Additive manufacturing-oriented scanning path solving method and system based on two-step deductive method

Abstract

The invention relates to a scanning path solving method and system based on a two-step deductive method for additive manufacturing, and the method comprises the following steps: obtaining a layer slice of a three-dimensional object, and planning a scanning path of the layer slice by adopting the two-step deductive method according to a set scanning mode, obtaining a scanning path; the step of solving the real-time position of the activation source by the two-step deductive method comprises the following steps: determining a current ordinal number ch; based on the ordinal number ch of the current channel, calculating the movement displacement # imgabs0 # of an activation source on the current channel ch; and obtaining the real-time position of the activation source based on the movement displacement # imgabs1 # of the activation source in the current channel ch and in combination with the initial position # imgabs2 # of the current channel ch. Compared with the prior art, the method has the advantages of realizing simplification and generalization of scanning path planning and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of additive manufacturing simulation technology, and in particular to a scanning path solving method and system based on a two-step deductive method for additive manufacturing. Background Art

[0002] Additive manufacturing creates three-dimensional objects by adding materials layer by layer. In contrast to traditional subtractive manufacturing processes, additive manufacturing builds objects directly from computer three-dimensional models, typically using materials such as plastics, metals, ceramics, etc. It is used in aerospace, medical, automotive, construction, consumer goods and other fields, and can be freely designed and personalized.

[0003] The scanning path is one of the important ways to control the additive manufacturing process. Its influences include: affecting the width and depth of the molten pool, and affecting the heat accumulation, heat distribution, and temperature field of the rotating path, which in turn affects the component (residual) stress distribution, deformation, and microstructure.

[0004] Since non-raster scanning is still in the stage of exploring the feasibility of basic theory, such as N-point melting scanning, this paper mainly discusses conventional raster scanning. In experimental and simulation studies, the scanning paths used include: unidirectional scanning, bidirectional scanning, island scanning, spiral scanning, contour scanning, cross scanning, and 45° rotation scanning. According to the characteristics of the scanning path, this paper divides it into several categories: single-zone straight, single-zone corner, single-zone complex, and multi-zone. Figure 2-5 shown.

[0005] The single-zone straight scanning method is relatively simple. According to the relevant literature that has been consulted, the earliest research time began in 2004, and the content is also relatively large. It has been studied in both experiments and simulations. Liu et al. conducted single-channel and multi-channel scanning experiments, simulated the changes in the width and depth of the molten pool under different laser powers and scanning speeds, and analyzed the thermal behavior of the laser on the powder bed with the help of finite element models to explore the changes in the molten pool morphology and temperature field. Considering the efficiency of laser scanning, a bidirectional reciprocating scanning strategy was developed based on unidirectional scanning. Doubenskaia et al. mainly used bidirectional scanning to study the selective laser melting (SLM) process of Ti-48Al-2Cr-2Nb powder, and analyzed the effects of different scanning speeds and laser powers on heat distribution and material evaporation. Yang et al. compared the thermal effects of two scanning strategies in a single direction and an alternating direction in single-layer and multi-layer construction, and studied the effects of these two strategies on the width and depth of the molten pool. The number of related experimental and theoretical studies on this type of scanning method is relatively similar and relatively mature; however, according to all the simulation literature consulted, the processing trajectory is not clearly explained, only the description and results of the simulation are involved.

[0006] In order to improve quality and reduce stress, a single-zone corner scanning method was developed in experimental and simulation research to make heat distribution more uniform. Among them, early studies used geometric and periodic symmetry, and 45° reciprocating multi-channel scanning became a hot topic. Ali et al. explored 45° and 90° alternating scanning and checkerboard scanning, and found that 90° alternating scanning performed best in reducing residual stress, while checkerboard scanning increased residual stress as the block size increased. Cheng et al. used 45° tilt scanning with an interlayer rotation angle of 45° to provide uniform temperature gradient and lower stress concentration. However, with the deepening of related research, the above-mentioned geometric and periodic symmetry will also bring about uneven heat accumulation, heat distribution, and temperature field of periodic or symmetrical superposition, which will lead to thermal stress deformation problems of periodic or symmetrical superposition. Liu and Malekipour et al. came into being to solve this problem with a non-periodic 67° reciprocating multi-channel scanning method. Mahmood et al. used 67° alternating scanning, that is, the scanning direction of each layer rotated 67° to reduce thermal stress and component deformation. Liang et al. combined numerical simulation with experiments to study the effects of the single-direction path in the parallel line scanning strategy and the 67° rotation path in each layer in the rotation line scanning strategy on heat accumulation and stress distribution. The number of literature studies on the theoretical simulation of the single-zone corner scanning method is significantly less than that of the experimental process. Combined with practice, it is shown that some geometric parameters in this scanning strategy are constantly changing during the process and need to be described by piecewise functions, and the path setting code is complex. In particular, the 67° alternating scanning cannot be described by periodicity and symmetry, and its path setting code is even more complex.

[0007] In order to achieve better thermal control through continuous and smooth path planning, thereby further optimizing heat distribution, dispersing stress, improving the uniformity of microstructure, and reducing deformation of components, research on single-zone complex paths, including spiral and fractal paths, has been pioneered. In terms of spiral scanning, Jia et al. explored bidirectional scanning, external spiral and internal spiral paths. Spiral and hexagonal scanning emphasize continuous and smooth paths to reduce stress concentration and uneven cooling. In terms of fractal paths, Fei, Catchpole-Smith et al. compared traditional "island" scanning with fractal scanning based on Hilbert and Peano-Gosper curves. Fractal scanning effectively reduces thermal gradients by shortening the scan vector length (about 100 µm). Yu et al. simulated four strategies: grid, external-inward offset, internal-outward offset, and fractal deposition, and found that fractal deposition and external-inward offset strategies can effectively reduce component deformation. However, the more complex path setting code has led to a general lack of simulation research, and fractal paths are difficult to be supported by conventional printing equipment, and experimental research is also less.

[0008] In view of the thermal control problem of large and complex components, a more suitable multi-zone method has been developed based on single-zone straightness and corners. It manages heat accumulation through regional division and path alternation, which is particularly effective in large-size components and complex structures. Among them, strip scanning manages thermal gradients by parallel strip partitioning. Mugwagwa et al. found through experiments that strip scanning is the most effective in reducing residual stress, which can reduce residual stress by 40% and reduce deformation. In contrast, island scanning is less effective in controlling residual stress. Promoppatum and Yao et al. constructed process windows with different scanning lengths and energy inputs through numerical simulation, and verified that strip scanning can reduce residual stress by more than half under optimal conditions. Checkerboard scanning optimizes heat and stress distribution by partitioning with small squares and alternating directions. Cai and Liang et al. studied the effects of unidirectional and bidirectional scanning strategies on temperature distribution, and reduced heat accumulation and residual stress by interlayer rotation angle. Wang et al. experimentally studied the effects of checkerboard and uniform scanning on residual stress and microstructure of AlSi10Mg alloy at different preheating temperatures. Hexagonal scanning relies on the honeycomb distribution of hexagons, which naturally has a high degree of symmetry. Sara et al. conducted an experimental analysis of the effects of different scanning strategies (standard linear, concentric ring and hexagonal) on the quality of 17-4PH stainless steel parts. However, compared with the number of literature on experimental research, multi-zone simulation work is very limited. In practice, the reason is that each zone needs to be switched, which significantly increases the complexity of the path setting code; and the simulation of hexagonal scanning was not found in the literature survey. In practice, the reason is due to the complex boundary problem of the hexagonal area.

[0009] In summary, with the continuous advancement of actual needs and simulation work, the complexity of simulation path setting is constantly increasing, and has restricted a large number of supporting simulation tests for actual process tests. During the early work, it was imagined that if there was a set of general methods and frameworks to implement path setting, then only a single study of the complex path would be required, and other scholars could directly call it, significantly reducing the research threshold for complex path additive manufacturing process simulation. Unfortunately, according to the existing literature survey, no relevant work was found, and most of the surveyed literature even avoided mentioning the mathematical expression of path setting or setting code. Summary of the invention

[0010] The purpose of the present invention is to provide a scanning path solving method and system based on a two-step deductive method for additive manufacturing that simplifies and generalizes scanning path planning.

[0011] A scanning path solving method based on a two-step deductive method for additive manufacturing includes the following steps: Acquire a layer slice of the three-dimensional object, and plan a scanning path of the layer slice using a two-step deductive method according to a set scanning mode, wherein the two-step deductive method obtains the scanning path by solving the real-time position of the activation source; The steps of solving the real-time position of the activation source by the two-step deductive method include: Determine the current channel number ch ; Based on the current track number ch , calculate the activation source at the current ch Track movement displacement ; Based on the activation source in the current ch Track movement displacement , combined with the current ch Initial position , get the real-time location of the activation source.

[0012] Furthermore, the current track number is determined ch The steps include: Determine the scanning path type and scanning speed of the activation source, and calculate the total time of the activation source moving on the layer slice nth time t n ; Based on the total duration of the nth movement t n , calculate the current channel number ch The time period of the scanning process, and the current channel number is determined according to the time period ch .

[0013] Furthermore, the total duration of the nth track movement is t n The calculation process includes: Based on the scanning path type and layer slice of the activation source, determine the total length of the nth path of the activation source on the layer slice L n ; Based on the total length of the nth track L n and scanning speed, calculate the total time the activation source moves in the nth channel t n , where the total moving time of the nth track is t n The calculation expression is: , In the formula, v is the scanning speed.

[0014] Furthermore, the calculation of the current track number ch The steps of the scanning process time period include: Based on the total duration of the nth moving t n , before the calculation is completed 1~ ch -Total time for 1 course : , Based on the total duration of the nth moving t n , calculate the total time required to be spent on the layer slice when the current pass is completed : , Based on the and , get the current channel number ch Scanning process time period: .

[0015] Further, the current track number is determined according to the time period ch The steps include: The total scanning time on the layer slice does not exceed the time of scanning the last track, that is: , In the formula, is the total time of active source movement in the current layer slice, che is the last ordinal number; Use sequential search test channel number , there is always satisfy: , In the formula, is the test track number; Determine the current channel number ch for: .

[0016] Furthermore, the calculation activation source is currently ch Track movement displacement The steps include: Calculate the activation source at the current ch Road travel time t ch : , In the formula, The total time of activating the source movement in the current layer slice, completing the first 1~ ch -Total time for 1 course ; Based on the displacement-velocity vector integral definition, combined with the current ch Road travel time tch , calculate the activation source at the current ch Track movement displacement , where the mobile displacement The calculation expression is: , In the formula, for t The unit vector in the scanning direction at any moment, for t Scan speed at all times.

[0017] Furthermore, the scanning mode includes one of unidirectional scanning, bidirectional scanning, 45° unidirectional scanning, 45° bidirectional scanning, variable speed 45° unidirectional scanning, and grid single-layer vase printing scanning.

[0018] Furthermore, the current ch Initial position The determination process is: 1) For one-way scanning: According to the activation source in the current ch Initial position of the road All on the Y axis, we get: , That is: , In the formula, is the initial coordinate, d is the scanning distance, Start with activation source y coordinate; 2) For bidirectional scanning: According to the initial position of each channel of the activation source, it is changed alternately on the two boundaries parallel to the Y axis, and we get: , That is: , In the formula, a, b are the layer slice length and width, L n is the total length of the nth track of the activation source on the layer slice; 3) For 45° unidirectional scanning: Divide the layer slice into 3 regions and calculate the L n ,get: , In the formula, For the ch The moving length of the activation source, For the ch Tao andx The intercept of the axis; according to L n , calculate the initial position of each of the three regions: , That is: ; 4) For 45° bidirectional scanning: Divide the layer slice into 3 regions and calculate the L n ,get: , according to L n , calculate the initial position of each of the three regions: , That is: ; 5) For variable speed 45° unidirectional scanning: Divide the layer slice into 3 regions and calculate the L n ,get: , according to L n , calculate the initial position of each of the three regions: , That is: ; 6) For the checkered single-layer vase print scan: According to the movement of the activation source on the grid boundary, the initial position of each path is the coordinates of the four vertices of the grid, that is: , In the formula, , , and are the coordinates of the four vertices.

[0019] The calculation expression of the real-time position of the activation source is: , In the formula, The real-time location of the activation source.

[0020] The present invention also provides a scanning path solving system based on a two-step deductive method for additive manufacturing, comprising: Option layer: used to set the scanning mode; General layer: used to plan the scanning path of the layer slices according to the scanning form set in the option layer by using a two-step deductive method, wherein the two-step deductive method obtains the scanning path by solving the real-time position of the activation source; The steps of solving the real-time position of the activation source by the two-step deductive method include: Determine the current channel number ch ; Based on the current track number ch , calculate the activation source at the current ch Track movement displacement ; Based on the activation source in the current ch Track movement displacement , combined with the current ch Initial position , get the real-time location of the activation source.

[0021] Compared with the prior art, the present invention has the following beneficial effects:

[0022] (1) The present invention transforms the planning of complex scanning paths into a standardized two-step solution process based on the basic principle of the two-step deductive method. Specifically, the moving distance of the current path is solved and the real-time position of the activation source is obtained in combination with the starting position of the current path, thereby achieving simplification and generalization of scanning path planning.

[0023] (2) The present invention can effectively solve the complex scanning path setting problem through a two-step deductive method, that is, the activation source position solution problem, which is unified into a set of standardized procedures for solving, and can solve any complex scanning path.

[0024] (3) The present invention designs a general layer and an option layer to modularize the path setting. The option layer solves the important parameters of different scanning methods according to different scanning paths. The general layer solves the path according to the principle of the two-step deductive method, providing an efficient and standardized path setting tool for this field, laying a foundation for the practical engineering application of complex path setting. The present invention also verifies the universality and flexibility of the two-step deductive method under different path conditions through six typical scanning strategies, including unidirectional scanning, bidirectional scanning, 45° unidirectional scanning, 45° bidirectional scanning, variable speed 45° unidirectional scanning, and single-layer vase path printing.

[0025] (4) The method of scanning path planning using a two-step deductive method proposed in the present invention provides new possibilities for constructing a digital twin model for additive manufacturing, further promoting process innovation and digital transformation in the field of additive manufacturing. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a schematic diagram of the derivation and verification process of the method of the present invention; Figure 2 It is a single-zone straight scanning path in the prior art of the present invention, wherein (a) is an experimental unidirectional scanning, (b) is a simulated unidirectional scanning, (c) is an experimental bidirectional reciprocating scanning, and (d) is a simulated bidirectional reciprocating scanning; Figure 3 The single-zone corner scanning path in the prior art of the present invention, wherein (a) is an experimental 45-degree unidirectional multi-channel, (b) is an experimental 45-degree reciprocating multi-channel, (c) is a simulated 45-degree reciprocating multi-channel, (d) is an experimental 67-degree reciprocating multi-channel, and (e) is a simulated 67-degree reciprocating multi-channel; Figure 4 It is a single-zone complex scanning path in the prior art of the present invention, wherein (a) is an experimental spiral, (b) is a simulated spiral, (c) is an experimental fractal path, and (d) is a simulated fractal path; Figure 5 It is a multi-zone scanning path in the prior art of the present invention, wherein (a) is an experimental strip, (b) is a simulation strip, (c) is an experimental chessboard, (d) is a simulation chessboard, and (e) is a hexagon; Figure 6 It is the principle diagram of the two-step deductive method of the present invention; Figure 7 It is a flow chart of the two-step deductive method solution process of the present invention; Figure 8 The corresponding relationship between the mathematical foundation of the two-step deductive method of the present invention and the menu model; Fig. 9 It is a schematic diagram of a one-way scanning method of the present invention; Fig.10 It is a schematic diagram of the bidirectional scanning method of the present invention; Fig.11 This is a schematic diagram of a 45° unidirectional scanning method of the present invention; Fig.12 It is a schematic diagram of a 45° bidirectional scanning method of the present invention; Fig.13 It is a schematic diagram of a variable speed 45° unidirectional scanning method of the present invention; Fig.14 This is a schematic diagram of printing a lattice single-layer vase of the present invention. DETAILED DESCRIPTION

[0027] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0028] The common scanning methods do not clearly describe the processing trajectory in experiments and simulations, and lack a universal path setting framework, which hinders the wide application of research results in simulation. The two-step deductive method describes the scanning path of the additive manufacturing activation source (fusion source) in any form in a clearer, universal and concise way, and clarifies the common principles of scanning path loading settings.

[0029] This embodiment provides a scanning path solving method based on the two-step deductive method for additive manufacturing. The method proposes a "menu-style model" with a "general layer" as a universal functional module and an "option layer" as a drop-down module, making it easier to set complex paths. Through the specific analysis of six typical scanning strategies, the feasibility and universality of the two-step deductive method are proved, so that the scanning path can be flexibly set in the simulation, which helps the additive manufacturing process simulation and digital twin to optimize and predict complex processes. Specifically: 1.2-step deductive model derivation The scanning path setting problem of additive manufacturing is essentially to solve the transient loading problem of the activation source, which can be described mathematically as solving the real-time position of the activation source. However, the real-time location of the activation source cannot be directly called and needs to be determined based on known information, including: (1) the current layer number ly : Since each layer printing process is generally set in one analysis step, the current analysis step is the current layer number; (2) Activation source (fusion source) scanning speed v: This value is a preset value. For some speed change processes, ; (3) The total time of activation source movement in the current layer ( ): The system can perform cumulative calculations based on incremental steps. (4) The scanning method is known, so the total length of the nth track can be solved based on the geometric relationship of the scanning method .

[0030] Table 1 Symbol index table

[0031] According to the above known information process analysis, we can get: and There is a corresponding relationship, which needs to be solved and then converted to , but the difficulty lies in the inability to determine the current scanning track number ( ch ). The "two-step deductive method" can solve the above problems, and on this basis, solve and The corresponding relationship.

[0032] according to Figure 6The principle shown in the two-step deduction method assumes that any complex additive manufacturing path planning problem is carried out in two steps: the first step is to move the activation source from the origin to the initial position of the current path. In the second step, we move from the initial position of the current path to the final activation source, and the displacement is recorded as Through the "two-step deduction method", the complete scanning process can be divided into the sequence number of the scanned channels (1~ ch -1), and the number of the track being scanned ch .

[0033] According to the above analysis, we first solve ch . Solution ch It is necessary to know the total time of the activation source moving in the nth channel , considering Solvable and Known, we can solve it according to formula (1.1):

[0034] in The solution example will be given in the second part of this article. According to the processing principle of the "two-step deduction method" above, the completed part (corresponding to the ordinal number: 1~ ch -1) The total time taken is:

[0035] When the current scan is completed, the total time spent on the current layer is

[0036] Any ch The scanning process corresponds to a time period:

[0037] Considering that the total scanning time of the current layer will not exceed the time to scan the last layer, that is:

[0038] Therefore, try to search the test track numbers sequentially. , there is always satisfy:

[0039] At this time, the current scan track number is On this basis, we can According to the basic principle of the “two-step deduction method”, it can be mathematically described as the activation source first reaching the starting point of the current path (position vector: ), and then the displacement from the starting point to the current real-time position ,but That is:

[0040] in, According to the specific geometric characteristics, a specific mathematical form is given. According to the definition of displacement-velocity vector integral, we can get equation (1.9). Considering the commonly used uniform speed and straight path situation, equation (1.9) also gives a simplified form:

[0041] In formula (1.8), the activation source moves at the current channel ch for a certain time. ,according to and (Equation 1.2) definition, we can get:

[0042] Figure 7 This is a flow chart of the "two-step deductive method" solution process obtained after the above derivation and sorting. The figure shows that the "two-step deductive method" can effectively solve the complex scanning path setting problem, that is, the activation source position solution problem, and unify it into a set of standardized procedures for solution. The key to this method is to use the starting point of the current chth track as the middle point, thereby dividing any scanning path into a steady-state problem of the completed part and a real-time dynamic problem of the unfinished track. From the steady-state problem, the time spent on the completed part can be easily solved. (Formula 1.2), so the time that has passed in the unfinished road can be (Equation 1.9), thus, any complex scanning path can be solved theoretically. In addition, Figure 7 The algorithm is implemented with the help of arrays. During the array generation process, the information of each channel time, each channel starting coordinate, each channel speed direction, each channel speed value, and each channel power value is obtained by direct input, interactive input, or automatic calculation by the program to obtain the corresponding array. The number of the above array elements is consistent with the number of scan channels.

[0043] also, Figure 8 The universal solution equations and important parameters for different scanning paths in the "two-step deductive method" are summarized and need to be solved according to the actual situation. According to programming thinking, the universal solution equations can be regarded as the "general layer" and the important parameters can be regarded as the "option layer". Figure 8In the "menu-style model", the general layer corresponds to the function tab, and the selection layer corresponds to any option in the drop-down menu. If it is packaged into a program plug-in, the complex path results can be directly called in the simulation, making the complex path setting extremely simple; and with the rise of digital twin research, this program plug-in can help the establishment of digital twin machines for additive manufacturing, making the scanning path setting of the simulation process "menu-based". In the next section, several typical and simple cases will be selected to show how to solve parameters according to actual conditions.

[0044] 2. Practical application of the two-step deductive method (turning general formula into special case)

[0045] In order to verify the feasibility and universality of the "menu model" of the two-step deductive method, this section introduces 6 cases in detail. One-way scanning and two-way scanning are mainly used to describe the processing trajectory in the simulation of a single-zone flat surface. 45° one-way scanning, 45° two-way scanning, and variable-speed 45° one-way scanning describe the single-zone corner simulation process in detail. The square single-layer vase scanning gives a detailed description of the complex processing trajectory of a single zone. The specific mathematical expressions of the 6 scanning strategies and their derivation process provide a further explanation of the "menu model" of the two-step deductive method.

[0046] Considering that the universal solution equation group (i.e., the "general layer") in the "two-step deductive method" has been solved and summarized in detail above, the general layer expression is the same for different scanning strategies, while the solution of important parameters (i.e., the "option layer") varies with the different scanning strategies. Therefore, this section only solves the important parameters in the option layer.

[0047] 2.1 One-way scanning

[0048] like Fig. 9 This is a schematic diagram of a one-way scanning method. Assuming that the grid length is mm, mm, scanning distance , the activation source starting coordinates are (0,0.05), and the scanning speed is , scan in one direction starting from the starting point.

[0049] Depend on Fig. 9 It can be seen that the distance moved by the activation source in each channel is equal, so we can get:

[0050] From the general layer formula (1.6), we know that there is a unique On this basis, we can obtain .

[0051] Depend on Fig. 9 It can be seen that the unit vector in the scanning direction is . Calculate the displacement of the activation source in the current channel ch , from the general layer formula (1.8) we can get:

[0052] Assume the initial position of the chth track is Since the activation source starts at (0, 0.05), the scanning interval , the initial position of each activation source is on the Y axis, so .

[0053] Will , The expression to be substituted , we can get:

[0054] In summary, we can get: .

[0055] 2.2 Bidirectional scanning

[0056] like Fig.10 The figure shows a bidirectional scanning method. Assuming the grid length is mm, mm, scanning distance , the activation source starting coordinates are (0,0.05), and the scanning speed is , scan back and forth from the starting point.

[0057] It can be seen that in the grid reciprocating multi-pass scanning, the distance moved by the activation source in each pass is equal, so we can get:

[0058] From the general layer formula (1.6), we know that there is a unique On this basis, we can obtain .

[0059] Depend on Fig.10 It can be seen that the scanning direction is parallel to the X-axis and changes direction alternately, and the unit vector in the scanning direction can be obtained . Calculate the displacement of the activation source in the current channel ch , from the general layer formula (1.8) we can get:

[0060] Assume the initial position of the chth track is Since the activation source starts at (0, 0.05), the scanning interval , the initial position of each activation source changes alternately on the two boundary lines parallel to the Y axis, and we can get .Will , Substitution , we can get:

[0061] In summary, we can get: .

[0062] 2.3 45° unidirectional scanning

[0063] like Fig.11 The figure shows a 45° unidirectional scanning method. Assuming the grid length is mm, mm, scanning distance , the starting coordinates of the laser heat source are (0,0.05), and the scanning speed is , starting from the starting point, scan in one direction at an angle of 45°.

[0064] The grid is scanned unidirectionally at 45°. The distance the activation source moves in each track is different, and the total length of each track changes with the change of the scan track number ch. , , where: d is the offset distance of each path on the coordinate axis, is the intercept of the chth channel with the x-axis.

[0065] like Fig.11 As shown, the grid scanning area can be divided into 3 areas, and the scanning track in each area can be calculated. The length is: , After finishing, we can get:

[0066] From the general layer formula (1.6), we know that there is a unique On this basis, we can obtain .

[0067] Depend on Fig.11 It can be seen that the scanning direction is x The axis angle is -45°, and the unit vector in the scanning direction can be obtained . Calculate the displacement of the activation source in the current channel ch , from the general layer formula (1.8) we can get:

[0068] Assume the initial position of the chth track is The grid scanning area is divided into three areas, and the initial position of each track in each area is obtained respectively.

[0069] Will , Substitution The expression of , we can get:

[0070] Will , Substitution The expression of can be sorted out as follows:

[0071] The review revealed:

[0072] in, .

[0073] 2.4 45° bidirectional scanning

[0074] like Fig.12 The figure shows a 45° bidirectional scanning method. Assuming the grid length is mm, mm, scanning distance , the starting coordinates of the laser heat source are (0,0.05), and the scanning speed is , starting from the starting point, scan in one direction at an angle of 45°.

[0075] The grid is scanned bidirectionally at 45°. The distance the activation source moves in each track is different, and the total length of each track changes with the change of the scan track number ch. , , where: d is the offset distance of each path on the coordinate axis, is the intercept of the chth channel with the x-axis.

[0076] like Fig.12 As shown, the grid scanning area can be divided into 3 areas, and the scanning track in each area can be calculated. The length is: , After finishing, we can get:

[0077] From the general layer formula (1.6), we can see that there is only one On this basis, we can obtain .

[0078] Depend on Fig.12 It can be seen that the scanning direction and the x-axis angle are -45° and 135°, and the unit vector in the scanning direction is obtained. . Calculate the displacement of the activation source in the current channel ch , from the general layer formula (1.8) we can get:

[0079] Assume the initial position of the chth track is The grid scanning area is divided into three areas, and the initial position of each track in each area is obtained respectively.

[0080] Will , Substitution The expression of , we can get:

[0081] Will , Substitution The expression of can be sorted out as follows:

[0082] In summary: 45° bidirectional scanning

[0083] in, .

[0084] 2.5 Variable speed 45° one-way scanning

[0085] like Fig.13 The figure shows a schematic diagram of a variable speed 45° unidirectional scanning method. Assuming the grid length mm, mm, scanning distance , the starting coordinates of the laser heat source are (0,0.05), and the scanning speed is , starting from the starting point, scanning in one direction at an angle of 45°. The variable speed 45° unidirectional scanning method is described using the two-step deduction method. Assume that the grid area is divided into 3 zones, and the specific speeds of zones 1 and 3 are: and , Indicates the speed of each lane.

[0086] The speed is changed to 45° bidirectional scanning. The distance of the activation source moving in each track is different. The total length of each track changes with the change of the scanning track number ch. , , where: d is the offset distance of each path on the coordinate axis, is the intercept of the chth channel with the x-axis.

[0087] like Fig.13 As shown, the grid scanning area can be divided into 3 areas, and the scanning track in each area can be calculated. The length is: , After finishing, we can get:

[0088] Since the specific speeds of zones 1 and 3 are: and , we can get:

[0089] From the general layer formula (1.6), we know that there is a unique On this basis, we can obtain .

[0090] Depend on Fig.13 It can be seen that the angle between the scanning direction and the x-axis is -45°, and the unit vector in the scanning direction is . Calculate the displacement of the activation source in the current channel ch , substituting formula (2.14) into the general layer formula (1.8) yields:

[0091] Assume the initial position of the chth track is The grid scanning area is divided into three areas, and the initial position of each track in each area is obtained respectively.

[0092] Will , Substitution The expression of , we can get: , Will , Substitution The expression of can be sorted out as follows:

[0093] In summary: variable speed 45° unidirectional scanning

[0094] in, .

[0095] 2.6 Grid single-layer vase printing

[0096] like Fig.14 The following is a schematic diagram of printing a single-layer vase with square grids. Assuming the length of the square grid is mm, mm, the starting coordinates of the laser heat source are (0,0), and the scanning speed is , scanning starts from the starting point in a rectangular frame. When printing a single-layer vase with a square grid, the activation source moves on the boundary, and the total length of each scan can be obtained. .

[0097]

[0098] From the general layer formula (1.6), we know that there is a unique On this basis, we can obtain .

[0099] Depend on Fig.14 It can be seen that the scanning direction of the square single-layer vase printing is rotated 90 degrees clockwise each time, and the unit vector in the scanning direction can be obtained . Calculate the displacement of the activation source in the current channel ch , from the general layer formula (1.8) we can get:

[0100] Assume the initial position of the chth track is Since the activation source starts at (0,0), the activation source moves on the boundary, and each initial position is the coordinates of the four vertices of the grid, we can get:

[0101] In summary, we can get:

[0102] In summary, the simplified case commonly used in the above research is the menu software implemented by QT software, which selects the scanning strategy on the menu.

[0103] This paper proposes a new "two-step deductive method" for scanning path settings in additive manufacturing simulation. This method transforms the simulation settings of complex scanning paths into a standardized two-step solution process, simplifies and generalizes scanning path planning, and provides a new solution for simulation research in the field of additive manufacturing. The main conclusions of the study are as follows:

[0104] 1. This study designed a "menu model" to modularize the path setting in the form of "general layer" and "option layer". This design can be directly applied to the development of simulation software plug-ins, providing an efficient and standardized path setting tool, laying the foundation for the practical engineering application of complex path setting.

[0105] 2. By analyzing six typical scanning strategies, including unidirectional scanning, bidirectional scanning, 45° unidirectional scanning, 45° bidirectional scanning, variable speed 45° unidirectional scanning, and single-layer vase path printing, the versatility and flexibility of the “two-step deductive method” under different path conditions were verified.

[0106] 3. The "two-step deductive method" solves the key problem of the lack of unified mathematical description and code implementation for complex paths, and promotes the integration of scanning paths and simulation processes. With the rise of digital twin technology, the introduction of this method provides new possibilities for building digital twin models for additive manufacturing, further promoting process innovation and digital transformation in the field of additive manufacturing.

[0107] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0108] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A scanning path solving method based on a two-step deductive method for additive manufacturing, characterized in that: The following steps are involved: Acquire a layer slice of the three-dimensional object, and plan a scanning path of the layer slice using a two-step deductive method according to a set scanning mode, wherein the two-step deductive method obtains the scanning path by solving the real-time position of the activation source; The steps of solving the real-time position of the activation source by the two-step deductive method include: Determine the current channel number ch ; Based on the current track number ch , calculate the activation source at the current ch Track movement displacement ; Based on the activation source in the current ch Track movement displacement , combined with the current ch Initial position , get the real-time location of the activation source.

2. The scanning path solving method based on two-step deductive method for additive manufacturing according to claim 1, characterized in that: Determining the current track number ch The steps include: Determine the scanning path type and scanning speed of the activation source, and calculate the total time of the activation source moving on the layer slice nth time t n ; Based on the total duration of the nth movement t n , calculate the current channel number ch The time period of the scanning process, and the current channel number is determined according to the time period ch .

3. The scanning path solving method based on two-step deductive method for additive manufacturing according to claim 2, characterized in that: The total duration of the nth moving t n The calculation process includes: Based on the scanning path type and layer slice of the activation source, determine the total length of the nth path of the activation source on the layer slice L n ; Based on the total length of the nth track L n and scanning speed, calculate the total time the activation source moves in the nth channel t n , where the total moving time of the nth track is t n The calculation expression is: ， In the formula, v is the scanning speed.

4. A scanning path solving method based on a two-step deductive method for additive manufacturing according to claim 2, characterized in that: The calculation of the current channel number ch The steps of the scanning process time period include: Based on the total duration of the nth movement t n , before the calculation is completed 1~ ch -Total time for 1 course : ， Based on the total duration of the nth movement t n , calculate the total time required to be spent on the layer slice when the current pass is completed : ， Based on the and , get the current channel number ch Scanning process time period: .

5. The scanning path solving method based on two-step deductive method for additive manufacturing according to claim 2, characterized in that: Determine the current channel number according to the time period ch The steps include: The total scanning time on the layer slice does not exceed the time of scanning the last track, that is: ， In the formula, is the total time of active source movement in the current layer slice, che is the last ordinal number; Use sequential search test channel number , there is always satisfy: ， In the formula, is the test track number; Determine the current channel number ch for: .

6. The scanning path solving method based on two-step deductive method for additive manufacturing according to claim 1, characterized in that: The calculation activation source is currently ch Track movement displacement The steps include: Calculate the activation source at the current ch Road travel time t ch : , In the formula, The total time of activating the source movement in the current layer slice, completing the first 1~ ch -Total time for 1 course ; Based on the displacement-velocity vector integral definition, combined with the current ch Road travel time t ch , calculate the activation source at the current ch Track movement displacement , where the mobile displacement The calculation expression is: ， In the formula, for t The unit vector in the scanning direction at any moment, for t Scan speed at all times.

7. The scanning path solving method based on two-step deductive method for additive manufacturing according to claim 1, characterized in that: The scanning mode includes one of unidirectional scanning, bidirectional scanning, 45° unidirectional scanning, 45° bidirectional scanning, variable speed 45° unidirectional scanning, and square single-layer vase printing scanning.

8. The scanning path solving method based on two-step deductive method for additive manufacturing according to claim 7, characterized in that: The current ch Initial position The determination process is: 1) For one-way scanning: According to the activation source in the current ch Initial position of the road All on the Y axis, we get: , That is: , In the formula, is the initial coordinate, d is the scanning distance, Start with activation source y coordinate; 2) For bidirectional scanning: According to the initial position of each channel of the activation source, it is changed alternately on the two boundaries parallel to the Y axis, and we get: ， That is: , In the formula, a, b are the layer slice length and width, L n is the total length of the nth track of the activation source on the layer slice; 3) For 45° unidirectional scanning: Divide the layer slice into 3 regions and calculate the L n ,get: ， In the formula, For the ch The moving length of the activation source, For the ch Tao and x The intercept of the axis; according to L n , calculate the initial position of each of the three regions: ， That is: ; 4) For 45° bidirectional scanning: Divide the layer slice into 3 regions and calculate the L n ,get: ， according to L n , calculate the initial position of each of the three regions: , That is: ; 5) For variable speed 45° unidirectional scanning: Divide the layer slice into 3 regions and calculate the L n ,get: ， according to L n , calculate the initial position of each of the three regions: , That is: ； 6) For the checkered single-layer vase print scan: According to the movement of the activation source on the grid boundary, the initial position of each path is the coordinates of the four vertices of the grid, that is: ， In the formula, , , and are the coordinates of the four vertices.

9. The scanning path solving method based on two-step deductive method for additive manufacturing according to claim 1, characterized in that: The calculation expression of the real-time position of the activation source is: ， In the formula, The real-time location of the activation source.

10. A scanning path solving system based on two-step deductive method for additive manufacturing, characterized in that: include: Option layer: used to set the scanning mode; General layer: used to plan the scanning path of the layer slices according to the scanning form set in the option layer by using a two-step deductive method, wherein the two-step deductive method obtains the scanning path by solving the real-time position of the activation source; The steps of solving the real-time position of the activation source by the two-step deductive method include: Determine the current channel number ch ; Based on the current track number ch , calculate the activation source at the current ch Track movement displacement ; Based on the activation source in the current ch Track movement displacement , combined with the current ch Initial position , get the real-time location of the activation source.

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