A method and system for generating three-dimensional digital models for polishing machines

Abstract

The present application relates to the technical field of digital model, especially to a three-dimensional digital model generation method and system applied to a polishing machine, which comprises the following steps: obtaining three-dimensional geometric data of a workpiece surface and kinematics parameter data of multiple swing grinding heads; performing grid discrete processing on the workpiece surface according to the three-dimensional geometric data to obtain surface grid node data containing spatial coordinate information and normal vector information; and performing mathematical modeling on the differential swing trajectory of each grinding head according to the kinematics parameter data to obtain grinding head space-time position mapping data, wherein the differential swing trajectory is specifically a uniform distribution of multiple grinding heads in the time domain and a maximum complementary coverage in the spatial domain by setting a sine function combination with different phase differences between different grinding heads. By setting different phase differences for different grinding heads, the present application realizes the optimal distribution of the grinding head motion trajectory in the time domain and the spatial domain, and eliminates the problems of trajectory overlap and coverage blind area in the multiple grinding head system.

Description

Technical Field

[0001] This invention relates to the field of digital modeling technology, and in particular to a method and system for generating three-dimensional digital models for polishing machines. Background Technology

[0002] A polishing machine is a mechanical device used to improve the surface finish and reduce roughness of workpieces. Depending on their structure and function, they can be categorized into handheld, benchtop, floor-standing, automated, and specialized types. Automated polishing machines achieve high-efficiency production through CNC and robotics technology. Their main components include a motor providing power, a polishing disc that directly contacts the workpiece, a speed control device, a control system for adjusting working parameters, workpiece clamps, a cooling system, and a dust extraction system. The polishing machine achieves a smooth and bright surface through high-speed friction between the polishing disc and the workpiece surface, divided into three stages: rough polishing, fine polishing, and mirror polishing. Key technical parameters include speed range, power, polishing accuracy, workpiece size range, and degree of automation. It is suitable for processing various materials such as metals, stainless steel, and glass. The three-dimensional digital model used in polishing machines is a virtual model constructed using computer-aided design (CAD) and computer-aided manufacturing (CAM) technologies to simulate the structure, performance, and working process of the polishing machine. Through precise modeling, the core components of the polishing machine are fully described, including the motor, polishing disc, speed change device, fixture, cooling system and dust collection device, and their operating characteristics, such as power transmission, speed adjustment and workpiece fixation, are simulated according to actual working conditions.

[0003] Traditional methods for generating 3D digital models for polishing machines often suffer from the following problems: Early polishing equipment mostly employed single-head or simple dual-head designs. These devices face an unavoidable physical limitation when processing complex workpiece surfaces: the movement trajectory of a single grinding head cannot geometrically achieve complete and uniform coverage of the workpiece surface. The polishing process involves not only the movement trajectory of the grinding head but also the complex contact mechanism between the grinding head and the workpiece surface. The contact state between each grinding head and the workpiece surface is dynamically changing at different times and positions. Factors such as pressure distribution, relative velocity, and material removal mechanisms during this contact process all affect the final polishing effect. Traditional analytical methods lack effective means to uniformly model and calculate these complex physical processes. Summary of the Invention

[0004] Therefore, it is necessary for the present invention to provide a method and system for generating three-dimensional digital models for polishing machines, in order to solve at least one of the above-mentioned technical problems.

[0005] To achieve the above objectives, a method for generating a three-dimensional digital model for a polishing machine includes the following steps:

[0006] Step S1: Obtain the three-dimensional geometric data of the workpiece surface and the kinematic parameter data of the multi-segment oscillating grinding head;

[0007] Step S2: Based on the three-dimensional geometric data, the workpiece surface is discretized into a mesh to obtain surface mesh node data containing spatial coordinate information and normal vector information;

[0008] Step S3: Based on the kinematic parameter data, perform mathematical modeling of the differential oscillation trajectory of each grinding head to obtain the spatiotemporal position mapping data of the grinding head. Specifically, the differential oscillation trajectory is achieved by setting a combination of sinusoidal functions of the π phase difference between different grinding heads to achieve uniform distribution of multiple grinding heads in the time domain and maximum complementary coverage in the spatial domain.

[0009] Step S4: Based on the surface mesh node data and the spatiotemporal position mapping data of the grinding head, perform dynamic coverage calculation on the contact relationship between the effective working area of ​​the grinding head and the workpiece surface to obtain three-dimensional polishing coverage data including the cumulative polishing time and the distribution of collaborative polishing intensity. Specifically, the dynamic coverage calculation process is to achieve accurate prediction of the polishing amount of each mesh node on the workpiece surface through the working radius of the grinding head and the polishing intensity distribution.

[0010] Step S5: Evaluate and optimize the uniformity of polishing quality based on the three-dimensional polishing coverage data to obtain three-dimensional digital polishing model data.

[0011] The present invention also provides a three-dimensional digital model generation system for a polishing machine, used to execute the above-described three-dimensional digital model generation method for a polishing machine, wherein the three-dimensional digital model generation system for a polishing machine includes:

[0012] The three-dimensional geometric data acquisition module is used to acquire the three-dimensional geometric data of the workpiece surface and the kinematic parameter data of the multi-segment oscillating grinding head;

[0013] The surface meshing module is used to perform mesh discretization on the workpiece surface based on three-dimensional geometric data to obtain surface mesh node data containing spatial coordinate information and normal vector information.

[0014] The grinding head trajectory modeling module is used to mathematically model the differential oscillation trajectory of each grinding head based on kinematic parameter data, and obtain the spatiotemporal position mapping data of the grinding head. Specifically, the differential oscillation trajectory is achieved by setting a combination of sinusoidal functions of π phase difference between different grinding heads to achieve uniform distribution of multiple grinding heads in the time domain and maximum complementary coverage in the spatial domain.

[0015] The dynamic coverage calculation module is used to perform dynamic coverage calculation on the contact relationship between the effective working area of ​​the grinding head and the workpiece surface based on the surface grid node data and the spatiotemporal position mapping data of the grinding head, and obtain three-dimensional polishing coverage data including the cumulative polishing time and the distribution of collaborative polishing intensity. Specifically, the dynamic coverage calculation process is to achieve accurate polishing amount prediction for each grid node on the workpiece surface through the working radius of the grinding head and the polishing intensity distribution.

[0016] The uniformity assessment and optimization module is used to assess and optimize the uniformity of polishing quality based on the three-dimensional polishing coverage data, and obtain three-dimensional digital polishing model data.

[0017] This invention significantly improves the uniformity and overall consistency of polished workpiece surface quality through a systematic and refined three-dimensional digital polishing model generation process. First, statistical analysis of polishing intensity based on three-dimensional polishing coverage data accurately captures global characteristics of the workpiece surface during polishing, such as mean, variance, and standard deviation, providing a scientific basis for subsequent quantification of uniformity deviation. This data-driven statistical feature analysis makes traditional experience-based polishing quality assessment more objective and precise, avoiding quality fluctuations caused by subjective human factors. By establishing a deviation distribution histogram, the system clearly reflects the deviation of polishing intensity in each region, achieving accurate assessment of workpiece surface uniformity deviation and laying a solid foundation for identifying and locating substandard areas. During the identification of quality anomaly areas, setting reasonable deviation thresholds and filtering out grid nodes exceeding the thresholds effectively distinguishes local defects or blind spots present during polishing, ensuring accurate location of anomaly areas. This fine-grained quality anomaly detection not only improves detection sensitivity but also provides a clear direction for precise adjustment of grinding head parameters, avoiding resource waste caused by blind adjustments. Furthermore, by calculating geometric feature parameters such as the centroid coordinates, area size, and boundary shape of the abnormal region, the system can characterize the spatial distribution features of the abnormal region in detail, enhancing the understanding of the spatial characteristics of defects. This geometric feature data not only aids in the matching analysis of the grinding head's working range but also promotes the precise correlation between the abnormal region and the grinding head's motion trajectory, improving the targeting and effectiveness of subsequent parameter optimization. Based on the calculation of the overlapping area ratio between the geometric features of the abnormal region and the grinding head's working range, the system establishes a grinding head responsibility scoring table, quantifying the grinding head's contribution to different abnormal regions. This scoring mechanism allows for the precise selection of key grinding heads, avoiding resource waste caused by indiscriminate adjustments and significantly improving the control efficiency and effectiveness of the polishing process. The setting of the responsibility threshold ensures that the identification of key grinding heads is neither too broad nor too stringent, balancing the comprehensiveness and accuracy of adjustments. For the selected grinding heads to be optimized, an adjustment strategy is systematically formulated based on the correspondence between defect type and parameter adjustment direction, ensuring the scientific rationality of parameter modifications. By meticulously adjusting the grinding head's oscillation amplitude, frequency, and phase difference, targeted optimization can be effectively performed for different defect types, improving the overall uniformity and coverage of the polishing process while avoiding process fluctuations and polishing quality degradation caused by over-adjustment. After updating the grinding head parameter configuration, the system generates new grinding head motion trajectories and three-dimensional polishing coverage effects through simulation, constructing a closed-loop feedback mechanism that enables continuous and dynamic adjustment of the polishing process. The coverage data after each parameter adjustment not only quantifies the optimization effect but also provides data support for the next round of optimization, ensuring the scientific rigor and precision of the adjustment process.This iterative process, through multiple rounds of parameter updates and simulation calculations, achieves gradual convergence of the polishing effect, ultimately forming a high-quality, uniform 3D digital polishing model. This technical approach, combining simulation and adjustment based on a digital model, overcomes the limitations of traditional empirical polishing methods, making the polishing process more intelligent and automated, reducing manual intervention, and improving production efficiency. The convergence judgment mechanism effectively avoids invalid loops and over-adjustment during the optimization process by quantitatively evaluating the changes in the statistical characteristics of polishing intensity in continuous iterations, ensuring the stability and accuracy of the model. This judgment process ensures that the final output 3D digital polishing model not only reflects the ideal polishing effect but also possesses high repeatability and reliability. Overall, this method, through multi-level data processing and parameter optimization, achieves precise matching between the polishing machine head movement and the workpiece surface quality, significantly improving the surface quality and processing consistency of polished workpieces, and reducing process risks and resource waste. This technical solution is applicable to various complex curved surfaces and high-precision polishing scenarios, especially in the fields of electronic components, optical components and precision mechanical parts. It can effectively improve polishing quality, meet the stringent requirements of high-end manufacturing for workpiece surface quality, and provide solid digital technical support for intelligent manufacturing and polishing processes. Attached Figure Description

[0018] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0019] Figure 1 This is a schematic diagram of the steps of a method for generating a three-dimensional digital model of a polishing machine according to the present invention;

[0020] Figure 2 for Figure 1 A detailed flowchart of step S3;

[0021] Figure 3 for Figure 1 A detailed flowchart of step S4. Detailed Implementation

[0022] The technical method of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0023] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor methods and / or microcontroller methods.

[0024] It should be understood that although the terms "first," "second," etc., may be used herein to describe various units, these units should not be limited by these terms. These terms are used merely to distinguish one unit from another. For example, without departing from the scope of the exemplary embodiments, a first unit may be referred to as a second unit, and similarly, a second unit may be referred to as a first unit. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0025] To achieve the above objectives, please refer to Figures 1 to 3 This invention provides a method for generating a three-dimensional digital model for a polishing machine, the method comprising the following steps:

[0026] Step S1: Obtain the three-dimensional geometric data of the workpiece surface and the kinematic parameter data of the multi-segment oscillating grinding head;

[0027] This invention first acquires the three-dimensional geometric data of the workpiece surface and the kinematic parameter data of the multi-segment oscillating grinding head. The three-dimensional geometric data can be obtained by acquiring point cloud data of the workpiece surface through a three-dimensional laser scanner. This point cloud data has high density and sub-millimeter accuracy. The original point cloud is converted into STL format data in the form of triangular patches by post-processing software for further use in subsequent modeling. The kinematic parameters of the multi-segment oscillating grinding head are obtained by reading the grinding head drive setting parameters in the polishing machine control system. The parameters include the oscillation frequency, amplitude, center position, initial phase of the oscillation path, periodic function type, etc. of each grinding head. In this embodiment, four independent oscillating grinding heads are used, with an oscillation frequency of 5 Hz, an amplitude of 20 mm, and initial phases of 0 degrees, 90 degrees, 180 degrees, and 270 degrees, respectively, to achieve uniform distribution on the time axis and provide a basis for subsequent spatial coverage optimization.

[0028] Step S2: Based on the three-dimensional geometric data, the workpiece surface is discretized into a mesh to obtain surface mesh node data containing spatial coordinate information and normal vector information;

[0029] After acquiring the three-dimensional geometric data, the system performs mesh discretization processing on the workpiece surface. Specifically, by importing the STL format triangular facet data into the self-developed mesh generation module for uniform subdivision, a regularly distributed triangular mesh is generated. The mesh density can be dynamically adjusted according to the complexity of the workpiece and the target polishing accuracy. In this embodiment, the mesh node spacing is set to 1 mm to ensure that small geometric undulations can be captured during polishing simulation. For each mesh node, its spatial coordinate value in three-dimensional space is calculated, and its unit normal vector is determined according to the normal direction of the triangular facet it belongs to. The coordinates and normal vectors of all nodes together constitute the surface mesh node data, providing an accurate geometric basis for subsequent polishing contact determination and strength calculation.

[0030] Step S3: Based on the kinematic parameter data, perform mathematical modeling of the differential oscillation trajectory of each grinding head to obtain the spatiotemporal position mapping data of the grinding head. Specifically, the differential oscillation trajectory is achieved by setting a combination of sinusoidal functions of the π phase difference between different grinding heads to achieve uniform distribution of multiple grinding heads in the time domain and maximum complementary coverage in the spatial domain.

[0031] This invention utilizes the kinematic parameter data of the grinding head extracted in step S1 to mathematically model the trajectory of the grinding head with multi-segment differential oscillation, thereby obtaining the precise spatial position of each grinding head at any given time. In this embodiment, the center trajectory of each grinding head is modeled as a periodic oscillation model based on a sine function, specifically representing a single-axis sinusoidal oscillation along a direction perpendicular to the normal to the workpiece surface. Different phase differences are set between the grinding heads to achieve differential motion. The phase differences of the four grinding heads are 0, π / 2, π, and 3π / 2, respectively, thus uniformly distributing their oscillation behavior on the time axis. Each time step is set to 10 milliseconds, and the spatial coordinates of each grinding head throughout the entire processing cycle are calculated using discrete time series, generating spatiotemporal position mapping data of the grinding head. Combined with the initial installation position of the grinding head and the workpiece posture relationship, the center position of the grinding head at each moment is uniformly represented in the global coordinate system, providing a basis for subsequent contact judgment and coverage modeling.

[0032] Step S4: Based on the surface mesh node data and the spatiotemporal position mapping data of the grinding head, perform dynamic coverage calculation on the contact relationship between the effective working area of ​​the grinding head and the workpiece surface to obtain three-dimensional polishing coverage data including the cumulative polishing time and the distribution of collaborative polishing intensity. Specifically, the dynamic coverage calculation process is to achieve accurate prediction of the polishing amount of each mesh node on the workpiece surface through the working radius of the grinding head and the polishing intensity distribution.

[0033] Based on the aforementioned surface mesh node data and grinding head spatiotemporal position mapping data, this invention performs dynamic coverage calculation processing, establishes an effective radius model for each grinding head, and constructs a spatial attenuation model for polishing intensity. In this embodiment, the effective effective radius of a single grinding head is set to 25 mm. A sphere with radius is constructed with the center of the grinding head as the center, and the Euclidean distance formula is used to determine whether the surface mesh node is within the sphere, thereby identifying all nodes affected by the grinding head at a certain time point. To simulate the phenomenon of actual polishing intensity weakening at the edge, a Gaussian distribution function is introduced as a polishing intensity attenuation model, i.e., the polishing intensity is greatest at the center of the grinding head and decreases exponentially with increasing distance. In this embodiment, the standard deviation of the Gaussian function is set to 10 mm. By superimposing all moments in the time dimension, the cumulative polishing time of each mesh node and the total polishing intensity received by the node at all moments are obtained, thereby forming three-dimensional polishing coverage data containing time cumulative characteristics and spatial intensity distribution.

[0034] Step S5: Evaluate and optimize the uniformity of polishing quality based on the three-dimensional polishing coverage data to obtain three-dimensional digital polishing model data.

[0035] In this embodiment of the invention, after obtaining three-dimensional polishing coverage data containing the cumulative polishing time and collaborative polishing intensity distribution of each grid node, the system evaluates and optimizes the quality uniformity of the coverage data. Specifically, the mean-variance analysis method is used to evaluate the dispersion of polishing intensity among the grid nodes on the entire workpiece surface, and the standard deviation is used as a quantitative indicator of polishing uniformity. The smaller the standard deviation, the more uniform the polishing quality. If it is found that the coverage time or intensity of a certain area is significantly lower, the system can adjust the grinding head oscillation parameters, such as appropriately changing the phase difference or increasing the amplitude to improve the coverage of that area. In this embodiment, the minimum polishing time required for areas with intensity lower than 80% of the average value is recalculated, and a new polishing strategy is generated by optimizing the control parameters. Finally, the polishing response results of all grid nodes are integrated into three-dimensional digital polishing model data. This model data can not only be used for pre-polishing strategy generation, but also as a reference standard for post-polishing quality verification to guide the next step of automatic calibration or intelligent compensation operation.

[0036] Of particular importance is that step S1 includes the following steps:

[0037] Step S11: Scan the surface of the workpiece using a 3D scanning device to obtain the original 3D geometric data containing the geometric contour information of the workpiece;

[0038] This invention employs a 3D scanning device to scan the surface of a workpiece, acquiring its geometric contour information to generate raw 3D geometric data. Specifically, this embodiment uses a laser line structured light scanner, which boasts a precision of 0.05 mm and can efficiently acquire the spatial morphology of complex curved workpieces (such as optical lens blanks and aero-engine blades). During the scanning process, the workpiece is mounted on an adjustable rotating platform, achieving full surface coverage through multi-angle rotation. The resulting scan is high-density point cloud data, where each point records its spatial 3D coordinate value, forming a raw 3D point cloud set representing the workpiece's true geometric structure. This data serves as the basis for geometric modeling, providing input for subsequent coordinate system standardization processing.

[0039] Step S12: Standardize the coordinate system of the workpiece surface based on the original three-dimensional geometric data, establish a unified spatial coordinate reference system, and transform the workpiece geometric data to this coordinate system to obtain the three-dimensional geometric data of the workpiece surface.

[0040] This invention standardizes the coordinate system of the workpiece surface. Specifically, point cloud data is imported into point cloud processing software (such as Geomagic or a self-developed modeling system). First, principal component analysis (PCA) is used to identify the principal direction of the point cloud to determine the principal axis direction of the workpiece. Based on this, a new spatial coordinate reference system is established. This reference system typically uses the workpiece's geometric centroid as the origin, the maximum length direction as the Z-axis, the second longest direction as the X-axis, and the remaining directions as the Y-axis, thereby achieving coordinate unification. Then, the original point cloud is transformed to this standard reference system through translation and rotation operations to eliminate geometric deviations caused by inconsistent scanning postures. In this embodiment, for a complex curved surface part, a local spatial coordinate system is established with the workpiece center as the origin and the major axis direction as the principal direction. Its three-dimensional geometric data is transformed to this coordinate system to ensure compatibility with the machine tool coordinate system used in polishing path calculation.

[0041] Step S13: Obtain the mechanical structure parameters of the multi-segment oscillating grinding head system, including the physical dimensions of each grinding head, installation position coordinates, grinding head material properties and effective radius of action, to obtain the physical property data of the grinding head;

[0042] This invention acquires the mechanical structure parameters of a multi-segment oscillating grinding head system to form physical property data of the grinding heads. Specifically, it involves consulting the mechanical design drawings and equipment parameter tables provided by the equipment manufacturer to extract the actual physical dimensions of each grinding head (e.g., diameter and length), fixed installation position coordinates (spatial position relative to the machine tool reference coordinate system), grinding head material properties (e.g., polyurethane, elastic rubber, etc., affecting polishing contact behavior), and the effective radius of action of the grinding head—that is, the spatial range within which the grinding head produces a significant polishing effect on the workpiece per unit time. Taking a practical four-grinding-head linkage polishing system as an example, each grinding head has a diameter of 50 mm, is made of medium-hardness polyurethane, and has an effective radius of 25 mm. They are installed on independent linkage arms at the ends of the XYZ axes, with the installation positions offset outwards from the machine tool center point by different distances. These parameters collectively constitute the physical property data of the grinding heads used for modeling and trajectory determination.

[0043] Step S14: Obtain the motion control parameters of the multi-segment oscillating grinding head, including the oscillation frequency range, oscillation amplitude range, oscillation center position, and oscillation plane direction of each grinding head, and obtain the motion characteristic data of the grinding head;

[0044] This invention collects motion control parameters of each grinding head to form grinding head motion characteristic data. Specifically, it reads the control system parameter setting file of the CNC polishing machine, which includes the oscillation frequency range (i.e., the range of oscillation period variation, generally 3 to 10 Hz), oscillation amplitude range (the position of maximum deviation from the center, usually 10 to 30 mm), the position point of the oscillation center in space (jointly determined with the grinding head installation position to determine its running trajectory starting point), and the oscillation plane direction (the main direction vector of the grinding head oscillation in space, usually represented by a vector normal direction). In this embodiment, to achieve a nonlinear uniform coverage strategy, the frequencies of the four grinding heads are set to 5, 6, 7, and 8 Hz, the oscillation amplitude is 20 mm, and the oscillation planes are XY, YZ, XZ, and a plane tilt of 30 degrees, respectively. These parameters are used to generate a multi-grinding head differential running trajectory model to improve the spatial distribution complementarity.

[0045] Step S15: Verify the validity of parameters based on the physical property data and motion characteristic data of the grinding head, check the reasonable range of parameter values ​​and identify parameter conflicts or missing information, and obtain the basic parameter data of the grinding head.

[0046] This invention implements parameter validity verification to generate basic grinding head parameter data. The specific method includes writing a parameter verification program to perform range logic judgments and internal consistency checks on the input data. For example, it checks whether the swing amplitude of each grinding head exceeds its effective radius, whether multiple grinding heads have overlapping installation positions, whether the swing direction is valid, and whether parameters are missing. If an anomaly is detected, the user is prompted to correct or supplement the information. In this embodiment, if a grinding head's set swing amplitude of 35 mm is found to exceed its physical effective radius of 30 mm (safe range), the system automatically issues an alarm and marks it as invalid, requiring resetting. Ultimately, only the set of parameters that pass verification is retained as the basic grinding head parameter data, providing a reliable basis for subsequent generation of identification indexes and kinematic models.

[0047] Step S16: Based on the basic parameter data of the grinding head, each grinding head is assigned a unique identifier, and an index mapping relationship between the grinding head identifier and the parameter information is established to obtain kinematic parameter data with identifier index.

[0048] In this embodiment of the invention, a unique identifier is assigned to each grinding head, and an index mapping relationship is established. Specifically, a unique code is generated sequentially for each grinding head based on its installation order or logical number (e.g., MH01, MH02, MH03, MH04), and an index table is constructed to establish a one-to-one mapping between each grinding head identifier and its corresponding physical attributes and motion characteristic data. This index structure supports rapid retrieval and correlation calculation, and is particularly suitable for the synchronous analysis of multiple grinding head trajectories in high-dimensional simulation scenarios. In this embodiment, a JSON-formatted parameter mapping data structure is established, with the identifier of each grinding head serving as the primary key, corresponding to all basic parameter information such as its oscillation frequency, amplitude, material, and direction. This structure serves as standard input data in the polishing path modeling module and the dynamic coverage calculation module, enabling unified management and retrieval of grinding head behavior during the subsequent 3D digital model generation process.

[0049] Preferably, step S2 includes the following steps:

[0050] Step S21: Perform triangular meshing on the surface area based on the three-dimensional geometric data to obtain triangular mesh data, wherein the mesh density is set to no less than 100 mesh nodes per square centimeter;

[0051] This invention performs triangular meshing on the surface region of the workpiece's three-dimensional geometric data, which has been transformed to a unified reference coordinate system, to construct a standard digital model suitable for subsequent polishing path simulation and surface interaction calculations. Specifically, a meshing module based on the Delaunay triangulation algorithm is used to reconstruct the point cloud data surface into a continuous triangular mesh surface. In this embodiment, the selected algorithm maintains mesh smoothness while adapting to complex surfaces with large curvatures. First, dense point cloud patches are generated through sampling and reconstruction. Then, mesh control is performed according to a density requirement of no less than 100 mesh nodes per square centimeter, that is, each square centimeter area is divided into approximately 50 to 60 triangles, ensuring that the model details are rich enough to reflect the surface morphology features. For example, for a complex optical component with a surface area of ​​150 square centimeters, approximately 15,000 nodes are generated, forming nearly 30,000 triangular patches. This meshing density meets the surface accuracy requirements of subsequent calculations while achieving a balance between computational performance and data volume.

[0052] Step S22: Assign coordinates and calculate normal vectors for each grid node based on the triangular mesh data to obtain node geometric attribute data with node coordinate information and normal vector information;

[0053] This invention extracts the geometric attributes of each mesh node in a triangular mesh, including spatial coordinate assignment and normal vector calculation. Specifically, firstly, based on the mesh division results, the XYZ coordinates of each node in the three-dimensional coordinate system are extracted as the spatial positioning value of that node. Then, for each adjacent triangular facet containing a node, the normal vector of the facet is calculated using the cross product of its vertex coordinates. Finally, the normal vectors of all facets belonging to a node are weighted and averaged (weighted by facet area) to obtain the node's unit normal vector. This normal vector is a key parameter in polishing path planning, determining the contact angle and direction control strategy of the grinding head. In this embodiment, for high-curvature regions (such as the edge of an aircraft blade), the accuracy of the normal vector direction is improved by increasing the weighting of surrounding facets, thereby ensuring more precise grinding head attitude adjustment in subsequent simulations. The final generated node geometric attribute data includes the three-dimensional coordinate values ​​and unit normal vector values ​​of each node, forming a high-precision set of surface point descriptions.

[0054] Step S23: Perform unique identifier assignment on the mesh nodes based on the node geometric attribute data to obtain surface mesh node data with index identifiers.

[0055] This invention assigns a unique identifier to each mesh node, resulting in surface mesh node data with indexed identifiers. Specifically, each node is assigned a globally unique index number according to its storage order or spatial layout order within the mesh data structure, for example, encoded as "GN00001" or "GN00002". Simultaneously, a mapping table is established between the node identifier and its coordinate and normal vector information, allowing the subsequent path calculation module to quickly access and reference each node's attributes. In this embodiment, for the approximately 15,000 mesh nodes, the system automatically generates corresponding node indexes and stores them in a database in JSON format. Each node record contains: an index ID, a 3D coordinate array, and a unit normal vector array. This structure is frequently used in processes such as grinding head path generation, coverage analysis, and polishing residual prediction, and is a key data organization form supporting the accuracy and efficiency of 3D digital model algorithms. Through this indexing mechanism, subsequent steps can efficiently match the spatial relationship between the grinding head model and specific surface areas, constructing a polishing behavior prediction model based on geometric constraints.

[0056] Preferably, step S3 includes the following steps:

[0057] Step S31: Extract the swing amplitude, swing frequency, swing center position and swing plane angle of each grinding head from the kinematic parameter data, and establish a structured grinding head parameter table for each grinding head;

[0058] This invention extracts the core motion parameters of each grinding head from established kinematic parameter data with indexed identifiers. These parameters include oscillation amplitude, oscillation frequency, oscillation center position, and oscillation plane angle. The oscillation amplitude refers to the maximum displacement of the grinding head from its center position within one cycle; the oscillation frequency is the number of oscillation cycles completed per unit time; the oscillation center position defines the reference point of the grinding head in the coordinate system; and the oscillation plane angle describes the angle between the plane of the oscillation motion and the XY plane of the reference coordinate system. After extracting these parameters, a grinding head parameter table is constructed using a structured data organization method. Each row of the table corresponds to one grinding head, and each column stores the grinding head's number, physical location, oscillation characteristics, and material type. For example, for a composite polishing machine equipped with six oscillating grinding heads, the third grinding head in the generated parameter table might contain the following field values: number H003, position (250, 0, 120), oscillation frequency 3Hz, oscillation amplitude 12mm, center coordinates (250, 0, 120), and oscillation plane angle 30 degrees. This table serves as the foundational input data for subsequent polishing path generation and synchronization control.

[0059] Step S32: Determine the phase difference value of each grinding head using the total number of grinding heads in the grinding head parameter table, and generate a phase difference configuration list by assigning different phase start points to each grinding head by equally dividing the complete cycle.

[0060] This invention designs different phase difference values ​​for each grinding head based on the total number of grinding heads and generates a phase difference configuration list. Phase difference refers to the time delay between multiple periodically moving parts, used to avoid mechanical interference or system resonance problems caused by multiple grinding heads reaching extreme positions simultaneously. In this embodiment, a complete cycle equal division strategy is used to allocate the phase starting point, that is, the 360-degree phase angle is evenly distributed among all grinding heads. For example, in the case of 6 grinding heads, the phase difference between adjacent grinding heads is set to 60 degrees, specifically allocated as follows: the first grinding head is 0 degrees, the second is 60 degrees, the third is 120 degrees, and so on. The final generated phase difference configuration list is a structured table containing grinding head numbers and corresponding phase offset angles, facilitating the introduction of personalized initial states in subsequent path description calculations.

[0061] Step S33: Generate a set of grinding head trajectory descriptions for each grinding head, including personalized phase difference oscillation trajectory descriptions, based on the grinding head parameter table and phase difference configuration list;

[0062] This invention, based on a grinding head parameter table and a phase difference configuration list, generates a personalized set of phase difference oscillation trajectory descriptions for each grinding head in step S33. Specifically, the oscillation behavior of each grinding head is abstracted as a two-dimensional reciprocating motion trajectory on its oscillation plane, and a time-displacement function is constructed by combining its oscillation amplitude and frequency. Simultaneously, a unique initial phase difference angle is introduced to ensure staggered operation. In implementation, a sinusoidal motion model driven by time-series parameters is used to generate a displacement sequence, and the oscillation plane direction vector and center coordinate position are superimposed for three-dimensional transformation. For example, grinding head H003 oscillates on a 30-degree inclined plane with an amplitude of 12mm, a frequency of 3Hz, and an initial phase of 120 degrees. Through simulation calculation, its trajectory vector at any time point in three-dimensional space can be obtained, and these vectors are integrated into a trajectory description set containing fields such as time step, position vector, and motion direction. This set will be used for subsequent spatiotemporal path unfolding and polishing point coverage calculations.

[0063] Step S34: Based on the grinding head trajectory description set, time sampling is performed on the entire polishing cycle at preset time intervals, and the three-dimensional spatial coordinate position of all grinding heads at each time point is calculated to form a grinding head position coordinate sequence table arranged in chronological order;

[0064] In this embodiment of the invention, based on the generated set of grinding head trajectory descriptions, time sampling is performed on the entire polishing cycle at fixed time intervals in step S34. The three-dimensional spatial coordinate position of each grinding head at that time point is calculated hourly, forming a grinding head position coordinate sequence table. The time sampling interval can be determined according to the minimum response time of the polishing motion control system, with a typical value of 10 milliseconds, i.e., 100 samples per second. At each time point, the spatial displacement value corresponding to the time in each grinding head trajectory description is read. The three-dimensional coordinates are calculated using the center point coordinates, swing direction angle, and displacement amplitude, ultimately yielding path data composed of timestamps and grinding head coordinate values. For example, within a 2-second polishing cycle, 200 time nodes will be generated, with each node recording the position vectors of 6 grinding heads. The entire sequence table contains a total of 1200 sets of coordinate points. The data organization structure uses a time primary key index, and each entry contains a timestamp and the three-dimensional position corresponding to multiple grinding head numbers.

[0065] Step S35: Establish a fast query correspondence between timestamps and grinding head position information using the grinding head position coordinate sequence table, thereby obtaining the spatiotemporal position mapping data of the grinding head.

[0066] This invention establishes a spatiotemporal position mapping data for grinding heads based on a sequence table of grinding head position coordinates, constructing a fast query relationship between timestamps and corresponding grinding head position information. This embodiment uses a hash mapping mechanism or a dictionary-based data structure to build an index, with the key being the sampling timestamp and the value being the set of spatial coordinates of all grinding heads at that moment, achieving millisecond-level fast access. The specific data structure can use nested JSON or binary tables, supporting rapid acquisition of grinding head state information at any time point in modules such as path planning simulation, collision detection, and grinding head attitude control. For example, a timestamp "1.230s" corresponds to the value: "H001:(x1,y1,z1), H002:(x2,y2,z2)...". This mapping data is used in the dynamic simulation software module to generate a real-time distribution map of grinding heads, determine spatial overlapping areas, and execute position feedback control logic. Through this step, the time resolution process from grinding head physical parameters to a high-precision spatial path is completed, providing accurate input for polishing effect simulation and path optimization.

[0067] Preferably, step S4 includes the following steps:

[0068] Step S41: Calculate the spatial distance between the grinding head and the mesh nodes based on the spatiotemporal position mapping data of the grinding head and the surface mesh node data. Then, calculate the three-dimensional Euclidean distance between the center position of each grinding head and each mesh node on the workpiece surface at each time point to obtain the grinding head node distance matrix data.

[0069] This invention requires spatial pairing of the data with the 3D mesh node data of the workpiece surface to calculate the 3D Euclidean distance between the centers of all grinding heads and all mesh nodes on the workpiece surface at each time point. Specifically, the mesh node data is a set of workpiece surface points obtained through 3D modeling techniques (such as laser scanning or CAD model partitioning), with each node having unique spatial coordinates and an index number. In actual implementation, a spatial vector calculation method is used to traverse each sampling time point, calculating the distance between the 3D coordinates of each grinding head at that moment and all mesh nodes to obtain the corresponding Euclidean distance value, which is the straight-line distance between the center point of the grinding head and the mesh node. For example, for a system containing 30,000 mesh nodes and 6 grinding heads, with a sampling period of 2 seconds and a total of 200 time points, 6 times 200 times 30,000, a total of 36 million distance calculations are required. To improve efficiency, this embodiment uses a spatial partitioning algorithm and a KD-tree acceleration structure to pre-divide the grid nodes spatially. Distance calculations are performed only on nodes that may enter the working radius of the grinding head, ultimately generating a grinding head node distance matrix. The matrix has the dimension of the number of time points × the number of grinding heads × the number of grid nodes, and each element records a specific three-dimensional distance value.

[0070] Step S42: Based on the distance matrix data of the grinding head nodes and the preset grinding head action radius threshold, the effective action area is determined. The grid nodes within the effective action range of each grinding head are selected by distance comparison to obtain the grinding head action area coverage relationship data.

[0071] This invention determines the effective radius of each distance value, filtering out the effective nodes actually covered by each grinding head at each moment, thereby establishing grinding head effective area coverage relationship data. The "effective radius threshold" here is a preset spatial influence range based on the structure and material properties of the specific grinding head. For example, for a flexible grinding head with a diameter of 30mm, its effective effective radius is set to 15mm, meaning that a node is considered to be affected by the grinding head only when the distance between a grid node and the center point of the grinding head is less than 15mm. In practice, the program compares each distance value in the aforementioned distance matrix with the effective radius of the corresponding grinding head. If the distance is less than the radius, the grid node is marked as "covered," and the node number, the covered time point, and the number of the grinding head involved are recorded. The final generated data structure is a set of triples: "grinding head-time point-node number," constituting the grinding head effective area coverage relationship data. This data is used to subsequently establish the spatial-temporal distribution of grinding intensity.

[0072] Step S43: Based on the coverage relationship data of the grinding head working area, calculate the instantaneous polishing intensity value of each grid node using the polishing intensity distribution model based on the Gaussian decay function, and obtain the instantaneous polishing intensity data of the node;

[0073] This invention calculates the instantaneous polishing intensity for each covered grid node, employing a Gaussian decay model to construct a physical distribution function for the polishing intensity. The Gaussian decay function takes the center of the grinding head as the point of maximum intensity, with the intensity decreasing exponentially with distance. This model realistically reflects the characteristic of the grinding head's edge having a smaller force and its center a larger force during actual polishing. Specifically, based on the grinding head number and the distance between the node and the grinding head, the corresponding intensity coefficient is first obtained from the Gaussian function. Then, combined with parameters such as the current grinding head speed, load, and material coefficient, the actual polishing intensity value experienced by the node at that time point is calculated. For example, if a node is 10mm from the center of the grinding head, and the grinding head's radius of action is 15mm, the Gaussian weight might be 0.5. Combined with its instantaneous load parameters, the final intensity is 0.5 multiplied by the base grinding force. The instantaneous polishing intensity of all nodes is recorded as a ternary dataset of node number, time point, and polishing intensity, serving as the basis for the next step of cumulative analysis.

[0074] Step S44: Perform time-series-based cumulative calculation processing based on the instantaneous polishing intensity data of the nodes to obtain the cumulative polishing amount data of the nodes. Specifically, the cumulative calculation processing is performed by performing time integration on the polishing intensity received by each grid node throughout the entire polishing cycle.

[0075] This invention, based on the aforementioned instantaneous polishing intensity data of each node, performs time integration over the entire polishing cycle for each grid node to obtain the cumulative polishing amount data. The cumulative calculation employs a time-series integration method, whereby the polishing intensity value of a node at each sampling time point is multiplied by the sampling interval and then summed item by item, representing the total energy density or total polishing amount received by the node during the polishing cycle. For example, if the sampling interval is 0.01 seconds, and the intensity of a node at 20 times is 0.3, 0.5, 0.6…, then the cumulative polishing amount of that node is the weighted sum of these values. A sparse matrix storage mechanism is introduced during the calculation process, recording only the nodes covered at any given time, avoiding redundancy in storage and calculation. The final result is a cumulative polishing amount dataset corresponding to each grid node, with a data structure of a tuple of node number and cumulative value, used to evaluate the processing depth and uniformity of different regions on the workpiece surface.

[0076] Step S45: Use the cumulative polishing amount data of nodes to perform superposition calculation on the effect of multi-grinding head synergy, and obtain the node synergy polishing intensity distribution data;

[0077] This invention utilizes node cumulative polishing amount data to analyze the synergistic effect of multiple grinding heads, generating synergistic polishing intensity distribution data. Since multiple grinding heads may overlap their effects on the same node at different time periods, it is necessary to superimpose the cumulative contributions of each grinding head to analyze their synergistic processing intensity within the spatially overlapping area. This embodiment employs a node-centric aggregation method, summing the cumulative polishing amounts of a node under all grinding heads and analyzing its coverage frequency (i.e., the number of times the node is simultaneously or staggeredly covered by multiple grinding heads) to quantify the synergistic effect. For example, if a node is acted upon by two grinding heads with polishing amounts of 2.1 and 1.7 respectively, the total synergistic amount is 3.8, and its synergistic overlap is recorded as 2. The final data structure consists of node number, synergistic polishing intensity value, and overlap information, forming a complete synergistic processing feature dataset that reflects the complex interactive effects under a multi-grinding head system.

[0078] Step S46: Based on the cumulative polishing amount data and the collaborative polishing intensity distribution data of the nodes, match the cumulative polishing duration information and the collaborative polishing intensity distribution information according to the grid node index identifier to obtain the three-dimensional polishing coverage data.

[0079] This invention integrates the cumulative polishing time (i.e., total processing time) and collaborative polishing intensity value of nodes based on the cumulative polishing amount data and the collaborative polishing intensity distribution data of nodes. A correspondence is established according to the node's index number in the surface mesh model to generate three-dimensional polishing coverage data. This data, on a per-mesh node basis, records the cumulative processing time, total energy received, and collaborative effect intensity throughout the polishing cycle, and is then mapped to the three-dimensional geometric model for visualization and evaluation. For example, a node with the number N1023 has a cumulative polishing time of 3.4 seconds and a collaborative intensity of 4.2 units. Through surface mapping technology, the node's location can be displayed in the CAD view using color depth or contour lines. The final three-dimensional polishing coverage data can serve as input parameters for CNC path optimization, residual error prediction, and quality evaluation, possessing high engineering application value and marking the completion of the three-dimensional digital modeling process for the entire polishing process.

[0080] Preferably, step S42 includes the following steps:

[0081] Step S421: Compare the distance values ​​one by one according to the grinding head node distance matrix data and the preset grinding head action radius threshold to obtain the distance determination result data;

[0082] In this embodiment of the invention, after obtaining the grinding head node distance matrix data calculated in step S41, the system compares the three-dimensional Euclidean distance value between each grinding head center point and each grid node on the workpiece surface at each moment with a pre-set grinding head effective radius threshold. This effective radius threshold can be set based on the actual physical size of the grinding head and experience with the effective polishing area, for example, set to 10 mm. During the comparison, a matrix traversal method is used to judge the distance value between each pair of grinding head centers and grid nodes. If the value is less than or equal to the radius threshold, the grid node is determined to be within the effective effective range of the grinding head, and the system records "1" as an effective effective marker; otherwise, it is recorded as "0". Finally, a Boolean distance judgment result data matrix is ​​formed. This matrix maintains the same structure as the original distance matrix, but only marks the effective effective range relationships for subsequent filtering steps.

[0083] Step S422: Based on the distance determination result data, filter and extract grinding head node pairs that meet the effective range conditions. By retaining grinding head node combinations with distance values ​​less than or equal to the effective radius threshold, a list of effective grinding head node pairs is obtained.

[0084] In this embodiment of the invention, the distance determination result data matrix generated in step S421 is used to extract the pairing relationships between all grinding heads and nodes marked "1". Valid combinations whose distance values ​​are less than or equal to the grinding head's radius of action are retained and recorded in a list to form a valid grinding head-node pairing list. Each record in this list includes a grinding head identifier, a node index identifier, and the corresponding spatial distance value. To ensure processing efficiency, the system uses a hash table structure to quickly index the valid node set corresponding to each grinding head, and arranges the node indices in ascending order for easy subsequent statistical processing. In a specific implementation, if a grinding head acts on the grid node numbered n_1, n_5, or n_12 at a certain moment, the list will contain records such as (H1, n_1, 8.6mm) and (H1, n_5, 9.2mm).

[0085] Step S423: Based on the effective grinding head node pairing list, group the functional node sets of each grinding head according to the grinding head identifier to obtain the grinding head group node set data;

[0086] This invention, based on the aforementioned list of valid grinding head node pairs, groups the data according to the grinding head identifier (e.g., H1, H2, H3, etc.) as the primary key, extracting all the active nodes corresponding to each grinding head to form grinding head group node set data. Each group contains a grinding head identifier and the set of grid nodes covered by that grinding head at all times during the entire polishing process. For example, for H1, its active node set may contain node numbers n_1, n_5, n_12, n_30, etc.; for H2, it may be n_5, n_6, n_15, n_18, etc. This process uses a dictionary data structure, with the grinding head identifier as the key and the corresponding node set as the value, supporting subsequent fast traversal and cross-analysis.

[0087] Step S424: Based on the grinding head group node set data, by traversing the action node set of each grinding head and counting the grinding heads covered by each node, a list of grinding heads covered by the node is obtained.

[0088] In this embodiment of the invention, the set of all working nodes of the grinding heads obtained in step S423 is traversed to count how many different grinding heads simultaneously cover each grid node. During the operation, the system initializes a dictionary structure with the grid node index as the key, and scans the node set of all grinding heads one by one. When a node appears in the set of multiple grinding heads, the system appends the identifier of the current grinding head to the corresponding dictionary entry. For example, if node n_5 is simultaneously covered by H1 and H2, then the record entry for this node is [n_5:[H1,H2]], indicating that it is acted upon by two grinding heads. Finally, a list of grinding heads whose nodes are covered is formed. This data is used to analyze the collaborative coverage of grinding heads and to construct the subsequent collaborative polishing model.

[0089] Step S425: Construct a bidirectional index mapping table from grinding head to node and from node to grinding head using the grinding head group node set data and the grinding head list data covered by the node, to obtain the grinding head action area coverage relationship data.

[0090] In this embodiment of the invention, the grinding head group node set data obtained in step S423 and the grinding head list data with covered nodes in step S424 are jointly processed to construct mapping index tables for "grinding head → node" and "node → grinding head" respectively. The "grinding head → node" table can be used to quickly query which node ranges a given grinding head is polishing in, while the "node → grinding head" table can be used to analyze whether a given grid node is in a multi-grinding head collaborative action area. In the implementation process, a dual-hash dictionary structure is used for storage and query operations, combined with an index compression algorithm to improve data processing efficiency. In specific applications, this bidirectional mapping table provides fundamental support for subsequent instantaneous polishing intensity calculation and collaborative intensity superposition, and also supports efficient rendering and annotation of 3D covered areas in the visualization model. Finally, the grinding head action area coverage relationship data output by the system contains all valid interaction relationships and multiple cross-action information between grinding heads and nodes, which is the key structural foundation data for generating a 3D digital polishing model.

[0091] Preferably, step S43 includes the following steps:

[0092] Step S431: Extract the distance value information between each grinding head and the grid nodes within its working range from the grinding head working area coverage relationship data to obtain an effective distance value data set;

[0093] This invention extracts the spatial distance values ​​between each grinding head and the grid nodes it interacts with based on the coverage relationship data of the grinding head's working area, forming a valid distance value dataset. Each record in this dataset consists of three parts: the grinding head identifier, the corresponding grid node index, and the Euclidean spatial distance from the grinding head to the node. In actual processing, the system traverses the "grinding head → node" mapping table, extracting the pairing information between the grinding head and the node while retrieving the corresponding three-dimensional distance values ​​from the original distance matrix data and adding them to the dataset. For example, if grinding head H1 interacts with node n_12 at a distance of 8.4 mm, it is recorded as (H1, n_12, 8.4). This dataset provides the physical basis for subsequent distance normalization and intensity calculation, recording the spatial coupling relationship between the polishing head and the target working area, and is key input data for establishing an intensity attenuation model.

[0094] Step S432: Perform normalized distance calculation using the effective distance value data set and the preset Gaussian attenuation parameter to obtain normalized distance ratio data;

[0095] In this embodiment of the invention, the effective distance value data set obtained in step S431 and the system-preset Gaussian attenuation parameter are used to perform normalized distance calculation. The Gaussian attenuation parameter mainly refers to the standard deviation σ in the Gaussian function, which is used to control the sensitivity of distance attenuation. Its value can be determined according to the actual working range of the grinding head, such as setting it to 5 mm. The normalized distance is calculated by dividing the distance value from each grinding head to the node by σ to obtain the normalized distance ratio of that node. For example, if the distance between a node and the grinding head is 8.4 mm and σ is 5 mm, then its normalized distance ratio is 1.68. The system stores all normalized distance ratios in a unified normalized distance ratio data list, maintaining the correspondence with the original distance data set, for the next step of calculating the exponential value of the Gaussian function.

[0096] Step S433: Based on the normalized distance ratio data, multiply the square of the normalized distance ratio by the negative Gaussian attenuation coefficient and take the natural exponent to obtain the Gaussian attenuation factor data;

[0097] In this embodiment of the invention, the normalized distance ratio data obtained in step S432 is subjected to Gaussian attenuation calculation. This involves multiplying the square of each ratio by a negative Gaussian attenuation coefficient, and then taking the exponent of the natural logarithm to obtain the Gaussian attenuation factor data corresponding to each node. This Gaussian attenuation factor reflects the degree of influence of distance on polishing intensity; the greater the distance, the smaller the factor. Continuing with the previous example, if the normalized ratio is 1.68, its square is 2.82, which multiplied by a negative sign is -2.82, and after taking the natural exponent, it is approximately 0.059. This attenuation factor indicates that the node's contribution to the final polishing intensity is weak due to its greater distance from the grinding head. The system uses an array structure to record all Gaussian attenuation factors and forms a triplet with the node index and grinding head identifier, constituting the basic data for node force attenuation, used for the next step of solving for the intensity value.

[0098] Step S434: Calculate the strength value based on the Gaussian attenuation factor data and the preset maximum polishing strength parameter of the grinding head to obtain the basic polishing strength value of the mesh node;

[0099] This invention calculates the basic polishing intensity value of each node based on the aforementioned Gaussian attenuation factor data and the preset maximum polishing intensity parameter of the grinding head. The maximum polishing intensity parameter of the grinding head is the maximum unit action intensity set according to the physical structure of the grinding head and the equipment debugging, and the unit can be Newtons per square millimeter (N / mm²). 2 For example, set it to 1.2 N / mm. 2The system multiplies the Gaussian attenuation factor corresponding to each node by the maximum strength value of the grinding head, thus obtaining the basic polishing strength value of that node at that location due to the grinding head H. For example, in the above example, the attenuation factor is 0.059 and the maximum strength is 1.2, so the final basic strength is approximately 0.0708 N / mm². All basic strength values, along with their corresponding node indices and grinding head identifiers, are recorded to generate a set of node basic polishing strength data, providing numerical input for the next step of combining surface normal vector correction.

[0100] Step S435: Based on the basic polishing intensity values ​​of the mesh nodes, perform correction and result solving based on the grinding head action direction and the surface normal vector of the mesh nodes to obtain the instantaneous polishing intensity data of the nodes.

[0101] This invention, based on the basic polishing strength, incorporates the grinding head's action direction and the node surface normal vector for directional correction. First, the system obtains the surface normal vector of each node through 3D geometric modeling or simulation data, and acquires the unit action direction vector of each grinding head's current motion trajectory. For each grinding head-node pair, the system calculates the cosine of the angle between the grinding head's action direction vector and the node normal vector, using this value as a directional correction factor. If the two directions are completely aligned (i.e., the angle is 0 degrees), the cosine value is 1, which does not affect the basic strength; if the directions differ by 90 degrees, the cosine value is 0, meaning there is no effective strength effect in that direction. The system multiplies the basic strength value by the directional correction factor to obtain the final instantaneous polishing strength value of the node. For example, if the basic strength is 0.0708 N / mm... 2 If the cosine of the included angle is 0.87, then the instantaneous intensity is approximately 0.0616 N / mm². 2 The resulting instantaneous polishing intensity data covers the entire 3D mesh area of ​​the workpiece, reflecting the comprehensive influence of spatial distance and directional coupling on the intensity of the action, and providing high-fidelity input data for modeling local surface changes in the 3D digital model.

[0102] Preferably, step S435 includes the following steps:

[0103] The angle correction calculation is performed on the angle between the grinding head and the normal vector of the node surface based on the basic polishing intensity value of the grid node. The cosine value of the grinding head action direction and the normal vector of the node surface is calculated and used as the correction coefficient to obtain the polishing intensity value after angle correction.

[0104] In the step of calculating the angle correction between the grinding head and the node surface based on the basic polishing strength value of the mesh nodes, the system has already obtained the basic polishing strength value of each node, as well as the action direction vector of the grinding head and the normal vector data of the node surface in the previous step. The key to this step is to quantify and correct the strength effectiveness caused by the difference in direction based on the physical action mechanism. To achieve this correction, the system first processes the pairing data of each "grinding head-node" and extracts the current action direction vector of the corresponding grinding head (usually derived from the grinding head pose information) and the unit normal vector of the node surface. Then, the cosine value of the angle between these two vectors is calculated. This value reflects the consistency of the two directions and ranges from -1 to 1. In actual engineering, considering that polishing is only effective when the grinding head and the surface are basically in the same direction, the system usually truncates negative values ​​to 0 and retains the non-negative cosine value as the "direction correction coefficient". This coefficient is multiplied by the basic strength value to obtain the polishing strength after angle correction. For example, if the basic polishing strength of a node is 0.085 N / mm 2 With a cosine value of 0.92, the strength after angle correction is approximately 0.0782 N / mm. 2 .

[0105] Based on the polishing intensity value and the grinding head movement speed information at the current time point, the speed influence factor is calculated and processed to obtain the grinding head node speed modulation intensity data;

[0106] In the step of calculating the speed influence factor based on the polishing intensity value and the grinding head movement speed information at the current time point, this embodiment of the invention introduces the influence of the grinding head's running speed on the polishing effect, forming a more realistic dynamic intensity model. This step is based on common empirical rules in the polishing process: under the same pressure, the faster the grinding head moves, the more dispersed the energy acting on a single surface per unit time, leading to a decrease in polishing intensity per unit area. Therefore, the system collects the movement speed information of each grinding head at the current time point, including the modulus of the tangential velocity or trajectory velocity vector, in millimeters per second. In the modulation model set by the system, a speed reference coefficient is usually defined, for example, a reference speed of 200 mm / s, and the actual speed value is compared with the reference value to obtain the speed modulation factor. Then, the system divides the angle-corrected polishing intensity by this speed modulation factor to obtain the grinding head node modulation intensity reflecting the speed influence. For example, if the intensity of a node after angle correction is 0.0782 N / mm... 2 If the current grinding head speed is 250 mm / s, then the modulation factor is 1.25, and the final speed modulation intensity corresponding to this node is approximately 0.0626 N / mm. 2 The system stores this intensity value, along with its corresponding node index and grinding head identifier, into the grinding head node speed modulation intensity data structure for superposition processing of multiple grinding head actions.

[0107] Based on the grinding head node speed modulation intensity data, the instantaneous polishing intensity data of the node is obtained by superimposing and summing the multiple grinding head actions on the same grid node at the current time point.

[0108] In the step of summing the effects of multiple grinding heads on the same grid node at the current time point based on the grinding head node velocity modulation intensity data in this embodiment of the invention, the system, for each grid node, searches for all records of its effects from multiple grinding heads at the current time point, and sums the velocity modulation intensities from all different grinding heads to obtain the instantaneous total polishing intensity data of that node. This process uses a node-based index merging strategy: the system traverses all modulation intensity records, categorizes and aggregates them according to the node index, collects the modulation intensity values ​​contributed by all grinding heads under each node entry, and performs a summation calculation. For example, if node n_123 is affected by grinding heads H1, H3, and H5 at the current time, and the velocity modulation intensities contributed by the three are 0.0626, 0.0491, and 0.0575 N / mm, respectively. 2 Therefore, the instantaneous polishing intensity of node n_123 is approximately 0.1692 N / mm. 2 After completing this processing, the system stores the node index and its corresponding instantaneous polishing intensity together in the final node intensity distribution model. This model is the core part of the entire 3D digital model generation, reflecting the comprehensive polishing intensity distribution experienced by different regions on the entire polished surface at any given time point, providing high-precision data support for further analysis of material removal, surface change modeling, and process optimization.

[0109] Preferably, step S45 includes the following steps:

[0110] Step S451: Based on the cumulative polishing amount data of the nodes, perform neighborhood relationship establishment processing on each grid node on the workpiece surface, identify the direct adjacent nodes of each node and establish the topological connection relationship between the nodes to obtain the node neighborhood topology data.

[0111] This invention, based on obtaining the cumulative polishing amount (i.e., the integral result of polishing intensity per unit time in the temporal dimension) of all nodes on the workpiece surface during the polishing process, further constructs the spatial topological relationships between nodes. This operation is based on a meshed 3D digital model, using structured or unstructured meshes (e.g., quadrilateral or triangular meshes) to define the node set. The system traverses all mesh cells, identifying other nodes sharing the same mesh cell in geometric space for each node. These nodes constitute the node's "directly adjacent nodes," and the spatial connections between them are the "neighborhood topological relationships." To facilitate subsequent processing, the system uses an adjacency list (adjacency dictionary) data structure to create an index list of neighboring nodes for each node, and organizes this adjacency structure along with the node's cumulative polishing amount data into "node neighborhood topological data." For example, for node n_57, its neighboring nodes might be n_41, n_42, n_56, n_58, n_73, n_74, etc. The system stores these adjacency relationships as a structured array as the basis for subsequent gradient calculations.

[0112] Step S452: Calculate the local polishing intensity gradient of each node based on the node neighborhood topology data and the node cumulative polishing amount data, and obtain the node polishing gradient data by calculating the polishing amount difference between the current node and its neighboring nodes and dividing it by the distance between the nodes.

[0113] This invention relies on established node neighborhood topology relationships, traversing each node and pairing it with all its neighboring nodes one by one. The ratio of polishing amount difference to spatial distance is calculated to depict the "local polishing gradient" of the node within the current topological neighborhood. Specifically, for any node n_i, the system extracts its cumulative polishing amount value and sequentially reads the polishing amount and position coordinates of its neighboring node n_j. The system calculates the Euclidean distance between n_i and n_j and divides the difference in their polishing amounts by this distance to obtain the gradient value in that direction. Subsequently, the system averages or weights the gradients in all neighborhood directions to obtain the comprehensive polishing gradient of n_i. This processing reflects the rate of change of polishing distribution within the microscopic region of the workpiece surface, which is beneficial for identifying areas of local over-polishing or uneven polishing. For example, if the average gradient of node n_57 within its neighborhood is 0.0045 mm / N·mm, it indicates that the polishing intensity of this node changes relatively slowly with spatial distribution, which is conducive to establishing a collaborative polishing mechanism.

[0114] Step S453: Based on the nodal polishing gradient data, perform quantitative calculation on the synergistic enhancement effect among multiple grinding heads to obtain nodal synergistic enhancement coefficient data;

[0115] This invention analyzes the synergistic effect of multiple grinding heads simultaneously on surface smoothness improvement based on calculated local polishing gradient data of nodes. The key to this step is extracting gradient smoothness as a quantitative indicator of synergistic potential—the smaller the gradient, the smaller the difference in the intensity of the multiple grinding heads near the node, and the easier it is to form an effective synergistic coverage effect. The system defines the gradient smoothness factor as the reciprocal of the gradient value (a lower threshold can be set to avoid zero values), and then converts it into a synergistic enhancement coefficient between 0 and 1 according to a normalization standard. The larger the coefficient, the more likely the node is to form an enhancement effect due to the action of multiple grinding heads. For example, on node n_57, if its local gradient is 0.0045 mm / N·mm, the system can calculate the corresponding synergistic enhancement coefficient as 0.89. The system pairs the enhancement coefficient of each node with its index to form "node synergistic enhancement coefficient data," which serves as an adjustment factor for subsequent synergistic modulation.

[0116] Step S454: Perform synergistic effect modulation calculation using node synergistic enhancement coefficient data and node cumulative polishing amount data. Amplify and modulate the original polishing intensity by multiplying the cumulative polishing amount by the synergistic enhancement coefficient to obtain node synergistic modulation intensity data.

[0117] This invention multiplies the cumulative polishing amount of each node by its corresponding synergistic enhancement coefficient to achieve dynamic amplification and modulation of the polishing amount, reflecting the strength of the synergistic effect. This operation simulates the situation where multiple grinding heads simultaneously cover the same area with consistent directions and similar intensities, resulting in a higher material removal efficiency in that area due to the energy superposition effect compared to a single grinding head. The system reads the corresponding synergistic enhancement coefficient and the original cumulative polishing amount data for each node index, performs multiplication, and calculates the "synergistically modulated polishing intensity." For example, if the original cumulative polishing amount of node n_57 is 0.038 mm and its synergistic enhancement coefficient is 0.89, then the synergistically modulated polishing intensity is 0.03382 mm. This operation not only provides an intensity model that better reflects actual process conditions but also lays the foundation for subsequent global polishing distribution optimization.

[0118] Step S455: Perform spatial distribution statistical processing on the overall synergistic effect of the workpiece surface using node synergistic modulation intensity data, and rearrange and normalize the synergistic modulation intensity of each node according to its spatial position to obtain node synergistic polishing intensity distribution data.

[0119] This invention uses node coordinates as an index to map the collaborative modulation intensity to a three-dimensional coordinate system on the workpiece surface according to its spatial location, forming a distributed visualization data model. This operation employs spatial grid reconstruction or point cloud remapping technology to label the intensity value of each node at its corresponding spatial location, forming a high-resolution collaborative polishing intensity map. Simultaneously, to eliminate intensity imbalances caused by differences in the number of polishing coverage times in different areas, the system normalizes all collaborative modulation intensities, for example, by linearly mapping all intensity values ​​to the 0-1 range, forming a relative intensity distribution map. Normalization also facilitates subsequent use of image processing algorithms or deep learning models for further flatness prediction and process optimization control. For example, if the system finds that the node collaborative intensity is concentrated in the range of 0.8-1.0 in a certain circular area, while in another corner area it is only around 0.3, it indicates that the collaborative effect in that area is weak under the current grinding head configuration, requiring trajectory optimization or increased action time. The resulting "node collaborative polishing intensity distribution data" will serve as an important physical field in the generation of the three-dimensional digital model, providing a data foundation for subsequent dynamic demonstrations, process simulations, and the formulation of precise control strategies.

[0120] Preferably, step S5 includes the following steps:

[0121] Step S51: Based on the three-dimensional polishing coverage data, perform statistical analysis on the polishing intensity distribution of the workpiece surface, calculate the mean, variance and standard deviation of the global polishing intensity, and obtain the statistical characteristic data of polishing intensity;

[0122] This invention reads node-coordinated polishing intensity distribution data, which includes the three-dimensional coordinates of each surface grid node and the coordinated polishing intensity value, forming a set of numerical points with spatial distribution attributes. The system then performs statistical processing to extract statistical characteristic indicators of the global polishing intensity, including the mean, variance, and standard deviation. Specifically, the system iterates through the intensity values ​​of all nodes, sums all intensity values, divides by the total number of nodes to obtain the mean, calculates the squared difference between each node's intensity value and the mean, sums these values, divides by the total number of nodes to obtain the variance, and finally takes the square root of the variance to obtain the standard deviation. These statistical results are encapsulated as "polishing intensity statistical characteristic data," used to describe the overall uniformity level of the entire workpiece surface under the current polishing coverage. For example, in a prototype test, the global average polishing intensity was 0.042 mm, and the standard deviation was 0.0067 mm, indicating that there may be some intensity fluctuations in local areas, thus providing a quantitative basis for subsequent uniformity assessment.

[0123] Step S52: Quantitatively evaluate the uniformity deviation of each region on the workpiece surface using the statistical characteristic data of polishing intensity, calculate the relative deviation between the polishing intensity of each grid node and the global mean, and establish a deviation distribution histogram to obtain uniformity deviation evaluation data;

[0124] In this embodiment of the invention, the average global polishing intensity obtained in step S51 is used as a benchmark value to calculate the point-by-point deviation of the polishing intensity of all nodes on the workpiece surface. Specifically, for any node, its relative deviation is defined as the percentage difference obtained by subtracting the mean from the node's intensity value and then dividing by the mean. This processing reflects the degree of deviation of each node from the overall polishing level. The system then performs binning statistics on the deviation values ​​of all nodes, for example, dividing them into intervals of 5%, counting the number of nodes in each interval, and plotting a deviation distribution histogram to visualize the dispersion of the polishing uniformity of the entire surface. For example, on a certain test piece, the system detects that 85% of the node deviations are within ±10%, while the remaining nodes have larger deviations, which may correspond to abnormal areas. Finally, the processing results are organized into "uniformity deviation evaluation data," which is not only used to evaluate the consistency performance of the overall workpiece surface but also provides a direct data source for identifying abnormal areas.

[0125] Step S53: Identify and mark areas with substandard polishing quality based on uniformity deviation evaluation data. By setting a deviation threshold range and filtering out the set of grid nodes that exceed the threshold, the quality abnormality area marking data is obtained.

[0126] In this embodiment of the invention, based on step S52, a deviation threshold range is further set. For example, a relative deviation absolute value greater than 15% is set as the criterion for judging quality anomalies. Then, a set of nodes exceeding this threshold is selected from all nodes. These nodes are determined to be areas with quality problems under the current polishing process. The system further performs spatial clustering processing on these abnormal nodes, grouping spatially adjacent or continuous abnormal nodes into an abnormal region and generating a unique identifier number for each abnormal region. Simultaneously, the system records the maximum deviation value, center position coordinates, and boundary range of each region to construct "quality anomaly region marking data." For example, an area of ​​approximately 32mm² is identified at the edge of a workpiece. 2 If a continuous abnormal area has a maximum deviation of +27%, it can be inferred that there is insufficient grinding head contact or a blind spot in the trajectory coverage in that area. This marked data not only provides a basis for decision-making by process engineers, but also provides target input for the subsequent automatic path replanning system.

[0127] Step S54: Adjust the grinding head motion parameters and optimize the polishing coverage effect based on the quality anomaly area marking data, and verify the convergence of the optimization effect to obtain the three-dimensional digital polishing model data.

[0128] In this embodiment of the invention, the abnormal region information identified in step S53 is received, and the polishing path optimization module is activated to dynamically adjust the trajectory planning, action time, or pressure of the grinding head in the corresponding region. Specifically, the system first performs perturbation simulation on the current process parameters, attempting to extend the residence time of the grinding head in the abnormal region or increase the pressure without changing the global path structure, while avoiding local over-polishing. Then, the system uses a digital twin simulation model to predict the adjusted collaborative polishing intensity distribution and compares it with the statistical characteristics in step S51 to determine whether the deviation has been significantly reduced. The system confirms whether the optimization target has been achieved (e.g., the deviation of nodes in the abnormal region is reduced to within ±10%) through iterative optimization and difference convergence judgment. Finally, the system reorganizes the collaborative polishing intensity data of all nodes after optimization into "three-dimensional digital polishing model data". This dataset contains both the final fitted intensity distribution and the workpiece surface morphology mapping relationship, which can be used for virtual reconstruction and digital verification of the polishing effect. For example, on a high-precision mirror-polished part, after optimizing the dwell time of two abnormal areas by 5 seconds, the overall standard deviation decreased from 0.0067mm to 0.0034mm. The optimization process showed good convergence and formed a model basis that can be directly applied to digital process control.

[0129] Of particular importance, step S54 includes the following steps:

[0130] Step S541: Calculate the geometric feature parameters of the centroid coordinates, area size, and boundary shape of the abnormal area based on the quality anomaly area marking data to obtain the geometric feature data of the abnormal area;

[0131] This invention, based on quality anomaly region marker data, aggregates all anomaly nodes within each anomaly region using spatial coordinate information. It calculates the centroid coordinates of the region, essentially averaging the spatial coordinates of all nodes within the region according to their area or weight to obtain a point representing the overall location of the region. Next, the system utilizes the spatial distribution boundary of the aggregated nodes and employs a two-dimensional point set boundary detection algorithm (such as the convex hull algorithm or the alpha shape algorithm) to extract the boundary contour of the anomaly region. This allows for the calculation of the region's area and geometric feature parameters of its boundary shape, such as boundary perimeter and shape regularity indices (circularity, aspect ratio, etc.). These parameters collectively constitute "anomaly region geometric feature data," used to accurately characterize the spatial morphological features of the anomaly region. In specific applications, for example, for areas with an area of ​​10 mm²... 2 Up to 50mm 2 The system can accurately describe the geometry of abnormal areas, thus laying the foundation for matching analysis of the grinding head coverage area.

[0132] Step S542: Calculate the overlap ratio between the working range of each grinding head and the abnormal area based on the geometric feature data of the abnormal area, and establish a grinding head responsibility rating table;

[0133] This invention, in its embodiments, calculates the overlap ratio between each grinding head and the abnormal region by considering the current operating range of each grinding head (typically determined by the grinding head's swing radius, motion trajectory envelope, and applied pressure area). Specifically, the two-dimensional projection of the grinding head's operating range is spatially superimposed on the boundary of the abnormal region. The intersection area is calculated using a grid discretization method and then divided by the area of ​​the abnormal region to obtain the ratio. The system uses the overlap ratio corresponding to each grinding head as its "responsibility" index, summarizing it into a grinding head responsibility score table. This table reflects the relative contribution of each grinding head to the abnormal region. For example, if the overlap area of ​​a certain grinding head in an abnormal region accounts for 40% of the region's area, then the responsibility score of that grinding head is 0.4. This score table provides a quantitative basis for subsequent selection of key grinding heads, helping to accurately locate the root cause of the problem.

[0134] Step S543: Screen and identify key grinding heads using the grinding head responsibility rating table. By setting a correlation threshold and extracting the set of grinding heads with correlation scores exceeding the threshold, a list of grinding heads to be optimized is obtained.

[0135] In this embodiment of the invention, a responsibility threshold (e.g., 0.2) is set for the grinding head responsibility score table obtained in step S542. All grinding heads with responsibility scores exceeding this threshold are selected to form a list of grinding heads to be optimized. The selection process involves traversing the responsibility score table, screening grinding heads that meet the criteria for each abnormal area, and then grouping these grinding heads into the set to be optimized. The purpose of this step is to highlight the grinding heads that have the greatest impact on the abnormal areas, avoid ineffective adjustments, and improve optimization efficiency. In specific applications, such as during the polishing process of a workpiece, 15 grinding heads with a responsibility score higher than 0.2 are selected as key optimization targets, providing targeted objectives for subsequent parameter adjustments.

[0136] Step S544: Based on the list of grinding heads to be optimized, establish a correspondence table between defect types and parameter adjustment directions, and modify the swing amplitude, frequency, or phase difference parameters of the corresponding grinding heads according to the preset adjustment step size to obtain grinding head parameter configuration data.

[0137] This invention adjusts the key parameters of each grinding head based on a pre-established "correspondence table between defect types and parameter adjustment directions" using a list of grinding heads to be optimized. This correspondence table, based on expert experience and historical test data, maps different types of defects (such as insufficient polishing intensity, blind spots, and significant edge effects) to specific adjustment directions for the grinding head's oscillation amplitude, oscillation frequency, or phase difference. The system modifies the corresponding grinding head parameters one by one according to a preset adjustment step size (e.g., oscillation amplitude adjusted by 0.5mm each time, frequency adjusted by 0.2Hz each time, or phase difference adjusted by 5 degrees), generating new parameter configuration data. This process ensures both precise and smooth adjustments, avoiding large parameter jumps that could lead to process instability. For example, for defects with insufficient edge polishing, the system appropriately increases the grinding head's oscillation amplitude and frequency to improve the polishing intensity in that area.

[0138] Step S545: Repeat the calculation process of steps S543 to S544 using the grinding head parameter configuration data, regenerate the grinding head trajectory and polishing coverage effect using the new parameters, and obtain the three-dimensional polishing coverage optimization data after parameter adjustment.

[0139] This invention, based on grinding head parameter configuration data, recalculates the grinding head's motion trajectory and its effective range according to the new parameters, generating a new grinding head trajectory path. Subsequently, a 3D digital model simulation engine is used to simulate the trajectory coverage effect, mimicking the polishing coverage state of the grinding head on the workpiece surface, generating the latest 3D polishing coverage optimization data. This data includes the updated node polishing intensity distribution and synergistic effects, serving as a digital representation of the new round of polishing effects. Through this closed-loop iterative approach, the system achieves dynamic matching between grinding head parameter adjustments and polishing coverage effects, ensuring that each optimization provides actual numerical feedback. For example, in a test path, by adjusting the grinding head frequency and oscillation parameters, the system simulation showed that the average polishing intensity in the abnormal area increased by approximately 12%.

[0140] Step S546: Determine the convergence of the optimization effect based on the updated 3D polishing coverage data to obtain 3D digital polishing model data.

[0141] This invention employs a convergence evaluation algorithm to assess optimization effectiveness based on updated 3D polishing coverage data. The evaluation criteria include changes in the global statistical characteristics of polishing intensity (mean and standard deviation), whether the deviation values ​​of key abnormal areas are below a preset threshold, and the relative improvement in coverage effect before and after grinding head parameter adjustment. The system calculates the difference in polishing intensity distribution between two consecutive optimization iterations. When this difference is below a predetermined convergence threshold (e.g., a mean change of less than 0.001 mm and a standard deviation change of less than 0.0005 mm), the optimization process is deemed to have reached a stable state, and the final 3D digital polishing model data is output. This data contains spatial distribution information of polishing coverage after multiple rounds of adjustment, reflecting a high-quality, uniform polishing effect on the workpiece surface, and is suitable for subsequent quality inspection and process control. In practical applications, the system typically converges after 3 to 5 iterations, ensuring that the workpiece polishing process is both efficient and precise.

[0142] The present invention also provides a three-dimensional digital model generation system for a polishing machine, used to execute the above-described three-dimensional digital model generation method for a polishing machine, wherein the three-dimensional digital model generation system for a polishing machine includes:

[0143] The three-dimensional geometric data acquisition module is used to acquire the three-dimensional geometric data of the workpiece surface and the kinematic parameter data of the multi-segment oscillating grinding head;

[0144] The surface meshing module is used to perform mesh discretization on the workpiece surface based on three-dimensional geometric data to obtain surface mesh node data containing spatial coordinate information and normal vector information.

[0145] The grinding head trajectory modeling module is used to mathematically model the differential oscillation trajectory of each grinding head based on kinematic parameter data, and obtain the spatiotemporal position mapping data of the grinding head. Specifically, the differential oscillation trajectory is achieved by setting a combination of sinusoidal functions of π phase difference between different grinding heads to achieve uniform distribution of multiple grinding heads in the time domain and maximum complementary coverage in the spatial domain.

[0146] The dynamic coverage calculation module is used to perform dynamic coverage calculation on the contact relationship between the effective working area of ​​the grinding head and the workpiece surface based on the surface grid node data and the spatiotemporal position mapping data of the grinding head, and obtain three-dimensional polishing coverage data including the cumulative polishing time and the distribution of collaborative polishing intensity. Specifically, the dynamic coverage calculation process is to achieve accurate polishing amount prediction for each grid node on the workpiece surface through the working radius of the grinding head and the polishing intensity distribution.

[0147] The uniformity assessment and optimization module is used to assess and optimize the uniformity of polishing quality based on the three-dimensional polishing coverage data, and obtain three-dimensional digital polishing model data.

[0148] Therefore, the embodiments should be considered as exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of the equivalents of the application are intended to be included within the invention.

[0149] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features of the invention herein.

Claims

1. A method for generating a three-dimensional digital model applied to a polishing machine, characterized by, The method comprises the following steps: Step S1: obtaining three-dimensional geometric data of the workpiece surface and kinematic parameter data of the multi-segment swing grinding head; Step S2: discretely processing the workpiece surface in a grid manner according to the three-dimensional geometric data to obtain surface grid node data containing spatial coordinate information and normal vector information; Step S3: mathematically modeling the differential swing trajectory of each grinding head according to the kinematic parameter data to obtain grinding head space-time position mapping data, wherein the differential swing trajectory is specifically a uniform distribution of the multi-grinding head in the time domain and a maximum complementary coverage in the spatial domain through setting a sine function combination with a pi phase difference between different grinding heads; Step S4: performing dynamic coverage calculation processing on the contact relationship between the effective action area of the grinding head and the workpiece surface according to the surface grid node data and the grinding head space-time position mapping data to obtain three-dimensional polishing coverage data containing cumulative polishing time and collaborative polishing intensity distribution, wherein the dynamic coverage calculation processing is specifically to realize accurate polishing amount prediction of each grid node of the workpiece surface through the grinding head action radius and the polishing intensity distribution; Step S5: evaluating and optimizing the polishing quality uniformity according to the three-dimensional polishing coverage data to obtain three-dimensional digital polishing model data.

2. The three-dimensional digital model generation method for a polishing machine according to claim 1, wherein, Step S2 comprises the following steps: Step S21: performing triangular grid division processing on the surface area according to the three-dimensional geometric data to obtain triangular grid data, wherein the grid density is set to not less than 100 grid nodes per square centimeter; Step S22: performing coordinate assignment and normal vector calculation processing on each grid node according to the triangular grid data to obtain node geometric attribute data of node coordinate information and normal vector information; Step S23: performing unique identifier allocation processing on the grid node according to the node geometric attribute data to obtain surface grid node data with index identification.

3. The method of claim 2, wherein the three-dimensional digital model is generated by a computer program. Step S3 comprises the following steps: Step S31: extracting the swing amplitude, swing frequency, swing center position and swing plane angle of each grinding head from the kinematic parameter data, and establishing a structured grinding head parameter table of each grinding head; Step S32: determining the phase difference value of each grinding head by using the total number of grinding heads in the grinding head parameter table, and assigning different phase starting points to each grinding head by equally dividing the complete cycle to generate a phase difference configuration list; Step S33: generating a grinding head trajectory description set containing a personalized phase difference swing trajectory description for each grinding head according to the grinding head parameter table and the phase difference configuration list; Step S34: time sampling the entire polishing cycle at a preset time interval based on the grinding head trajectory description set to calculate the three-dimensional spatial coordinate position of all grinding heads at each time point, thereby forming a grinding head position coordinate sequence table arranged in chronological order; Step S35: establishing a quick query correspondence between the time stamp and the grinding head position information by using the grinding head position coordinate sequence table, thereby obtaining the grinding head space-time position mapping data.

4. The method of claim 3, wherein the three-dimensional digital model is generated by using a three-dimensional modeling software. Step S4 comprises the following steps: Step S41: According to the spatial position mapping data of the grinding head and the surface grid node data, the spatial distance calculation process of the grinding head and the grid node is carried out, and the three-dimensional Euclidean distance between the center position of each grinding head at each time point and the grid node of the workpiece surface is calculated to obtain the grinding head node distance matrix data; Step S42: According to the grinding head node distance matrix data and the preset grinding head action radius threshold, the effective action area judgment process is carried out, and the grid nodes in the effective action range of each grinding head are filtered out through distance comparison to obtain the grinding head action area coverage relationship data; Step S43: Based on the grinding head action area coverage relationship data, the instantaneous polishing intensity value calculation of the polishing intensity distribution model based on the Gaussian attenuation function is carried out for each grid node to obtain the node instantaneous polishing intensity data; Step S44: According to the node instantaneous polishing intensity data, the time series based cumulative calculation process is carried out to obtain the node cumulative polishing amount data, wherein the cumulative calculation process is specifically through time integral operation on the polishing intensity received by each grid node in the entire polishing period; Step S45: The node cumulative polishing amount data is used to carry out superposition calculation process on the multi-grinding head synergistic effect to obtain the node synergistic polishing intensity distribution data; Step S46: According to the node cumulative polishing amount data and the node synergistic polishing intensity distribution data, the cumulative polishing time length information and the synergistic polishing intensity distribution information are matched according to the grid node index to obtain the three-dimensional polishing coverage data.

5. The method of claim 4, wherein the three-dimensional digital model is generated by using a computer program. Step S42 includes the following steps: Step S421: According to the grinding head node distance matrix data and the preset grinding head action radius threshold, the distance value comparison process is carried out one by one to obtain the distance judgment result data; Step S422: According to the distance judgment result data, the grinding head node pairs meeting the action range condition are filtered and extracted, and the effective grinding head node pairing list is obtained by retaining the grinding head node combinations with distance values less than or equal to the action radius threshold; Step S423: According to the effective grinding head node pairing list, the action node set of each grinding head is grouped based on the grinding head identifier to obtain the grinding head grouping node set data; Step S424: Based on the grinding head grouping node set data, the action node set of each grinding head is traversed and the covered grinding heads of each node are counted to obtain the node covered grinding head list data; Step S425: The grinding head grouping node set data and the node covered grinding head list data are used to construct a bidirectional index mapping table from grinding head to node and from node to grinding head to obtain the grinding head action area coverage relationship data.

6. The method of claim 5, wherein the three-dimensional digital model is generated by a computer program. Step S43 includes the following steps: Step S431: Extract the distance value information of each grinding head and the grid node in its action range from the grinding head action area coverage relationship data to obtain the effective distance value data set; Step S432: The effective distance value data set and the preset Gaussian attenuation parameter are used to carry out normalized distance calculation process to obtain the normalized distance ratio data; Step S433: According to the normalized distance ratio data, the square of the normalized distance ratio is multiplied by the negative Gaussian attenuation coefficient and the natural exponential is taken to obtain the Gaussian attenuation factor data; Step S434: intensity value calculation processing is performed according to the Gaussian attenuation factor data and a preset maximum polishing intensity parameter of the polishing head, to obtain a grid node basic polishing intensity value; Step S435: correction and result solving processing based on the action direction of the polishing head and the surface normal vector of the grid node is performed according to the grid node basic polishing intensity value, to obtain node instantaneous polishing intensity data.

7. The method of claim 6, wherein the three-dimensional digital model is generated by a computer program. Step S435 includes the following steps: An angle correction calculation processing is performed on the angle between the normal vector of the polishing head and the surface of the node based on the grid node basic polishing intensity value, wherein a cosine value of the action direction of the polishing head and the surface normal vector of the node is calculated and used as a correction coefficient, to obtain an angle-corrected polishing intensity value; A speed influence factor calculation processing is performed according to the polishing intensity value and the motion speed information of the polishing head at the current time point, to obtain polishing head node speed modulation intensity data; The node instantaneous polishing intensity data is obtained by superimposing and summing the effects of multiple polishing heads on the same grid node at the current time point according to the polishing head node speed modulation intensity data.

8. The method of claim 7, wherein the three-dimensional digital model is generated by a computer program. Step S45 includes the following steps: Step S451: neighborhood relationship establishment processing is performed on each grid node of the workpiece surface according to the node cumulative polishing amount data, direct neighboring nodes of each node are identified, and a topological connection relationship between the nodes is established, to obtain node neighborhood topological data; Step S452: a local polishing intensity gradient of each node is calculated based on the node neighborhood topological data and the node cumulative polishing amount data, and the polishing amount difference between the current node and its neighborhood nodes is calculated and divided by the distance between the nodes, to obtain node polishing gradient data; Step S453: a gradient flatness-based quantitative calculation processing is performed on the synergistic enhancement effect among multiple polishing heads according to the node polishing gradient data, to obtain node synergistic enhancement coefficient data; Step S454: synergistic effect modulation calculation processing is performed using the node synergistic enhancement coefficient data and the node cumulative polishing amount data, and the original polishing intensity is amplified and modulated by multiplying the cumulative polishing amount by the synergistic enhancement coefficient, to obtain node synergistic modulation intensity data; Step S455: spatial distribution statistical processing is performed on the overall synergistic effect of the workpiece surface by using the node synergistic modulation intensity data, and the synergistic modulation intensity of each node is rearranged and normalized according to the spatial position, to obtain node synergistic polishing intensity distribution data.

9. The method of claim 8, wherein the three-dimensional digital model is generated by a computer program. Step S5 includes the following steps: Step S51: statistical analysis processing is performed on the polishing intensity distribution of the workpiece surface based on the three-dimensional polishing coverage data, the mean, variance and standard deviation of the global polishing intensity are calculated, and polishing intensity statistical characteristic data is obtained; Step S52: uniformity deviation of each region of the workpiece surface is quantitatively evaluated by using the polishing intensity statistical characteristic data, the relative deviation between the polishing intensity of each grid node and the global mean value is calculated, and a deviation distribution histogram is established, to obtain uniformity deviation evaluation data; Step S53: a quality abnormal region marking data is obtained by identifying and marking the polishing quality substandard region according to the uniformity deviation evaluation data, by setting a deviation threshold range and screening out a grid node set exceeding the threshold. Step S54: Adjust the motion parameters of the grinding head according to the quality abnormal area marking data, optimize the polishing coverage effect, and verify the convergence of the optimization effect, thereby obtaining three-dimensional digital polishing model data.

10. A three-dimensional digital model generation system applied to a polishing machine, characterized by, The three-dimensional digital model generation system applied to the polishing machine comprises: a three-dimensional geometric data acquisition module for acquiring three-dimensional geometric data of a workpiece surface and kinematic parameter data of a multi-segment swing grinding head; a surface gridding processing module for performing gridding and discrete processing on the workpiece surface according to the three-dimensional geometric data, to obtain surface grid node data containing spatial coordinate information and normal vector information; a grinding head trajectory modeling module for mathematically modeling the differential swing trajectories of the grinding heads according to the kinematic parameter data, to obtain grinding head space-time position mapping data, wherein the differential swing trajectory is specifically a combination of sine functions with different phase differences between the grinding heads, for uniform distribution of the grinding heads in the time domain and maximum complementary coverage in the spatial domain; a dynamic coverage calculation module for performing dynamic coverage calculation processing on the contact relationship between the effective action area of the grinding head and the workpiece surface according to the surface grid node data and the grinding head space-time position mapping data, to obtain three-dimensional polishing coverage data containing cumulative polishing time and collaborative polishing intensity distribution, wherein the dynamic coverage calculation processing is specifically to realize accurate polishing amount prediction for each grid node of the workpiece surface by the grinding head action radius and the polishing intensity distribution; a uniformity evaluation and optimization module for evaluating and optimizing the polishing quality uniformity according to the three-dimensional polishing coverage data, to obtain three-dimensional digital polishing model data. a three-dimensional geometric data acquisition module for acquiring three-dimensional geometric data of a workpiece surface and kinematic parameter data of a multi-segment swing grinding head; a surface gridding processing module for performing gridding and discrete processing on the workpiece surface according to the three-dimensional geometric data, to obtain surface grid node data containing spatial coordinate information and normal vector information; a grinding head trajectory modeling module for mathematically modeling the differential swing trajectories of the grinding heads according to the kinematic parameter data, to obtain grinding head space-time position mapping data, wherein the differential swing trajectory is specifically a combination of sine functions with different phase differences between the grinding heads, for uniform distribution of the grinding heads in the time domain and maximum complementary coverage in the spatial domain; a dynamic coverage calculation module for performing dynamic coverage calculation processing on the contact relationship between the effective action area of the grinding head and the workpiece surface according to the surface grid node data and the grinding head space-time position mapping data, to obtain three-dimensional polishing coverage data containing cumulative polishing time and collaborative polishing intensity distribution, wherein the dynamic coverage calculation processing is specifically to realize accurate polishing amount prediction for each grid node of the workpiece surface by the grinding head action radius and the polishing intensity distribution; a uniformity evaluation and optimization module for evaluating and optimizing the polishing quality uniformity according to the three-dimensional polishing coverage data, to obtain three-dimensional digital polishing model data.

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