actual feed direction, normal vector, and compensation coefficient. Step 4: Discretize the cutting conditions into multiple orthogonal cutting elements, and use a neural network trained based on simulation and experimental data to predict the cutting forces of each participating cutting edge element. Step 5: Integrate the cutting forces of all participating cutting edge elements to obtain the synthetic cutting force field for each analysis step.

2. The discrete point-based cutting force prediction method for supporting any cutting edge shape according to claim 1, wherein: The construction of the cutting tool and cutting edge models in Step 1 includes the construction of the cutting tool and the cutting edge. Among them, the cutting tool adopts a dual-modal modeling strategy: the rotating body part is constructed by triangular meshes, which are used for the calculation of the tool swept volume and dynamic meshing analysis; the cutting edge part adopts a high-density point cloud topology, and each discrete point corresponds to an orthogonal cutting element. The specific construction process is as follows: the rotating body is generated by rotating a two-dimensional contour around an axis to form triangular meshes. The data structure of the triangular meshes consists of three parts, namely a 3×N point array to store the point coordinates on the contour, and two 3×N surface arrays to store the indices of the points forming the triangular faces and the normal vectors of the triangular faces respectively; the multi-dimensional geometric parameters of the cutting edge point cloud are independently stored in the cache in the form of arrays, including the spatial coordinates (3×N edge ), the tangent / normal / axial unit vectors (3×3×N edge ), the rotation radius (1×N edge ), and the rake / clearance angles (2×N edge ) attributes. Among them, N point represents the number of grid points of the tool rotating body, N surface represents the number of triangular faces of the tool rotating body, and N edge represents the number of cutting edge elements after discretization of the cutting edge.

3. A discrete point-based cutting force prediction method for supporting any cutting edge shape according to claim 2, characterized in that In the construction of the cutting edge, by introducing a compensation coefficient k for each cutting edge microelement i , the influence of the spatial distribution of the cutting edge is eliminated and the accurate chip thickness is obtained. The expression of the compensation coefficient k i is as follows: where α nominal represents the nominal proportion of each cutting edge element in a single revolution, N flute is the nominal number of cutting edges of the tool, and α i represents the actual proportion of each cutting edge element.

4. A discrete point-based cutting force prediction method for supporting any cutting edge shape according to claim 3, characterized in that The Tri-Dexel workpiece model uses the Tri-Dexel model for three-dimensional digital reconstruction. The Tri-Dexel model is discretized along the orthogonal coordinate axes, decomposing the workpiece geometric structure into a set of parallel line segments on a regular grid. The data structure is "matrix + linked list", where the matrix is used to store the header nodes of the linked list, including the address of the next section of the linked list and the two coordinates (a, b) corresponding to the parallel lines; the linked list nodes store the address of the next section of the linked list and the line segment information; each line segment is precisely anchored to the workpiece surface by two endpoints, and the endpoint coordinates t1, t2 (t1 < t2) and the corresponding normal vector information are integrated and stored; for irregular blank geometries, initialization is achieved by constructing an over-bound Tri-Dexel model and performing a Boolean intersection operation with the original blank; the model sampling accuracy is determined by the grid density, and its value is quantified by the sampling interval, and the corresponding interval is directly proportional to the geometric detail restoration degree.

5. A discrete point-based cutting force prediction method for supporting any cutting edge shape according to claim 4, characterized in that: The process of obtaining the tool swept volume is as follows: According to the coordinate vectors of the starting and ending positions of each NC step and the tool axial vector, perform equidistant interpolation on the tool triangular mesh to obtain the tool swept volume.

6. A discrete point-based cutting force prediction method for supporting any cutting edge shape according to claim 5, characterized in that: The process of material removal is the change of the workpiece geometry as the tool feeds along the milling trajectory. Detect the engagement area by calculating the intersection points of each grid and the Tri-Dexel rays of the workpiece and the corresponding normals, and obtain the corresponding removed material. Among them, the convex algorithm is used to obtain the corresponding intersection points, and the normal at the intersection point is obtained through cross product calculation. The specific calculation process is as follows: Denote the grid points of the triangular mesh as (x i , y i , z i ), where i = 1, 2, 3. Represent the points within the triangular mesh as: Among them, m, n, and (1 - m - n) respectively represent the barycentric coordinates of the point (x, y, z) in the triangle with vertices (x1, y1, z1), (x2, y2, z2), (x3, y3, z3). Arbitrarily given two of x, y, z, solve for m, n through the above formula, and determine whether the point is within the grid to obtain the intersection point; through cross product calculation, the normal at the intersection point is obtained simultaneously, and the expression is as follows:

7. A discrete point-based cutting force prediction method for supporting any cutting edge shape according to claim 6, characterized in that The process of extracting the cutting engagement zone in Step 3 is as follows: An improved empty sphere determination algorithm is used to determine the engagement state of the cutting micro-elements. With the cutting micro-element as the center, two characteristic spheres are constructed by combining adjacent engagement points. The centers of the spheres are coplanar with the cutting element and the engagement points, and the four points form a rhombus topological structure on the normal vector plane. When there are no other engagement points within the sphere domain, it is determined as an empty sphere. All engagement points within a radius of 2R are traversed to generate spheres. If any empty sphere exists, it is determined that the cutting micro-element is out of the engagement zone and does not participate in cutting. Otherwise, the cutting micro-element is within the engagement zone and participates in cutting.

8. A discrete point-based cutting force prediction method for supporting any cutting edge shape according to claim 7, characterized in that The calculation expression of the nominal instantaneous undeformed chip thickness of each cutting edge element in Step 3 is as follows: where h i represents the nominal instantaneous undeformed chip thickness of each cutting edge element; represents the feed vector; represents the normal vector; k i represents the compensation coefficient.

9. A discrete point-based cutting force prediction method for supporting any cutting edge shape according to claim 8, characterized in that The process of predicting the cutting forces of each participating cutting edge element using a neural network trained based on simulation data in Step 4 is as follows: The engagement analysis decouples the instantaneous cutting process into a set of serial orthogonal cutting elements. Each element is compiled into a structured input vector containing the cutting width, chip thickness, and velocity vector, which is used as the input of the neural network to establish a non-linear mapping between cutting parameters and the acting forces, and outputs the tangential, radial, and axial three-component force vectors. Among them, the neural network adopts a hybrid training strategy, specifically: Finite element simulation generates multi-physical field coupling data, including cutting width, chip thickness, and velocity vector, and an orthogonal cutting test bench obtains the measured data of tool-material cutting, including the three-direction average cutting force vector, to train the neural network. Finally, the cutting forces of each participating cutting edge element are predicted through the trained neural network.

10. A discrete point-based cutting force prediction method for supporting any cutting edge shape according to claim 9, characterized in that: The expression of the synthesized cutting force field F in Step 5 is as follows: In the formula, represents the radial force of each cutting edge element; represents the tangential force of each cutting edge element; represents the axial force of each cutting edge element; represents the x-axis component of the cutting force of each cutting edge element; represents the y-axis component of the cutting force of each cutting edge element; represents the z-axis component of the cutting force of each cutting edge element; R i represents the rotation matrix of the coordinate system of each cutting edge element with respect to the workpiece coordinate system; F i represents the cutting force vector of each cutting edge element in the cutting edge element coordinate system; represents the coordinates of the radial unit vector of the cutting edge element coordinate system in the workpiece coordinate system; represents the coordinates of the tangential unit vector of the cutting edge element coordinate system in the workpiece coordinate system; represents the coordinates of the axial unit vector of the cutting edge element coordinate system in the workpiece coordinate system.

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