Tri-dexel model based on linked list and machining simulation method

Abstract

The application discloses a tri-dexel model based on a linked list and a machining simulation method, and belongs to the technical field of precision machining. The model adopts a three-level linked list structure of a line segment node, a ray node and a grid node to replace a traditional array to construct a dexel grid in X, Y and Z directions. The method comprises the following steps: initializing the model to construct a workpiece digital twin; calculating a tool-workpiece engagement area; dynamically updating a line segment through in-situ adding, deleting and modifying operations of the linked list node, realizing material removal simulation, and synchronizing three-direction data; and finally, visualizing and outputting results. The tri-dexel model based on the linked list and the machining simulation method provided by the application dynamically store through the linked list and cooperatively manage in three directions, overcome the problems of low dynamic operation efficiency, large memory redundancy and poor cooperativeness of the traditional method, and significantly improve the real-time performance, precision and memory efficiency of the machining simulation.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of precision machining, and particularly relates to a tri-dexel model based on a linked list and a machining simulation method. BACKGROUND

[0002] In the field of precision numerical control machining, such as the manufacturing process of complex parts such as aircraft engine blades and blisks, machining simulation technology is crucial for predicting cutting force, optimizing tool path, ensuring workpiece surface quality and avoiding tool and machine tool collision. Among them, the dynamic, accurate and efficient expression of the geometric appearance of the workpiece blank in the cutting process is the core and bottleneck of the simulation system.

[0003] Currently, the technical route for realizing the simulation of the geometric evolution of the workpiece in the machining process mainly includes the following categories:

[0004] The first category is the finite element method (FEM). This method can realize the coupling simulation of multiple physical fields and has high calculation accuracy. However, the calculation amount is extremely large, and the single-step simulation of complex tool paths usually takes more than 100 milliseconds, which is difficult to meet the efficiency requirements of online real-time simulation, and is mainly used for offline analysis and process verification.

[0005] The second category is the analytical method. This method is based on empirical formula and simplified assumptions for mechanical prediction, and has fast calculation speed. However, when dealing with asymmetric spiral angles, variable pitch and other special-shaped tools or complex cutting conditions, the model simplification will introduce a large error, and the force prediction error may exceed 15%, limiting the accuracy and adaptability.

[0006] The third category is the machine learning method. This method predicts through data-driven, but the generalization ability is seriously dependent on the coverage of the training data, and it is difficult to cover all the combinations of cutting parameters in all working conditions, and the model lacks clear physical mechanism inside, making it difficult to accurately represent the three-dimensional dynamic changing tool-workpiece contact domain.

[0007] The fourth category is geometric representation methods based on voxels or dexels (depth pixels). Among them, the tri-dexel model, due to its relatively simple geometric representation and high Boolean operation efficiency, has become one of the mainstream technologies for dynamic description of remaining material in workpieces. Traditional tri-dexel models typically use arrays or static lists as the underlying storage structure. However, this structure has significant drawbacks: First, dynamic operation efficiency is low. Machining simulation requires frequent addition, deletion, modification, and query operations on dexel segments. When performing these operations, the array structure often needs to move a large amount of data, resulting in long calculation times per analysis step, often exceeding 1 millisecond, which cannot meet the microsecond-level response requirements of online real-time simulation. Second, memory utilization is poor. To avoid dynamic expansion during simulation, the static array needs to pre-allocate the memory required under maximum working conditions. In non-full-load scenarios, the memory redundancy rate often exceeds 30%, making it particularly unsuitable for long-term, multi-step machining simulations of complex parts. Finally, multi-directional coordination is insufficient. The dexel data in the X, Y, and Z directions are usually stored independently, lacking a unified and efficient dynamic interface. This makes it difficult to respond synchronously and accurately to local geometric changes in the 3D machining area, resulting in a trade-off between simulation accuracy and real-time performance.

[0008] In summary, existing technologies all suffer from shortcomings in computational efficiency, memory usage, or model accuracy. Therefore, constructing a novel tri-dexel data structure that enables efficient dynamic operation, low memory consumption, and accurate synchronous representation of three-dimensional geometric changes has become crucial for overcoming existing technological bottlenecks and achieving high-precision real-time machining simulation of complex parts. Summary of the Invention

[0009] The purpose of this invention is to provide a tri-dexel model based on linked lists and a processing simulation method to solve the problems of low dynamic operation efficiency, large memory consumption, and poor multi-directional coordination in existing technologies.

[0010] To achieve the above objectives, this invention provides a tri-dexel model based on linked lists, comprising three dexel grids arranged along three orthogonal directions (X, Y, Z); the data structure of each dexel grid adopts a three-level linked list structure, which includes:

[0011] A LineNode is used to dynamically store a single dexel line segment. The LineNode records the start and end coordinates of the line segment and contains a dynamic pointer to the next LineNode.

[0012] A RayNode is used to associate a sampled ray. The RayNode records the spatial coordinates of the ray and contains a pointer to the head node of a linked list composed of line segment nodes.

[0013] A grid node (Dexel) is used for managing global information of a dexel grid in one direction, and records the dimension, coordinate range and sampling direction identifier of the grid, and contains a matrix for storing all ray nodes.

[0014] Preferably, the line segment node is a variable structure body, and its member variables include: c1 representing the starting coordinates of the line segment, c2 representing the ending coordinates of the line segment, and a dynamic pointer LineNext pointing to the next line segment node.

[0015] Preferably, the ray node is a variable structure body, and its member variables include: a representing the first coordinate of the ray on the plane perpendicular to the sampling direction, b representing the second coordinate of the ray on the plane perpendicular to the sampling direction, and a pointer LineHead pointing to the head node of the line segment linked list.

[0016] Preferably, the grid node is a structure body, and its member variables include: the number of rows n of the grid in the a coordinate direction, the number of columns m of the grid in the b coordinate direction, the minimum value a_min of the a coordinate, the minimum value b_min of the b coordinate, a statistical matrix statis for storing the number of line segment nodes corresponding to each ray node, a matrix blocks for storing all ray nodes, and an identifier dir representing the sampling direction.

[0017] The application also provides a machining simulation method based on a linked list tri-dexel model, which comprises the following steps:

[0018] Step 1: constructing a workpiece geometric digital twin by initializing a Tri-Dexel model; creating a three-direction dexel grid according to machining task parameters to construct a workpiece geometric digital twin body;

[0019] Step 2: determining the instantaneous removal area by calculating the tool-workpiece engagement relationship; constructing a tool instantaneous model in real time for each machining analysis step to solve the contact area and determine the instantaneous removal area;

[0020] Step 3: realizing material removal simulation by performing Boolean operation and line segment dynamic update; performing Boolean operation based on the engagement relationship, completing dexel line segment update through in-situ operation of the linked list, and realizing material removal simulation;

[0021] Step 4: realizing real-time feedback and data archiving by visualizing the machining process and outputting the results; converting the updated geometric data into visual effects, monitoring the machining state in real time and completing data archiving, and realizing simulation feedback.

[0022] Preferably, the process of step 1 is as follows:

[0023] S11, parameter input: specify the three-dimensional coordinate range of the blank (x_min / x_max, y_min / y_max, z_min / z_max), geometric tolerance (control edge accuracy, usually 0.01mm), and sampling interval (control grid density, set according to the minimum machining feature size, such as 0.1mm);

[0024] S12, grid generation: call the tri-dexel initialization interface, automatically calculate the X / Y / Z three-direction grid dimension (n x m), create a ray node for each grid unit, and initialize the line segment node linked list (the initial line segment covers the entire blank range, representing the workpiece in the unprocessed state);

[0025] S13, data verification: count the total number of initial line segments in each direction through the statis matrix, and ensure that the three-direction dexel grid completely covers the blank area.

[0026] Preferably, the process of step 2 is as follows:

[0027] S21, tool posture acquisition: read the current tool position (X / Y / Z coordinates) and spindle angle (such as A / C axis angle for five-axis machining) from the numerical control system, and construct a three-dimensional instantaneous tool model combined with tool geometric parameters, including diameter, edge length and helix angle;

[0028] S22, meshing area solving: through the space intersection operation of the tri-dexel model and the instantaneous three-dimensional tool model, the workpiece area cut by the tool is determined, specifically: use the tri-dexel model and the triangular mesh model of the tool rotating body to carry out efficient intersection calculation. The line-surface intersection points of the material removal part and the tool rotating body grid are obtained, and the point cloud formed by these intersection points is the tool-workpiece meshing area corresponding to the current time. According to the relative position of these intersection points and the dexel line segment, the dexel that needs to be removed or modified is obtained;

[0029] S23, result output: generate a "ray index-to-be-removed line segment range" list to clearly specify the line segment node that needs to be modified in each ray node and its c1 / c2 coordinate interval.

[0030] Preferably, the process of step 3 is as follows:

[0031] S31, line segment splitting and deletion: for each ray node to be processed, the following processing is performed: first, traverse its line segment node linked list to find the line segment that overlaps with the meshing area; then judge and operate the overlapping area of the line segment and the tool;

[0032] S32, three-directional cooperative update: synchronously processing X / Y / Z three-directional dexel grids, ensuring that the removal of the same material area is reflected in the three-directional models, and avoiding inconsistent geometric representations;

[0033] S33, statistical matrix update: after completing the line segment modification of each ray node, synchronously updating the line segment count of the corresponding unit in the statis matrix, and providing data scale reference for subsequent visualization.

[0034] Preferably, the content of judging and operating the overlapping area of the line segment and the tool in S31 comprises:

[0035] If the line segment is completely covered by the tool, the line segment node is removed through the in-situ deletion operation (modifying the LineNext pointer of the predecessor node);

[0036] If the line segment is partially covered, the original line segment node is split into a non-removed segment and a removed segment, the non-removed segment is retained (updating its c1 / c2 coordinates), and the removed segment is deleted.

[0037] Preferably, the process of step 4 is as follows:

[0038] S41, real-time visualization generation: after completing each analysis step, calling the point cloud generation interface to extract all line segment endpoint coordinates from the line segment node linked list of the three-directional dexel grid;

[0039] S42, coordinate mapping and rendering: mapping the endpoint coordinates to three-dimensional space points (converting a / b / c to X / Y / Z according to the sampling direction), differentiating the color according to the direction, and then rendering and displaying through the visualization interface;

[0040] S43, interaction and monitoring: the visualization interface supports zooming and rotating operations, real-time monitoring of the relative position of the tool trajectory and the remaining material of the workpiece, and archiving of the machining data.

[0041] Therefore, the tri-dexel model and the machining simulation method based on the linked list have the following beneficial effects:

[0042] (1) By using the linked list structure to store the dexel line segment, only the pointer of the related node needs to be modified when inserting, deleting and splitting the line segment, without large-scale data migration, which meets the stringent requirements of online real-time simulation;

[0043] (2) The linked list structure dynamically allocates and releases memory on demand, only stores the actual existing effective line segment, and avoids the memory waste caused by the static array pre-allocation;

[0044] (3) Through the unified interface, the dexel grids in X, Y and Z directions are synchronously managed and updated, so that the geometric changes in any position can be accurately captured and uniformly reflected by the model in at least one direction, the problem of incomplete geometric representation of single-direction dexel is effectively solved, and the unification of high precision and high real-time is realized.

[0045] The technical solutions of the present application will be further described in detail below with the aid of drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 A tri-dexel model data structure based on a linked list in an embodiment of the present application;

[0047] Figure 2 A visual effect diagram of cavity machining material removal simulation in an embodiment of the present application; wherein, (a) is an initial blank tri-dexel model diagram, and (b) is a cavity tri-dexel model diagram;

[0048] Figure 3 A block diagram of the overall process of the machining simulation method in an embodiment of the present application. DETAILED DESCRIPTION

[0049] The detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative labor are within the scope of protection of the present application.

[0050] Please refer to Figure 1 A tri-dexel model based on a linked list, comprising three dexel grids arranged along three orthogonal directions X, Y and Z; the data structure of each dexel grid adopts a three-level linked list structure, and the three-level linked list structure comprises:

[0051] A line segment node (LineNode) for dynamically storing a single dexel line segment, the line segment node recording the starting coordinates and the ending coordinates of the line segment and containing a dynamic pointer pointing to the next line segment node; wherein, the line segment node is a variable structure body, and its member variables include: c1 representing the starting coordinates of the line segment, c2 representing the ending coordinates of the line segment, and a dynamic pointer LineNext pointing to the next line segment node.

[0052] RayNode, used for associating a sampling ray, the RayNode records the spatial position coordinates of the ray, and contains a pointer to the head node of the chain table composed of line segment nodes; wherein the RayNode is a variable structure body, and its member variables include: a representing the first coordinate of the ray in the plane perpendicular to the sampling direction, b representing the second coordinate of the ray in the plane perpendicular to the sampling direction, and a pointer to the line segment chain table head node LineHead.

[0053] Dexel, used for managing the global information of a dexel grid in one direction, the Dexel records the dimension, coordinate range, and sampling direction identifier of the grid, and contains a matrix storing all RayNodes; wherein the Dexel is a structure body, and its member variables include: the number of rows n of the grid in the a coordinate direction dimension, the number of columns m of the grid in the b coordinate direction dimension, the minimum value of the a coordinate a_min, the minimum value of the b coordinate b_min, the statistical matrix statis for storing the number of line segment nodes corresponding to each RayNode, the matrix blocks for storing all RayNodes, and the identifier dir representing the sampling direction.

[0054] Please refer to Figure 3 A machining simulation method based on a tri-dexel model of a linked list, comprising the following steps:

[0055] Step 1, constructing a workpiece geometric digital twin by initializing a Tri-Dexel model; creating a three-direction dexel grid according to machining task parameters, and constructing a workpiece geometric digital twin body; the specific process is as follows:

[0056] S11, parameter input: clearly defining the three-dimensional coordinate range of the blank (x_min / x_max, y_min / y_max, z_min / z_max), geometric tolerance (controlling edge accuracy, usually taking 0.01mm), and sampling interval (controlling grid density, setting according to the minimum machining feature size, such as 0.1mm);

[0057] S12, grid generation: calling the tri-dexel initialization interface, automatically calculating the X / Y / Z three-direction grid dimension (n×m), creating a RayNode for each grid unit, and initializing the line segment node chain table (the initial line segment covers the entire blank range, representing the workpiece in the unprocessed state);

[0058] S13, data verification: counting the total number of initial line segments in each direction through the statis matrix, and ensuring that the three-direction dexel grid completely covers the blank area.

[0059] Effect: establishing a one-to-one correspondence between the digital twin and the physical workpiece, and providing a basic geometric carrier for subsequent material removal simulation;

[0060] Step 2, determine the instantaneous removal area by calculating the tool-work engagement relationship; each machining analysis step constructs a tool instantaneous model in real time, solves the contact area to determine the instantaneous removal area; the specific process is as follows:

[0061] S21, tool posture acquisition: read the current tool position (X / Y / Z coordinates) and spindle angle (such as A / C axis angle of five-axis machining) from the numerical control system, combine with the tool geometric parameters, including diameter, edge length and helix angle, to construct a tool instantaneous three-dimensional model;

[0062] S22, engagement area solving: determine the workpiece area cut by the tool through the spatial intersection operation of tri-dexel model and tool instantaneous three-dimensional model, specifically: first traverse the ray nodes in the three-direction dexel grid that overlap with the current position of the tool; then calculate the intersection points of each ray node and the tool surface to obtain the line segment to be removed (i.e. the part of the original LineNode covered by the tool);

[0063] S23, result output: generate a "ray index-to-be removed line segment range" list to clearly indicate the line segment nodes that need to be modified in each ray node and their c1 / c2 coordinate intervals.

[0064] Action: accurately locate the material removal area of each step of machining to provide operation basis for dexel line segment update;

[0065] Step 3, realize material removal simulation by performing Boolean operation and line segment dynamic update; perform Boolean operation based on engagement relationship, complete dexel line segment update through in-place operation of linked list to realize material removal simulation; the specific process is as follows:

[0066] S31, line segment splitting and deletion: for each ray node to be processed, the following processing is performed: first traverse its line segment node linked list to find the line segment that overlaps with the engagement area; then judge and operate the overlapping area of the line segment and the tool, specifically:

[0067] If the line segment is completely covered by the tool, remove the line segment node through in-place deletion operation (modify the LineNext pointer of the predecessor node);

[0068] If the line segment is covered, split the original line segment node into a non-removed segment and a removed segment, keep the non-removed segment (update its c1 / c2 coordinates), delete the removed segment, which includes the left / right end coverage and uncovered end point, only covers the middle segment of the line segment, for the left / right end coverage, modify, for the uncovered end point, only cover the middle segment of the line segment, modify and add two ways, such as a line segment with starting coordinate c1 as 1 and ending coordinate c2 as 8, which is covered by a new line segment (c1 is 5, c2 is 9), then c2 is changed to 5; When this line segment with starting coordinate c1 as 1 and ending coordinate c2 as 8 is covered by another new line segment (c1 is 5, c2 is 7), then c2 is changed to 5; And add a new line segment with c1 as 7 and c2 as 8;

[0069] S32, three-directional cooperative update: synchronous processing of X / Y / Z three-directional dexel grid, ensuring that the removal of the same material area is reflected in the three-directional model, avoiding inconsistent geometric representation;

[0070] S33, statistical matrix update: after completing the line segment modification of each ray node, the line segment count of the corresponding unit in the statis matrix is updated synchronously to provide data scale reference for subsequent visualization.

[0071] Key advantage: in-situ operation based on linked list without data movement, single analysis step update time ≤0.05ms, meeting the real-time simulation requirements;

[0072] Step 4, process visualization and result output to realize real-time feedback and data archiving; convert the updated geometric data into visual effects, real-time monitor the processing state and complete data archiving, realize simulation feedback; the specific process is as follows:

[0073] S41, real-time visualization generation: after completing each analysis step, call the point cloud generation interface to extract all line segment endpoint coordinates from the line segment node linked list of the three-directional dexel grid;

[0074] S42, coordinate mapping and rendering: map the endpoint coordinates to three-dimensional space points (convert a / b / c to X / Y / Z according to the sampling direction, where c includes c1 / c2), differentiate coloring according to direction and render through the visualization interface;

[0075] S43, interaction and monitoring: the visualization interface supports zooming and rotating operations, real-time monitors the relative position of the tool path and the remaining material of the workpiece, and completes the archiving of the processing data.

[0076] It should be noted that based on multi-threading technology, the initialization and update operation of dexel grid are accelerated in parallel, and the core strategy is:

[0077] The blocks matrix is split into multiple thread tasks by row / column, and each thread is responsible for RayNode / LineNode operation of a part of grid cells (such as node creation at initialization and line segment traversal at update);

[0078] Hardware adaptation: In the environment of a 12-core CPU (Intel Core i7-12700K), multi-thread parallel processing can reduce the total time of multi-analysis steps by 40%-50%, which is suitable for machining simulation of large-scale complex parts (such as aircraft engine blades).

[0079] Embodiment

[0080] To verify the practicability and engineering adaptability of the technical scheme of the present application, a typical cavity machining scene is selected for simulation test, and the specific parameters and results are as follows:

[0081] Machining object and task: A square blank with a size of 106mm x 95mm x 24mm is selected as the blank, and the target machining task is cavity turning - machining a cavity structure with a size of 101mm x 90mm x 20.25mm and a fillet radius of 2.5mm on the blank, which meets the machining requirements of box and shell parts in mechanical manufacturing.

[0082] Simulation parameter setting: To balance the display effect and operation precision, the sampling interval is set to 0.1mm to ensure accurate representation of the fillet, side wall and other detailed features of the cavity; a 5mm ball end mill is selected as the tool, and the machining path adopts spiral downcut + ring cutting mode, which meets the actual cavity machining process specification.

[0083] Simulation results and data:

[0084] The total time of complete material removal simulation is 96.25s, and there is no geometric distortion or lag throughout the process, meeting the real-time simulation requirements;

[0085] Data storage performance: The tri-dexel model of the blank is saved as a local file with a size of only 11.3MB; the point cloud csv file generated by extracting all the sampling line segments has a size of 1.44MB; the tri-dexel model file corresponding to the cavity workpiece after machining has a size of 12.4MB, and the point cloud csv file has a size of 1.98MB, which has obvious advantages in storage lightweight and is convenient for subsequent data transmission and secondary processing;

[0086] Visualization effect: The blank and cavity workpiece images drawn based on point cloud data are shown in Figure 2 (a) and Figure 2 (b), which clearly restore the size accuracy, fillet transition and other key features of the cavity without obvious geometric deviation.

[0087] ​The application case proves that the tri-dexel model based on a linked list and the machining simulation method have engineering practical values in machining precision, calculation efficiency, storage lightweight, etc., and can be directly adapted to the machining simulation demand of complex parts in the field of mechanical manufacturing through the simulation verification of typical cavity machining scenes.

[0088] Therefore, the tri-dexel model based on a linked list and the machining simulation method are adopted, the model adopts a three-level linked list structure of a line segment node, a ray node and a grid node to replace a traditional array to construct a dexel grid in X, Y and Z directions, the whole method includes: initializing the model to construct a workpiece digital twin, calculating a tool-workpiece engagement relationship, in-situ adding, deleting, modifying and inquiring a line segment based on a linked list, dynamically updating a three-direction model to simulate material removal, and finally visualizing and outputting results.

[0089] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application but not to limit it, although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can still be modified or replaced by equivalents, 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 application.

Claims

1. A machining simulation method based on a linked list tri-dexel model, characterized in that, Includes the following steps: Step 1: Construct a workpiece geometric digital twin by initializing the Tri-Dexel model; create a three-directional dexel mesh based on the machining task parameters to construct the workpiece geometric digital twin; The tri-dexel model consists of three dexel grids arranged along the three orthogonal directions X, Y, and Z; the data structure of each dexel grid adopts a three-level linked list structure, which includes: A line segment node is used to dynamically store a single dexel line segment. The line segment node records the start and end coordinates of the line segment and contains a dynamic pointer to the next line segment node. A ray node is used to associate a sampling ray. The ray node records the spatial coordinates of the ray and contains a pointer to the head node of a linked list composed of line segment nodes. A mesh node is used to manage global information of a dexel mesh in a certain direction. The mesh node records the dimension, coordinate range, sampling direction identifier of the mesh, and contains a matrix that stores all ray nodes. Step 2: Determine the instantaneous removal area by calculating the tool-workpiece meshing relationship; construct the tool instantaneous model in real time for each machining analysis step, solve the contact area to determine the instantaneous removal area; Step 3: Implement material removal simulation by performing Boolean operations and dynamic line segment updates; perform Boolean operations based on the meshing relationship, and complete the dexel line segment update through in-situ linked list operations to achieve material removal simulation; Step 4: Visualize the processing process and output results to achieve real-time feedback and data archiving; transform the updated geometric data into a visualization effect, monitor the processing status in real time and complete data archiving to achieve simulation feedback.

2. The processing simulation method based on a linked list tri-dexel model according to claim 1, characterized in that: The line segment node is a mutable structure, whose member variables include: c1 representing the starting coordinates of the line segment, c2 representing the ending coordinates of the line segment, and a dynamic pointer LineNext pointing to the next line segment node.

3. The machining simulation method based on a linked list tri-dexel model according to claim 2, characterized in that: The ray node is a variable structure whose member variables include: a, which represents the first coordinate of the ray in the plane perpendicular to the sampling direction; b, which represents the second coordinate of the ray in the plane perpendicular to the sampling direction; and a pointer LineHead, which points to the head node of the line segment linked list.

4. The processing simulation method based on a linked list tri-dexel model according to claim 3, characterized in that: The grid node is a structure whose member variables include: the number of rows n in the a-coordinate dimension of the grid, the number of columns m in the b-coordinate dimension of the grid, the minimum value a_min in the a-coordinate, the minimum value b_min in the b-coordinate, the statistical matrix statis used to store the number of line segment nodes corresponding to each ray node, the matrix blocks used to store all ray nodes, and the identifier dir representing the sampling direction.

5. The machining simulation method based on a linked list tri-dexel model according to claim 4, characterized in that, The process of step 1 is as follows: S11. Parameter Input: Specify the three-dimensional coordinate range, geometric tolerance, and sampling interval of the blank; S12, Mesh Generation: Call the tri-dexel initialization interface to automatically calculate the mesh dimensions in the X / Y / Z directions, create ray nodes for each mesh cell, and initialize the line segment node linked list; S13. Data verification: The total number of initial line segments in each direction is counted by the statis matrix to ensure that the three-directional dexel grid completely covers the blank area.

6. The machining simulation method based on a linked list tri-dexel model according to claim 5, characterized in that, Step 2 is as follows: S21. Tool attitude acquisition: The current tool position and spindle angle are read from the CNC system, and combined with the tool geometry parameters, an instantaneous 3D model of the tool is constructed. Tool geometry parameters include diameter, cutting edge length, and helix angle; S22. Solving the meshing region: By performing spatial intersection operations between the tri-dexel model and the instantaneous three-dimensional model of the tool, the workpiece region to be cut by the tool is determined. Specifically, first, the ray nodes that overlap with the current position of the tool in the three-directional dexel mesh are traversed; then, the intersection points of each ray node and the tool surface are calculated to obtain the line segments to be removed. S23. Output: Generate a list of "Ray Index - Range of Line Segments to be Removed", specifying the line segment nodes that need to be modified in each ray node and their c1 / c2 coordinate intervals.

7. The machining simulation method based on a linked list tri-dexel model according to claim 6, characterized in that, Step 3 is as follows: S31. Segment splitting and deletion: For each ray node to be processed, the following processing is performed: First, traverse its segment node linked list to find the segment that overlaps with the meshing area; then, judge and operate the overlapping area between the segment and the tool. S32, Three-directional collaborative update: Simultaneously process the dexel mesh in the X / Y / Z directions to ensure that the removal of the same material region is reflected in the model in all three directions, avoiding inconsistencies in geometric representation; S33. Statistical Matrix Update: After each line segment modification of a ray node is completed, the line segment count of the corresponding cell in the statis matrix is ​​updated synchronously.

8. The machining simulation method based on a linked list tri-dexel model according to claim 7, characterized in that, The content of S31 regarding the judgment and operation of the overlapping area between the line segment and the tool includes: If a line segment is completely covered by the tool, the line segment node is removed by in-situ deletion. If a segment is partially covered, the original segment node is split into an unremoved segment and a removed segment. The unremoved segment is retained, and the removed segment is deleted.

9. The machining simulation method based on a linked list tri-dexel model according to claim 8, characterized in that, Step 4 is as follows: S41. Real-time visualization generation: After each analysis step is completed, the point cloud generation interface is called to extract the coordinates of all line segment endpoints from the line segment node linked list of the three-way dexel grid. S42. Coordinate Mapping and Rendering: Map the endpoint coordinates to three-dimensional spatial points, color them differently according to direction, and then render them through a visual interface. S43. Interaction and monitoring: The visual interface supports zooming and rotation operations, real-time monitoring of the relative position of the tool path and the remaining material on the workpiece, and archiving of machining data.

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