A method for generating and sequencing ruled surface wire saw roughing paths
By optimizing the wire cutting path using a comprehensive objective function and a traveling salesman problem model, the problems of uneven allowance and physical instability in wire cutting path planning are solved, achieving an efficient and stable cutting process.
Patent Information
- Application Number
- CN202610425857.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2026-04-02
- Publication Date
- 2026-07-07
- Estimated Expiration
- 2046-04-02
Smart Images
Figure CN121956812B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of automatic path planning technology in subtractive manufacturing and CNC machining, and particularly to a method for generating and sorting rough machining paths for ruled surface wire cutting. Background Technology
[0002] The core principle of subtractive manufacturing is to remove excess material from a workpiece through processes such as cutting, milling, and wire EDM to obtain an object of the desired shape and size. Modern subtractive manufacturing typically employs a two-stage workflow: roughing and finishing. In the roughing stage, the main objective is to maximize material removal rate and machining efficiency, while ensuring process stability and leaving a uniform and appropriate allowance for finishing. Compared to other methods such as milling, wire EDM imposes stricter constraints on path planning because the ends of the cutting line must always remain outside the workpiece to prevent the robotic arm from colliding with the material being processed.
[0003] Currently, existing technologies typically transform path generation into the Next Best Viewpoint (NBV) problem. In each iteration, a viewpoint that removes the maximum amount of material is selected, and the outer contour at that viewpoint is approximated with a smooth curve and squeezed into a ruled surface cutting path. However, existing technologies do not consider the uniformity of the machining allowance and ignore the distribution of approximation errors, which is crucial for the stability of subsequent finishing. Furthermore, existing technologies neglect the physical stability of the material during the cutting process, such as gravity-induced swaying, deformation, or stress in overhanging portions, and using two-dimensional projected area as a surrogate index for the material removal volume leads to insufficient accuracy. Additionally, the lack of sequential optimization between the multiple cutting paths generated by existing algorithms results in long idle cutting times for the robotic arm transferring between paths, making manual specification of start and end positions time-consuming and labor-intensive.
[0004] Therefore, how to generate uniformly distributed and physically stable wire cutting paths under multiple manufacturing constraints, and minimize the empty cutting time, has become a technical problem that urgently needs to be solved. Summary of the Invention
[0005] The main objective of this invention is to provide a method for generating and sorting roughing paths for ruled surface wire EDM, which aims to generate uniformly distributed and physically stable wire EDM paths under multiple manufacturing constraints and minimize idle cutting time.
[0006] To achieve the above objectives, this invention proposes a method for generating and sorting rough machining paths for ruled surface wire cutting, comprising the following steps:
[0007] Step 1: Find the viewpoint based on the global optimization algorithm, and evaluate the viewpoint using the comprehensive objective function. The comprehensive objective function includes a volume term characterizing the material removal efficiency, a uniformity term characterizing the quality of the remaining material distribution, and a geometric constraint term characterizing the physical stability of the material during processing.
[0008] Step 2: Extract the projected contour of the target shape along the obtained viewpoint direction, approximate the projected contour with a smooth curve, and compensate for the offset according to the Hausdorff distance between the smooth curve and the projected contour to eliminate collision interference and generate a ruled surface cutting path.
[0009] Step 3: Iteratively execute the viewpoint optimization and path generation steps until the deviation between the target shape and the remaining blank material meets the preset termination condition, and obtain the cutting path set;
[0010] Step 4: Model each cutting path as a path segment containing at least one internal constraint node, transform the set of cutting paths into a traveling salesman problem model, and force the tool to perform a cutting action through the interior of the workpiece by setting the connection weights between nodes, and minimize the empty cutting distance between paths to determine the cutting sequence.
[0011] Preferably, the formula for calculating the comprehensive objective function is as follows:
[0012]
[0013] in, Remove the volume term from the material. For the error distribution uniformity term, This is the centroid offset term. For the suspension constraint term, , , These are the corresponding weighting coefficients.
[0014] Preferably, the error distribution uniformity term The calculation steps include:
[0015] Traverse the vertices of the target mesh Calculate the difference between the distance from the vertex to the remaining blank material and the average distance from one of the adjacent vertices of the vertex to the remaining blank material. The error distribution uniformity term... The expression is:
[0016]
[0017] in, Indicates the first The remaining blank material after the next iteration Represents vertices The set of adjacent vertices in a ring, This represents the total number of vertices.
[0018] Preferably, the centroid offset term The calculation method is as follows: calculate the center of gravity of the remaining blank material. To the center axis of the worktable The distance;
[0019] The suspension constraint item The calculation method is as follows: for a surface with the normal pointing downwards, calculate the sum of the products of its area, the distance from the centroid to the central axis, and the depth to which the vertically upward ray first penetrates the interior of the material.
[0020] Preferably, the global optimization algorithm uses a differential evolution algorithm to globally optimize the viewpoint parameters, which include the azimuth angle. and elevation angle Differential evolution is a stochastic optimization method based on population evolution. It continuously updates candidate solutions through mutation, crossover, and selection operations, thereby gradually approaching the optimal solution of the objective function.
[0021] First, an initial population is generated in the viewpoint parameter space, where each individual represents a candidate viewpoint. The population size is denoted as . The i-th individual is denoted as .
[0022] Preferably, the specific steps in step two of approximating the projected contour using a smooth curve and compensating for the offset include:
[0023] Interpolate the outer contour polygon obtained by projection using cubic B-spline curves;
[0024] If the cubic B-spline curve collides with the outer contour polygon, calculate the Hausdorff distance between the cubic B-spline curve and the outer contour polygon. The cubic B-spline curve is shifted positively outward from the projected contour. The distance.
[0025] Preferably, the preset termination condition in step three includes at least one of the following:
[0026] The Hausdorff distance between the target mesh and the remaining material is less than 1% of the diagonal length of the target mesh bounding box;
[0027] In three consecutive iterations, the relative change in the Hausdorff distance between the target mesh and the remaining material is less than 1%.
[0028] Preferably, in step four, each cutting path is modeled as three nodes: a first entry node, a second internal node, and a third exit node.
[0029] Preferably, the weight settings between nodes in the traveling salesman problem model include:
[0030] Within the same cutting path, the weight of the first edge between the first entry node and the second internal node, and the weight of the second edge between the third exit node and the second internal node are both set to 0;
[0031] The second internal node is not connected to any other node except the first entry node and the third exit node, and its connection weight is set to infinity.
[0032] Preferably, the endpoint transfer weights between different cutting paths are established using a safe sphere, specifically as follows:
[0033] The endpoints of different paths are radially translated onto a safe, enclosed sphere centered on the target shape. The lengths of the great circles at the endpoints on the sphere are calculated, and the radial translation distance is used as the weights of the corresponding edges in the traveling salesman problem model.
[0034] The above technical solution has the following advantages:
[0035] This invention introduces a comprehensive objective function including volume, uniformity, and geometric constraints during the viewpoint selection stage. This achieves improved processing efficiency while effectively controlling the distribution quality of machining allowance and the physical stability of the material during cutting, preventing workpiece breakage or significant chatter caused by its own weight or gravitational lever effect. Hausdorff distance is used for collision avoidance compensation offset, ensuring that the generated smooth B-spline curve fits the target contour to the maximum extent without collisions. Furthermore, a pioneering three-node representation method transforms path sorting into a Traveling Salesman Problem (TSP) model for solution, forcing the tool to fully execute the cutting action through the workpiece's interior and minimizing the robotic arm's empty cutting distance from a global perspective, achieving a high degree of automation and path optimization in the roughing process. Attached Figure Description
[0036] The present invention will now be described in detail with reference to specific embodiments and accompanying drawings, wherein:
[0037] Figure 1 This is a schematic diagram of the overall process of the method for generating and sorting rough machining paths for ruled surface wire EDM under multiple constraints provided in an embodiment of the present invention.
[0038] Figure 2 This is a schematic diagram illustrating the principle of viewpoint selection and ruled surface generation process provided in an embodiment of the present invention.
[0039] Figure 3 This is a schematic diagram of the TSP graph model structure based on the three-node representation method provided in an embodiment of the present invention. Detailed Implementation
[0040] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0041] Example 1
[0042] This embodiment provides a method for generating and sorting roughing paths in ruled surface wire EDM under multiple constraints. This method is mainly used to solve technical problems such as uneven allowance distribution, poor machining stability, and excessively long idle time when performing wire EDM on complex geometries, such as linear hot wire cutting. Figure 1 As shown, the method flow described in this embodiment mainly includes the following four core stages.
[0043] The first stage involves viewpoint selection based on the Differential Evolutionary Algorithm (DE). During each iteration of the roughing process, the algorithm needs to determine an optimal cutting viewpoint, i.e., the next optimal viewpoint, which determines the direction in which the cutting line enters the workpiece. A triangular mesh representing the target shape is given. and the Remaining raw material after secondary cutting In this embodiment, the viewpoint parameters include azimuth angle. and elevation angle Perform global optimization. Specifically, combine... Figure 2 As shown in (a), the azimuth angle With elevation angle The spatial direction of the triangular mesh $T$ of the observed target shape is defined, and this direction determines the shape of the subsequent projected contour and the viewing angle for material removal.
[0044] To evaluate the merits of different viewpoints, this embodiment constructs a novel comprehensive objective function. This function not only considers processing efficiency but also incorporates multiple physical manufacturing constraints. Its calculation process aims to find the minimum value of this objective function. The formula for calculating the comprehensive objective function is shown in LaTeX format as follows:
[0045]
[0046] In the above formula, each parameter has a clear physical meaning and calculation logic. This step removes the volume term from the material to improve processing efficiency; it directly corresponds to the removal of the actual three-dimensional volume of the material in a single operation. ,in Indicates the first The volume of material removed each time. This is the error distribution uniformity term, used to ensure that the cut surface conforms to the target shape. The approximation error distribution is more uniform, avoiding excessive local margins. The calculation steps for this item include traversing the vertices of the target mesh. Calculate the sum of the absolute values of the differences between the distance from the vertex to the remaining blank material and the average distance from the vertex to the remaining blank material of its adjacent ring of vertices. The expression is shown in LaTeX format as follows:
[0047]
[0048] Indicates the first The remaining blank material after the next iteration Represents vertices The set of adjacent vertices in a ring, This represents the total number of vertices. In addition, the synthesis objective function also includes a barycenter offset term. It calculates the center of gravity of the remaining blank material. To the center axis of the worktable The distance is used to characterize this, aiming to ensure the physical equilibrium of the material during the cutting process. (Overhang constraint term) This method is used to avoid excessive overhangs during processing, which could lead to sagging deformation due to gravity. Specifically, for surfaces with the normal pointing downwards, it calculates the sum of the products of their area, the distance from the center of gravity to the central axis, and the depth to which a vertically upward ray first penetrates the material. The formula is:
[0049]
[0050] in, For a facet in mesh T that satisfies the condition of being normal downwards, It is noodles center of mass, It is noodles The area, and From Starting from, a ray passes through in a vertically upward direction. The first segment of the interior. , , These are preset weighting coefficients used to balance the importance of various constraints. Since the objective function contains multiple non-differentiable terms, this embodiment employs the Differential Evolutionary Algorithm (DE) for global search, finding the optimal constraint through initialization, mutation, crossover, and selection processes. The smallest optimal viewpoint.
[0051] (1) Population initialization
[0052] In the k-th material removal iteration, let the population be... ;
[0053] in:
[0054] This represents the parameters of the i-th candidate viewpoint;
[0055] For population size, select the best =50.
[0056] To improve the global representativeness of the initial solution, in the initial iteration phase, it is preferable to generate the initial population on a unit sphere using the farthest point sampling technique. This sampling technique ensures a high degree of spatial uniformity of the initial viewpoint by iteratively selecting candidate points with the maximum and minimum distances to the already sampled point set.
[0057] (2) Mutation operation
[0058] For each individual in the population Generate corresponding mutated individuals :
[0059]
[0060] in:
[0061] For the current population, the objective function is to... The individual that achieves the minimum value;
[0062] Let be a randomly selected individual integer index, and satisfy . ;
[0063] As a scaling factor, preferred .
[0064] This mutation strategy introduces mutations into the current population that affect the objective function. Individuals that achieve the minimum value The search direction is guided by a random difference vector to maintain population diversity, thereby balancing the algorithm's global exploration and local exploitation capabilities.
[0065] (3) Cross operations
[0066] mutated individuals With the original individual Perform component crossover to generate experimental individuals Its calculation method is as follows:
[0067]
[0068] in:
[0069] A uniform random number on the interval [0,1];
[0070] The crossover probability;
[0071] The component index is randomly selected to ensure that the experimental individual inherits at least one variant component;
[0072] Represents the original individual The Each component.
[0073] When j=0, it represents the parameter. When j=1, it represents the parameter. .
[0074] Crossover probability satisfies Preferred
[0075] (4) Select operation
[0076] Calculate the experimental individuals Corresponding objective function value The population is updated according to the following rules:
[0077]
[0078] Through the above mutation, crossover, and selection operations, the population gradually evolves toward the optimal solution of the objective function in multiple iterations.
[0079] The second stage involves generating the ruled surface cutting path and approximating the contour. For example... Figure 2 As shown, for the optimal viewpoint determined in the previous stage, the algorithm measures the target shape along the direction of that viewpoint. Perform orthogonal projection onto the workbench. Refer to [link / reference] for details. Figure 2 Subgraph display in: Figure 2 In (a), the projected contour is extracted along the selected viewpoint; as shown... Figure 2 As shown in (b), the outer contour polygon obtained by projection using a cubic B-spline curve B. Interpolation approximation is performed, and a magnified view in the figure shows the collision interference between the initial curve and the contour; subsequently, as... Figure 2 As shown in (c), the calculated Hausdorff distance Shifting the curve outwards eliminates interference, resulting in a safe path; ultimately, as shown... Figure 2 As shown in (d), the smoothed curve is squeezed along the viewpoint direction to generate a ruled surface cutting path.
[0080] In this embodiment, the outer contour polygon obtained by projection is extracted by performing a union operation using the Clipper library. Subsequently, a smooth curve, i.e., a cubic B-spline curve, was used. For projected outline polygons The vertices are approximated using interpolation. During the approximation process, to ensure absolute machining safety, anti-collision measures are required, i.e., real-time monitoring of the generated spline curves. With projected contour Does collision or interference exist between them? If a spline curve is detected... With projected outline polygon If an intersection occurs (i.e., a collision), then the Hausdorff distance between the two objects is calculated. The cubic B-spline curve is shifted positively outward from the projected profile. The distance. The Hausdorff distance is used to rigorously measure the shape of a triangular mesh of a target. Mesh of remaining material after cutting The maximum mismatch between the two meshes is calculated geometrically as follows: Assuming there are meshes A and B, for each point on the surface of mesh A, calculate the shortest distance from it to all points on the surface of mesh B, and record the maximum value among these shortest distances. This value is the one-way Hausdorff distance from A to B. Then, conversely, calculate the one-way Hausdorff distance from mesh B to mesh A; the larger of the two values is the true two-way Hausdorff distance between the two meshes. This detection and compensation process is iterated until the spline curve and the projected profile completely disjoint. Finally, the smooth and collision-free curve is squeezed along the viewpoint direction to generate the corresponding ruled surface cutting path.
[0081] The third stage is the iteration termination judgment. After generating a path, a Boolean subtraction operation is performed between it and the current remaining material to update the remaining blank mesh. The algorithm repeats the above viewpoint optimization and path generation steps. The preset termination conditions set in this embodiment include the following two cases, and the algorithm will stop when either one is met. The first case is the target shape mesh. With remaining materials The first case is where the Hausdorff distance between the two meshes is less than 1% of the diagonal length of the target mesh bounding box. The second case is where the relative change in the Hausdorff distance is less than 1% over three consecutive iterations. When the above conditions are met, the iteration stops, resulting in an unordered set of cut paths containing multiple ruled surface cut paths. .
[0082] The fourth stage involves optimizing the cutting sequence based on the three-node representation, i.e., solving the Traveling Salesman Problem (TSP). To minimize the idle cutting time of the robotic arm between different cutting tasks and improve overall processing efficiency, this embodiment transforms the path sequencing problem into a TSP model. For example... Figure 3As shown, each cutting path is modeled as three core nodes, namely the entry node. Internal nodes and export nodes .exist Figure 3 In the physical path diagram on the left, solid lines represent the endpoints of the cutting path, and dashed lines represent the cutting action that passes through the inside of the workpiece. Figure 3 The right side shows the corresponding TSP graph model structure, where solid lines connecting nodes represent mandatory constraints within a path, with a weight of 0; cross-path connections (such as from the exit node of the i-th path) represent constraints within a path. Entry node to the j-th path Represents air cut transfer
[0083] In the TSP model, the connection weights between nodes follow specific rules to enforce physical cutting actions. Within the same cutting path, the edge weights between the entry node and internal nodes, as well as between the exit node and internal nodes, are all set to 0, indicating that the processing does not include empty cutting penalties. The internal node constraints are specifically: internal nodes... It is not connected to any other node except the entry and exit nodes of its own path, and its connection weight is set to 1. This setting forces the solver to pass through internal nodes and exit from the exit node after entering the entry node. By using solid lines to represent endpoints and dashed lines to represent internal nodes in the graphical model, it eliminates connection ambiguity and prevents the path from being bypassed, ensuring that the tool completely cuts through the entire path.
[0084] For the endpoint transfer weights, i.e., the idle tool travel distances, between different cutting paths, this embodiment establishes a safety sphere. Specifically, a safety bounding sphere with the target shape center as the center and a radius of R is used, where R is greater than the maximum outer diameter of the target shape's bounding box. The length of the great circle arc on the sphere at both endpoints is calculated, and this arc length, combined with the radial translation distance, is used as the weight of the corresponding edge in the graph model. Finally, the TSP graph model is solved using an integer programming solver such as Google OR-Tools' CP-SAT to determine the globally optimal coherent cutting sequence.
[0085] Example 2
[0086] Based on the method described in Embodiment 1 above, this embodiment further expands and explains the key algorithm parameters and specific implementation details of the method. When executing the Differential Evolutionary Algorithm (DE algorithm) in the first stage to globally optimize the viewpoint parameters, the viewpoint parameters specifically include the azimuth angle. and elevation angle To ensure both coverage and convergence speed in the optimization process, in a specific application scenario of this embodiment, the initial population size of the differential evolution algorithm is set. The scaling factor is 50. The crossover rate is 0.9. The value is 0.9. The algorithm first randomly generates an initial population in a two-dimensional parameter space consisting of azimuth and elevation angles. The specific value range is 0 to 360°, elevation angle The specific value range is from 0 to 180°.
[0087] For each generated random viewpoint, the algorithm utilizes the comprehensive objective function. An evaluation is conducted. This includes calculating the error distribution term. At that time, by traversing all vertices of the target mesh. Get the set of adjacent vertices in a ring around a given vertex. This refers to the adjacent vertices directly connected to the given vertex via an edge. This calculation process can keenly capture the sharp fluctuations in the cutting allowance locally, thus guiding the viewpoint selection towards producing a smoother processing allowance. Furthermore, in the centroid offset term... In the calculation, the algorithm monitors the center of gravity of the remaining blank material in real time. Ensure it is aligned with the center axis of the worktable. Minimize the distance to reduce mechanical chatter during processing. For the overhang constraint term... The algorithm effectively avoids material deformation or fracture caused by gravity by calculating the sum of the products of the area of the facet with the normal pointing downwards, the distance from the center of gravity to the central axis, and the depth to which the vertically upward ray first penetrates the interior of the material.
[0088] In the second stage of generating the cutting path, in order to extract the accurate outer contour polygon... This embodiment calls the Clipper library to perform Boolean union operations on polygons. For the extracted discrete polygon vertices, cubic B-spline curves are used for interpolation, resulting in the interpolated curve... It can provide a continuous and smooth motion trajectory for the robotic arm. In collision avoidance processing, Hausdorff distance is used to rigorously measure the triangular mesh of the target shape. Mesh of remaining material after cutting The algorithm calculates the maximum mismatch between the spline curve and the outer contour. If an intersection (collision) is detected between the spline curve and the outer contour polygon, the algorithm automatically calculates the Hausdorff distance between the cubic B-spline curve and the outer contour polygon. and curve Offset to the outside of the projected contour in a positive direction Repeat this process until the interference is completely eliminated.
[0089] In the third stage of iteration termination judgment, the system determines whether to stop by monitoring the status of the machining allowance in real time. This embodiment verifies through experiments that when the Hausdorff distance between the target mesh and the remaining material is less than 1% of the diagonal length of the target mesh bounding box, or when the relative change of the Hausdorff distance in three consecutive iterations is less than 1%, the cutting process has achieved the expected roughing accuracy requirements.
[0090] In the fourth stage of path sequencing, the weight calculation of the idle travel distance is crucial for achieving efficient machining. To prevent collisions between the robotic arm and the workpiece during movement, this embodiment translates the endpoints of different paths radially onto a safe enclosing sphere with a radius of 2. The length of the great circle arc at each endpoint on the sphere is calculated and combined with the radial translation distance as the weight of the corresponding edge in the TSP model. This ensures that the robotic arm switches between cutting poses using the shortest and safest path. Subsequently, using integer programming solvers such as Google OR-Tools' CP-SAT, the globally optimal coherent cutting sequence is obtained.
[0091] Furthermore, this invention also provides an electronic device, including a memory and a processor. The memory stores a computer program, and the processor, when executing the computer program, can implement the path generation and sorting method described in any of the above embodiments. Simultaneously, this invention also relates to a computer-readable storage medium and a computer program product, which, by carrying the relevant computer program, enables the processor to perform the aforementioned complex geometric calculations and path planning tasks. By adopting the above technical solutions, this invention can significantly reduce the approximation error under the same number of cuts. For example, for a certain test model, the average Hausdorff error is reduced from... Down to Because of the introduction of the error distribution term In addition to the center of gravity and overhang constraints, not only is the uniformity of the allowance improved, but the physical stability during the machining process is also greatly enhanced, realizing a high degree of automation and intelligence in the roughing process.
[0092] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for generating and sorting rough machining paths for ruled surface wire cutting, characterized in that, Includes the following steps: Step 1: Find the viewpoint based on the global optimization algorithm, and evaluate the viewpoint using the comprehensive objective function. The comprehensive objective function includes a volume term characterizing the material removal efficiency, a uniformity term characterizing the quality of the remaining material distribution, and a geometric constraint term characterizing the physical stability of the remaining material relative to the central axis of the worktable during the processing. Step 2: Extract the projected contour of the target shape along the obtained viewpoint direction, approximate the projected contour with a smooth curve, and compensate for the offset according to the Hausdorf distance between the smooth curve and the projected contour to eliminate collision interference and generate a ruled surface cutting path. Step 3: Iteratively execute the viewpoint optimization and path generation steps until the deviation between the target shape and the remaining blank material meets the preset termination condition, and obtain the cutting path set; Step 4: Model each cutting path as a path segment containing at least one internal constraint node. Transform the set of cutting paths into a traveling salesman problem model. By setting the connection weights between nodes, model each cutting path as a three-node model containing an entry node, an internal node, and an exit node. By setting the weights between nodes within the same path to zero and restricting internal nodes to only connect to endpoints of the same path, determine the optimal cutting order with the goal of minimizing the weight transfer between paths.
2. The method for generating and sorting rough machining paths for ruled surface wire cutting according to claim 1, characterized in that, The formula for calculating the comprehensive objective function is as follows: in, Remove the volume term from the material. For the error distribution uniformity term, This is the centroid offset term. For the suspension constraint term, , , These are the preset weighting coefficients.
3. The method for generating and sorting rough machining paths for ruled surface wire cutting according to claim 2, characterized in that, The error distribution uniformity term The calculation steps include: Traverse the vertices of the target mesh Calculate the difference between the distance from the vertex to the remaining blank material and the average distance from one of the adjacent vertices of the vertex to the remaining blank material. The error distribution uniformity term... The expression is: in, Indicates the first The remaining blank material after the next iteration Represents vertices The set of adjacent vertices in a ring, Represents the total number of vertices. Represents vertices To the remaining raw materials Euclidean distance.
4. The method for generating and sorting rough machining paths for ruled surface wire cutting according to claim 2, characterized in that, The center of gravity offset term The calculation method is as follows: calculate the center of gravity of the remaining blank material. To the central axis of the worktable The distance; The suspension constraint item The calculation method is as follows: For the facet with the normal pointing downwards, calculate its area, the distance from the centroid to the central axis, and the first time the vertically upward ray passes through the remaining blank material. The sum of the products of the internal depths.
5. The method for generating and sorting rough machining paths for ruled surface wire EDM according to claim 1, characterized in that, The global optimization algorithm employs a differential evolution algorithm to globally optimize the viewpoint parameters, including the azimuth angle. and elevation angle .
6. The method for generating and sorting rough machining paths for ruled surface wire EDM according to claim 1, characterized in that, The specific steps in step two of approximating the projected contour using a smooth curve and compensating for the offset include: Interpolate the outer contour polygon obtained by projection using cubic B-spline curves; If the cubic B-spline curve collides with the outer contour polygon, calculate the Hausdorff distance between the cubic B-spline curve and the outer contour polygon. The cubic B-spline curve is shifted positively outward from the projected contour. The distance.
7. The method for generating and sorting rough machining paths for ruled surface wire EDM according to claim 1, characterized in that, The preset termination condition in step three includes at least one of the following: The Hausdorff distance between the target mesh and the remaining material is less than 1% of the diagonal length of the target mesh bounding box. In three consecutive iterations, the relative change in the Hausdorff distance between the target mesh and the remaining material is less than 1%.
8. The method for generating and sorting rough machining paths for ruled surface wire EDM according to claim 1, characterized in that, In step four, each cutting path is modeled as three nodes: the first entry node, the second internal node, and the third exit node.
9. The method for generating and sorting rough machining paths for ruled surface wire EDM according to claim 8, characterized in that, The weight settings between nodes in the traveling salesman problem model include: Within the same cutting path, the weight of the first edge between the first entry node and the second internal node, and the weight of the second edge between the third exit node and the second internal node are both set to 0; The second internal node is not connected to any other node except the first entry node and the third exit node, and its connection weight is set to infinity.
10. The method for generating and sorting rough machining paths for ruled surface wire cutting according to claim 9, characterized in that, The endpoint transfer weights between different cutting paths are established using a safe sphere, specifically as follows: The endpoints of different paths are radially translated onto a safe, enclosed sphere centered on the target shape. The lengths of the great circles at the endpoints on the sphere are calculated, and the radial translation distance is used as the weights of the corresponding edges in the traveling salesman problem model.
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