Continuous additive deposition path planning method for metal additive manufacturing

Through the combination of taboo search algorithm, genetic algorithm and B-spline curve, metal additive manufacturing path planning is optimized, and the problems of path discontinuity and inefficiency in the existing technology are solved, and efficient and stable metal additive manufacturing is achieved.

CN120382167APending Publication Date: 2025-07-29SHANGHAI JIAOTONG UNIV +1
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Patent Information

Application Number
CN202510453351.6
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-04-11
Publication Date
2025-07-29

AI Technical Summary

Technical Problem

The existing metal additive manufacturing path planning methods are prone to problems such as discontinuous deposition paths, uneven overlapping rates, and excessively long non-additive motion paths when dealing with complex shape structural parts, resulting in reduced WAAM quality and low manufacturing efficiency. Commercial software fails to effectively optimize key parameters, affecting welding stability and forming quality.

Method used

The taboo search algorithm and genetic algorithm combined with the B-spline curve method are used to optimize the connection order and planning path of multi-layer deposition paths, and the additive deposition trajectory points are obtained through interpolation method, and a mathematical model is constructed to minimize the path length and steering angle, eliminate geometric interference, and realize continuous additive deposition path planning.

Benefits of technology

The continuity and forming quality of metal additive structural parts are improved, the manufacturing cost and manufacturing time are reduced, the efficiency and stability of WAAM are improved, and the continuity of the welding process and the smoothness of the path are ensured.

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Abstract

The invention discloses a continuous additive deposition path planning method for metal additive manufacturing, which comprises the following steps of: importing a three-dimensional model of a metal structural part, and slicing layer by layer to obtain the section contour of each layer; and according to the section contour of each layer and the technological condition parameters, discrete filling points of a filling area in the section contour and boundary points of the section contour are determined to serve as additive deposition track points. And in combination with the process condition parameters and the additive deposition trajectory points, an additive deposition path planning mathematical model is constructed to plan an additive deposition path, and the deposition path is solved and smoothed to obtain an optimal deposition path. And optimizing the connection sequence of the multilayer deposition path based on a tabu search algorithm. And after connection, a complete continuous additive deposition path is exported. By means of the method, continuous additive deposition path planning of metal WAAM can be achieved, the problems of interruption and discontinuity of the deposition path are effectively solved, and the continuity and forming quality of the metal additive structural part are improved.
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Description

Technical Field

[0001] The present invention belongs to the field of metal additive manufacturing, and particularly relates to a continuous additive deposition path planning method for metal additive manufacturing. Background Art

[0002] With the increasing demand for complex metal structural parts in high-end equipment manufacturing fields such as aerospace, shipbuilding, and nuclear power, the wire arc additive manufacturing (WAAM) technology, as an advanced manufacturing process, has gradually received extensive attention. This technology uses an electric arc as the heat source, melts the metal wire layer by layer, and stacks the metal materials layer by layer into a three-dimensional metal structural part with a predetermined shape, having significant advantages such as high forming accuracy, high material utilization rate, and the ability to manufacture complex structures.

[0003] In the process of metal WAAM, the planning of continuous additive manufacturing deposition paths plays an important role. A reasonable deposition path can not only ensure the forming quality of metal structural parts, but also significantly reduce welding stress and thermal deformation, improve manufacturing efficiency and reduce manufacturing costs. However, currently in the field of metal WAAM, the existing path planning methods still have certain limitations.

[0004] Traditional path planning methods often rely on simple geometric filling patterns, such as grid filling, spiral filling, etc. When planning paths for complex-shaped structural parts and porous-shaped structural parts, these methods generally tend to have problems such as discontinuous deposition paths, uneven overlap ratios, and relatively long non-additive movement paths, resulting in a decline in WAAM quality and low manufacturing efficiency. In addition, when dealing with the filling of complex regions inside the model, these methods usually only divide the cross-sectional contour of the three-dimensional model into multiple sub-regions according to regional characteristics, and then perform internal filling path planning separately. However, this path planning method often has frequent arc starting and arc extinguishing, and generates redundant deposition paths. At the same time, the path planning of arc extinguishing points is not fully considered for optimization, making it difficult to meet the high-quality deposition requirements for metal structural parts in high-end equipment manufacturing.

[0005] More importantly, many commercial software for additive manufacturing also has the above-mentioned limitations in the path planning of metal three-dimensional models. Especially in the field of metal WAAM, it is difficult to achieve precise planning of continuous deposition paths. Although some commercial software (such as Cura) has path planning functions, it does not consider the important influence of key parameters such as overlap ratio on the forming process, resulting in the continuity and density of the weld beads not being effectively guaranteed. In addition, commercial software such as Cura fails to effectively optimize path planning, resulting in too long additive deposition paths, too many non-additive movement paths, and too many arc extinguishing points that will cause the welding arc to start and stop frequently. This not only significantly increases the manufacturing time and cost, but also affects the stability of the deposition process and is not conducive to manufacturing high-performance metal structural parts.

[0006] Therefore, developing a continuous additive deposition path planning method suitable for metal WAAM, comprehensively considering key influencing factors such as the overlap rate, additive bead width, and adjacent center distance, and taking the total length of the additive deposition path, path turning angle, etc. as optimization objectives to achieve the planning of multi-layer paths with the optimal deposition path is of great practical significance and application value for improving the forming quality and manufacturing efficiency of metal WAAM and promoting the wide application of this technology in the field of high-end equipment manufacturing. Summary of the Invention

[0007] The technical objective of the present invention is to provide a continuous additive deposition path planning method for metal additive manufacturing to solve the technical problems of many limitations existing in the existing path planning.

[0008] To solve the above problems, the technical solution of the present invention is as follows: A continuous additive deposition path planning method for metal additive manufacturing includes the following steps: Import the three-dimensional model of the metal structural part and perform layer-by-layer slicing processing on it to obtain the cross-sectional contour of each layer; According to the cross-sectional contour of each layer and the process condition parameters, respectively determine the discrete filling points in the internal filling area of the cross-sectional contour and the boundary points of the cross-sectional contour as the additive deposition trajectory points; Combined with the process condition parameters and the additive deposition trajectory points, construct a mathematical model for additive deposition path planning to plan the additive deposition path, and solve and smooth the deposition path to obtain the optimal deposition path; Based on the tabu search algorithm, optimize the connection order of the multi-layer deposition paths; After connection, export the complete continuous additive deposition path.

[0009] Among them, the cross-sectional contour of each layer represents the boundary of the corresponding metal deposition; assume that the three-dimensional model is composed of multiple triangular facets Each triangular facet is composed of three vertex coordinates , , During the layer-by-layer slicing process, for the layer height of each layer of slicing being , calculate the intersection points of the triangular facet and the slicing layer height by the interpolation method, which are the cross-sectional contours of this layer of slicing and are obtained through the following calculation formula: Among them, , represents the total number of triangular facets, , represents the total number of layers, represents the point coordinates on the intersection line, Represents the interpolation parameter.

[0010] Further preferably, after obtaining the cross-sectional profile, it is also necessary to eliminate the geometric interference of each layer of the cross-sectional profile, specifically as follows: Decompose the cross-sectional profile into multiple monotonic chains; By solving the self-intersection point set, locate all possible self-intersection points; Traverse the self-intersection point set and generate multiple loops, and determine the validity of these loops; Based on the validity determination result, optimize and reconstruct to obtain a cross-sectional profile without interference.

[0011] Among them, the discrete filling points are points arranged at preset intervals and rules within the filling area inside the cross-sectional profile, specifically including the following steps: The process condition parameters include the center distance between additive welding beads , the width of the additive welding bead and the overlap rate , and satisfy the following formula: Among them, the overlap rate is defined as the ratio of the overlapping part of adjacent additive welding beads to the width of the additive welding bead; If the required overlap rate is not less than 1 / 3, then the center distance between additive welding beads should satisfy the following formula: Let the width of the internal filling area of the cross-sectional profile be , then the number of additive welding beads along the width direction of the additive welding bead satisfies the following formula: According to the starting point and ending point of the additive welding bead, calculate the coordinates of the discrete filling points on each additive welding bead; Let the starting point coordinates of the additive welding bead be , and the ending point coordinates be , then the coordinates of the discrete filling points along the length direction of the welding bead can be calculated by the following formula: Among them, and are the step lengths along the length direction of the welding bead, , represents the number of points.

[0012] Among them, the boundary points of the cross-sectional profile are key points on the cross-sectional profile. By sampling each cross-sectional profile line segment of the filling area proportionally and using the interpolation method to calculate the discretized set of boundary points , where , represents the total number of profile line segments.

[0013] Among them, constructing the mathematical model for additive deposition path planning is specifically as follows: The goal of additive deposition path planning is to obtain the minimum total length of the deposition path and the turning angle of the deposition path , which are calculated respectively by the following formulas: The corresponding comprehensive objective function is: Among them, represents the objective function, and represent the weight coefficients.

[0014] Among them, using the genetic algorithm to solve the constructed mathematical model for additive deposition path planning is specifically as follows: Encoding the arrangement order of the additive deposition trajectory points as chromosome individuals to represent the possible solutions for supporting the deposition path; Iteratively optimizing the chromosomes through the selection, crossover, and mutation operations of the genetic algorithm to make the corresponding additive deposition path gradually approach the optimal solution to obtain the optimal deposition path; Each iterative optimization includes: Calculating the fitness of each chromosome and selecting the chromosomes through the selection operation of the genetic algorithm. The probability of each chromosome being selected is related to the fitness; Taking two randomly selected chromosomes as parent chromosomes and exchanging their gene segments through the crossover operation to generate a new generation of offspring chromosomes; Randomly changing the genes in the chromosomes with a preset probability through the mutation operation to enhance the population diversity; Until the iterative termination condition is satisfied, outputting the optimal deposition path.

[0015] Among them, further smoothing the optimal deposition path obtained by the genetic algorithm is specifically as follows: According to the coordinates of the additive deposition trajectory points, calculating the control points of the B-spline curve, and generating a smooth deposition path through the combination of the basis functions of the B-spline curve and the above control points; Assume there are control points , and adopt order B-spline curve, then the mathematical expression of the B-spline curve can be expressed as: where represents the basis function of the B-spline, which is calculated through a recursive formula:

[0016] Specifically, the tabu search algorithm is used to optimize the connection order of the multi-layer deposition path, with the goal of minimizing the length of the non-additive motion path and reducing the thermal effect caused by excessive heat accumulation, so as to realize the connection of the multi-layer additive deposition path.

[0017] Further preferably, the connected multi-layer additive deposition path will be inspected to judge the continuity and rationality of its path. If it does not meet the standard, it will return to the corresponding step for adjustment and optimization; if it meets the standard, the connected multi-layer additive deposition path will be used for metal additive manufacturing.

[0018] Due to the adoption of the above technical solutions, the present invention has the following advantages and positive effects compared with the prior art: The present invention can realize the continuous additive deposition path planning of metal WAAM, effectively avoid the problems of deposition path interruption and discontinuity, and improve the continuity and forming quality of metal additive structural parts.

[0019] By comprehensively considering key process constraint parameters such as the overlap ratio, additive bead width, and center distance of additive beads, and taking the total length of the additive deposition path, deposition path turning angle, etc. as the optimization objectives, the obtained additive deposition path is more in line with the process requirements of metal WAAM, improving the efficiency of WAAM and reducing the manufacturing cost.

[0020] Using the genetic algorithm for path planning and solution can effectively search for the global optimal solution or approximate global optimal solution, avoid the problem of local optimal solution, and improve the reliability and stability of additive deposition path planning.

[0021] Using the B-spline curve method to smooth the additive deposition path makes the path smoother and more continuous, reducing the arc swing and the acceleration change during the movement of the welding torch.

[0022] By using the tabu search algorithm to optimize the connection of the multi-layer additive deposition path, a shorter non-additive motion path and a good welding sequence can be realized, reducing the additive time and non-additive time, and further improving the manufacturing efficiency of metal WAAM. Brief Description of the Drawings

[0023] By reading the following detailed description of the preferred embodiments, various other advantages and benefits will become clear to those of ordinary skill in the art. The drawings are only for the purpose of showing the preferred embodiments and are not considered to be a limitation of the present invention.

[0024] Figure 1 It is a continuous additive deposition path planning method for metal additive manufacturing of the present invention; Figure 2 It is a flow schematic diagram of the optimal deposition path of the present invention; Figure 3 It is a schematic diagram of the additive deposition path planning of the metal structural member of the present invention. Specific embodiments

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or in the prior art, the following will describe the specific embodiments of the present invention with reference to the accompanying drawings. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained according to these drawings and other embodiments can be obtained.

[0026] To make the drawings concise, only the parts related to the present invention are schematically shown in each drawing, and they do not represent their actual structures as products. In addition, to make the drawings concise and easy to understand, in some drawings, components with the same structure or function are only schematically shown one of them, or only one of them is marked. In this article, "one" not only means "only this one", but also means "more than one" situation.

[0027] The following further details a continuous additive deposition path planning method for metal additive manufacturing proposed by the present invention in conjunction with the accompanying drawings and specific embodiments. According to the following description and the claims, the advantages and features of the present invention will be clearer.

[0028] Embodiment Refer to Figures 1 to 3 , this embodiment provides a continuous additive deposition path planning method for metal additive manufacturing, which includes the following steps: First, import the three-dimensional model of the metal structural member, which is the target of additive manufacturing, and perform layer-by-layer slicing on the three-dimensional model to obtain the cross-sectional contour of each layer. The contour line of each layer's cross-sectional contour represents the boundary of metal deposition for that layer, providing the basic data for the subsequent deposition path planning, and can be calculated by the following formula: Specifically, assume that the three-dimensional model is composed of multiple triangular patches constituting, and each triangular patch is in turn composed of three vertex coordinates , , Composition. During the layer-by-layer slicing process, for each layer, the layer height of the slice is , and the intersection points of the triangular facets and the slice layer height are calculated by interpolation method, which are the cross-section contours of the slice layer. This process can be obtained through the following calculation formula: Among them, , represents the total number of triangular facets, , represents the total number of layers, represents the point coordinates on the intersection line, represents the interpolation parameter.

[0029] Then, in order to ensure the accuracy and continuity of the deposition path offset contour during the WAAM process and avoid the problem of metal material accumulation caused by the overlap of the deposition path, it is necessary to eliminate the possible geometric interference of each cross-section contour to ensure the feasibility of the additive deposition path and the final forming quality. Eliminating the geometric interference of each cross-section contour specifically includes: 1) decomposing the cross-section contour into multiple monotonic chains to more accurately identify potential interference areas; 2) locating all possible self-intersection points by solving the self-intersection point set; 3) traversing the self-intersection point set and generating multiple loops, and determining the validity of these loops; 4) finally, based on the validity determination result, optimizing and reconstructing to obtain a non-interfering cross-section contour, so as to ensure that the deposition path during the WAAM process has no interference and no overlap.

[0030] According to the cross-section contour after dealing with the interference problem and the process condition parameters, the discrete filling points in the internal filling area of the cross-section contour and the boundary points of the cross-section contour are determined respectively as the additive deposition trajectory points. These additive deposition trajectory points will be used as the key nodes for subsequent path planning to ensure the reasonable distribution and connection of the additive weld beads. Specifically, the process condition parameters include the center distance of the additive weld beads, the width of the additive weld beads and the overlap rate .

[0031] Among them, the discrete filling points are the points arranged at preset intervals and rules in the internal filling area of the cross-section contour. By reasonably setting the discrete filling points, the metal filled in the cross-section contour can be evenly distributed to avoid the occurrence of under-filled areas.

[0032] Specifically, the following formula is used to comprehensively consider the relationship between the center distance of the additive weld beads, the width of the additive weld beads and the overlap rate : Among them, the overlapping rate is defined as the ratio of the overlapping part of adjacent additive weld beads to the width of the additive weld bead.

[0033] Furthermore, if it is required that the overlapping rate is not less than 1 / 3, then the center distance between additive weld beads should satisfy the following formula: .

[0034] Next, assuming that the width of the internal filling area of the cross-sectional profile is , then the number of additive weld beads along the width direction of the additive weld bead satisfies the following formula: According to the starting point and ending point of the additive weld bead, calculate the coordinates of the discrete filling points on each additive weld bead. Let the starting point coordinates of the additive weld bead be , and the ending point coordinates be , then the coordinates of the discrete filling points along the length direction of the weld bead can be calculated by the following formula: Among them, and are the step lengths along the length direction of the weld bead, , indicating the number of points.

[0035] Among them, the boundary points of the cross-sectional profile are the key points on the cross-sectional profile. These points are used to ensure that the weld bead can be correctly connected at the boundary of the filling area and avoid path interruption. In order to obtain the key points of the cross-sectional profile, each cross-sectional profile line segment of the filling area (whose endpoints are respectively and ) is sampled proportionally, and the discrete boundary point set is calculated by using the interpolation method, where , indicating the total number of profile line segments.

[0036] After successfully obtaining the additive deposition trajectory points, considering the center distance between additive weld beads, the width of the additive weld bead, and the overlapping rate and other key process condition parameters in the WAAM process, a mathematical model for additive deposition path planning is constructed to plan the additive deposition path, and the deposition path is solved and smoothed to obtain the optimal deposition path.

[0037] Specifically, the mathematical model for additive deposition path planning is constructed as follows: The goal of additive deposition path planning is to obtain the minimum total length of the deposition path and the turning angle of the deposition path , which are calculated respectively by the following formulas: The corresponding comprehensive objective function is: Among them, represents the objective function, and represent the weight coefficients.

[0038] See Figure 2 . Immediately afterwards, the genetic algorithm is used to solve the constructed mathematical model for additive deposition path planning, specifically: The arrangement order of the additive deposition trajectory points is encoded as chromosome individuals to represent the possible solutions of the support deposition path. Then, the chromosomes are iteratively optimized through the selection, crossover, and mutation operations of the genetic algorithm, so that the corresponding additive deposition path gradually approaches the optimal solution to obtain the optimal deposition path.

[0039] Each iterative optimization includes: calculating the fitness value of each chromosome , and this fitness value is determined by the comprehensive objective function, and its calculation formula satisfies: Then, the chromosomes are selected through the selection operation of the genetic algorithm, specifically the roulette wheel selection method. The probability of each chromosome being selected is , and it satisfies the following formula: Next, two chromosomes are randomly selected as parent chromosomes according to the above probability, and their gene segments are exchanged through the crossover operation to generate a new generation of offspring chromosomes to accelerate the convergence process of the algorithm.

[0040] Finally, through the mutation operation, some genes in the chromosomes are randomly changed with a certain probability to enhance the population diversity and prevent falling into the local optimal solution. Repeat the above steps until the iteration termination condition is met, and output the optimal deposition path.

[0041] Furthermore, the optimal deposition path obtained by the genetic algorithm is further smoothed by a B-spline curve. The B-spline curve can accurately fit the additive deposition path points through reasonably set control points and curve orders, thereby eliminating sharp corners in the path and ensuring the smoothness and continuity of the path. This smoothing process helps to improve the stability of the WAAM process and can also improve the forming quality of metal structural parts. Specifically: According to the coordinates of the additive deposition trajectory points, calculate the control points of the B-spline curve to ensure that the curve can be as close as possible to the actual deposition trajectory points. Through the combination of the basis function of the B-spline curve and the above control points, a smooth deposition path is then generated; Suppose there are control points , and a -order B-spline curve is used. Then the mathematical expression of this B-spline curve can be expressed as: where represents the basis function of the B-spline, which is calculated through a recursive formula:

[0042] Furthermore, for the optimization problem of multi-layer deposition paths in the metal WAAM process, this embodiment also optimizes the connection order of multi-layer deposition paths based on the tabu search algorithm. The optimization objective is to minimize the length of the non-additive movement path, reduce the thermal effect caused by excessive heat accumulation, and at the same time achieve an efficient additive deposition path order. Through this method, the optimal connection scheme of multi-layer additive deposition paths can be found in the search space. To improve the search efficiency, a tabu list and an aspiration criterion are introduced to record the accessed path connection states. Combining local search with the tabu mechanism avoids repeated searches, significantly improves the search efficiency, and successfully finds the optimal inter-layer connection path and starting arc point, thereby achieving the efficient connection of multi-layer continuous deposition paths.

[0043] Specifically, the total non-additive movement path of multi-layer additive deposition path connection is expressed as: .

[0044] Among them, represents the non-additive movement path from the th layer to the th layer; The heat accumulation amount can be calculated from parameters such as the heat input during each layer of the WAAM process and the inter-layer cooling time. The tabu search algorithm continuously adjusts the connection order of multi-layer paths to minimize the objective function .

[0045] wherein and represent weight coefficients.

[0046] Finally, through the above steps of additive deposition path planning, optimization and connection, a complete continuous additive deposition path can be derived. For the derived continuous additive deposition path, check the continuity and rationality of the deposition path. If it does not meet the standards, it is necessary to return to the corresponding steps for adjustment and optimization. If it meets the standards, it can be used in the WAAM process of metal structural parts to achieve precise printing of different metal structural parts.

[0047] In summary, this embodiment takes the three-dimensional model of a complex porous metal structural part as an example and proposes an additive deposition path planning method based on the genetic algorithm. This method first considers the constraint conditions of process condition parameters, such as the center distance between additive weld beads, the width of additive weld beads and the overlap ratio, etc. By mathematically modeling the additive deposition area of the target structural part, the corresponding additive deposition trajectory points are calculated. Then, through the genetic algorithm, these deposition trajectory points are traversed, and the optimal additive deposition path is optimized and planned, and finally a continuous additive deposition trajectory that meets the process requirements is formed. This method can not only effectively handle the complex geometric shapes of metal three-dimensional structural part models, but also has strong versatility and can adapt to the path planning requirements under different process condition parameter settings. Taking Figure 3 as an example, the additive deposition path planning results obtained by the method of this embodiment are shown.

[0048] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments. Even if various changes are made to the present invention, if these changes fall within the scope of the claims of the present invention and their equivalent technologies, they still fall within the protection scope of the present invention.

Claims

1. A continuous additive deposition path planning method for metal additive manufacturing, characterized in that, It includes the following steps: Import the 3D model of the metal structural part, slice it layer by layer, and obtain the cross-sectional contour of each layer; According to the cross-sectional contour of each layer and the process condition parameters, respectively determine the discrete filling points in the internal filling area of the cross-sectional contour and the boundary points of the cross-sectional contour as the additive deposition trajectory points; Combine the process condition parameters and the additive deposition trajectory points to construct a mathematical model for additive deposition path planning to plan the additive deposition path, and solve and smooth the deposition path to obtain the optimal deposition path; Based on the tabu search algorithm, optimize the connection order of the multi-layer deposition paths; After connection, export the complete continuous additive deposition path.

2. The continuous additive deposition path planning method for metal additive manufacturing according to claim 1, wherein The cross-sectional profile of each layer is represented as the boundary of the corresponding metal deposition; it is assumed that the 3D model consists of multiple triangular facets which are composed of three vertex coordinates , , ; during the layer-by-layer slicing process, for each layer slice with a height of , the intersection points of the triangular facet and the slice height are calculated by interpolation method, and these intersection points are the cross-sectional profile of the layer slice. The cross-sectional profile is obtained through the following calculation formula: Among them, , represents the total number of triangular patches, , represents the total number of layers, represents the point coordinates on the intersection line, represents the interpolation parameter.

3. The continuous additive deposition path planning method for metal additive manufacturing according to claim 1, wherein After obtaining the cross-sectional contour, it is also necessary to eliminate the geometric interference of each layer of cross-sectional contour. Specifically: Decompose the cross-sectional contour into multiple monotonic chains; Locate all possible self-intersection points by solving the self-intersection point set; Traverse the self-intersection point set and generate multiple loops, and determine the validity of these loops; Based on the validity determination result, optimize and reconstruct to obtain a non-interfering cross-sectional contour.

4. The continuous additive deposition path planning method for metal additive manufacturing according to claim 3, wherein The discrete filling points are the points arranged at preset intervals and rules within the internal filling area of the cross-sectional contour. Specifically, it includes the following steps: The process condition parameters include the center spacing of the additive weld beads , the width of the additive weld beads and the overlap rate , and satisfy the following formula: Among them, the lapping rate is defined as the ratio of the overlapping part of adjacent additive weld beads to the width of the additive weld bead; If a lap joint rate is not less than 1 / 3, the center spacing of the additive weld beads shall satisfy the following formula: Let the width of the internal filling area of the cross-sectional profile be , then the number of additive weld beads along the width direction of the additive weld bead satisfies the following formula: Calculate the coordinates of the discrete filling points on each additive weld bead according to the starting point and the ending point of the additive weld bead; Let the starting point coordinates of the additive weld bead be , and the ending point coordinates be . Then the discrete filling point coordinates along the weld bead length direction can be calculated by the following formula: Among them, and are the step lengths along the length direction of the weld bead, , indicating the number of points.

5. The continuous additive deposition path planning method for metal additive manufacturing according to claim 1, characterized in that The boundary points of the cross-sectional profile are key points on the cross-sectional profile. By sampling each cross-sectional profile line segment of the filled area at a certain ratio and using the interpolation method, a discretized set of boundary points is calculated , where , represents the total number of profile line segments.

6. The continuous additive deposition path planning method for metal additive manufacturing according to claim 1, wherein Specifically, the mathematical model for constructing the additive deposition path planning is as follows: The goal of additive deposition path planning is to obtain the minimum total length of the deposition path and the turning angle of the deposition path , which are calculated by the following formulas respectively: The corresponding comprehensive objective function is: Among them, represents the objective function, and represents the weight coefficient.

7. The continuous additive deposition path planning method for metal additive manufacturing according to claim 6, characterized in that Use the genetic algorithm to solve the constructed mathematical model for additive deposition path planning. Specifically: Encode the arrangement order of the additive deposition trajectory points as chromosome individuals to represent the possible solutions to support the deposition path; Iteratively optimize the chromosomes through the selection, crossover, and mutation operations of the genetic algorithm, so that the corresponding additive deposition path gradually approaches the optimal solution to obtain the optimal deposition path; Each iterative optimization includes: Calculate the fitness of each chromosome, and select the chromosomes through the selection operation of the genetic algorithm. The probability of each chromosome being selected is related to the fitness; Take two randomly selected chromosomes as the parent chromosomes, exchange their gene segments through the crossover operation, and generate a new generation of offspring chromosomes; Randomly change the genes in the chromosomes with a preset probability through the mutation operation to enhance the population diversity; Until the iteration termination condition is met, output the optimal deposition path.

8. The continuous additive deposition path planning method for metal additive manufacturing according to claim 7, wherein Further perform smoothing processing on the optimal deposition path obtained by the genetic algorithm. Specifically: Calculate the control points of the B-spline curve according to the coordinates of the additive deposition trajectory points, and generate a smooth deposition path through the combination of the basis functions of the B-spline curve and the above control points; Suppose there is control points , and an -order B-spline curve is adopted. Then the mathematical expression of the B-spline curve can be expressed as: Among them represents the basis function of the B-spline, which is calculated by a recursive formula: 。 9. The continuous additive deposition path planning method for metal additive manufacturing according to claim 7, wherein Use the tabu search algorithm to optimize the connection order of the multi-layer deposition paths, with the goal of minimizing the length of the non-additive movement path and reducing the thermal effect caused by excessive heat accumulation, to achieve the connection of the multi-layer additive deposition paths.

10. The continuous additive deposition path planning method for metal additive manufacturing according to claim 9, wherein It will also check the connected multi-layer additive deposition path, judge the continuity and rationality of its path. If it does not meet the standard, return to the corresponding step for adjustment and optimization; if it meets the standard, use the connected multi-layer additive deposition path for metal additive manufacturing.