Scanning Path Solving Method and System Based on Two-Step Deduction Method for Additive Manufacturing

Abstract

The present invention relates to a method and system for solving a scanning path based on a two-step deduction method for additive manufacturing. The method includes the following steps: obtaining a layer slice of a three-dimensional object, and planning a scanning path for the layer slice by using the two-step deduction method according to a set scanning method, wherein the two-step deduction method obtains the scanning path by solving the real-time position of an activation source; the steps of the two-step deduction method for solving the real-time position of the activation source include: determining the current track ordinal number ch ; based on the current track ordinal number ch , calculating the moving displacement of the activation source in the current ch track; based on the moving displacement of the activation source in the current ch track, and combining the initial position of the current ch track, obtaining the real-time position of the activation source. Compared with the prior art, the present invention has the advantages of simplifying and generalizing the realization of scanning path planning, etc.

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, in experimental and simulation studies, a single-zone angular scanning method has been developed to make the heat distribution more uniform. Among them, early studies utilized geometric and periodic symmetries, and 45° reciprocating multi-pass scanning became a popular object. Ali et al. explored 45° and 90° alternating scanning and checkerboard scanning, and found that 90° alternating scanning showed the best performance in reducing residual stress, while checkerboard scanning would increase residual stress as the square size increased. Cheng et al. adopted 45° inclined scanning with an interlayer rotation angle of 45° to provide a uniform temperature gradient and lower stress concentration. However, with the in-depth study of related research, the above geometric and periodic symmetries will also bring uneven heat accumulation, heat distribution, and temperature field caused by the superposition of periods or symmetries, which will further lead to the problem of thermal stress deformation caused by the superposition of periods or symmetries. To solve this problem, Liu, Malekipour et al. developed a non-periodic 67° reciprocating multi-pass scanning method. Mahmood et al. adopted 67° alternating scanning, that is, the scanning direction of each layer was rotated by 67° to reduce thermal stress and component deformation. Liang et al. studied the influence of the path in a single direction in the parallel line scanning strategy and the path with a 67° rotation of each layer in the rotating line scanning strategy on heat accumulation and stress distribution through a combination of numerical simulation and experiment. The number of literature studies on the theoretical simulation of the single-zone angular scanning method is significantly less than that of the experimental process. Combining practice shows that some geometric parameters in this scanning strategy constantly change during the process and need to be described by piecewise functions, and the path setting code is complex. Especially for 67° alternating scanning, it 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 the heat distribution, dispersing stress, improving the uniformity of the microstructure, and reducing the deformation of components, the research on single-zone complex paths has been initiated, including spiral and fractal paths. In terms of spiral scanning, Jia et al. explored bidirectional scanning, outer spiral, and inner spiral paths. Spiral and hexagonal scanning emphasized continuous and smooth paths to reduce stress concentration and non-uniform 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 reduced the thermal gradient by shortening the scanning vector length (about 100 µm). Yu et al. simulated four strategies of grid, outward-inward offset, inward-outward offset, and fractal deposition, and found that the fractal deposition and outward-inward offset strategies could effectively reduce component deformation. However, similarly, the more complex path setting code has led to generally fewer simulation studies, and fractal paths are difficult to be supported by conventional printing equipment, and there are also fewer experimental studies.

[0008] For the thermal control problems of large and complex components, based on single-zone straight and corner configurations, a more suitable multi-zone approach has been developed. By dividing regions and alternating paths to manage heat accumulation, it is particularly effective in large-sized components and complex structures. Among them, stripe scanning manages the thermal gradient through parallel stripe partitioning. Mugwagwa et al. found through experiments that stripe scanning is the most effective in reducing residual stress, which can reduce residual stress by 40% and decrease deformation. In contrast, island scanning is less effective in controlling residual stress. Promoppatum and Yao et al. verified through numerical simulation that stripe scanning can reduce residual stress by more than half under optimal conditions by constructing process windows with different scanning lengths and energy inputs. The checkerboard scanning optimizes heat and stress distribution through small square partitioning and alternating directions. Cai and Liang et al. studied the influence of unidirectional and bidirectional scanning strategies on temperature distribution and reduced heat accumulation and residual stress through the interlayer rotation angle. Wang et al. experimentally studied the influence of checkerboard and uniform scanning on the residual stress and microstructure of AlSi10Mg alloy at different preheating temperatures. Hexagonal scanning relies on the honeycomb distribution of hexagons and naturally has high symmetry. Sara et al. experimentally analyzed the influence of different scanning strategies (standard linear, concentric circular, and hexagonal) on the quality of 17-4PH stainless steel parts. However, compared with the number of experimental research literatures, the simulation work in multi-zone is very limited. Combining with practice, the reason is that the regions in each zone need to be switched, significantly increasing the complexity of the path setting code. And the simulation of hexagonal scanning was not found in the literature research. Combining with practice, the reason is caused by the complex boundary problem of the hexagonal region.

[0009] In summary, with the continuous advancement of actual requirements and simulation work, the complexity of simulation path setting is constantly increasing, and it has restricted the supporting simulation tests for a large number of actual process tests. During the previous work, it was envisaged that if there was a general method and framework to achieve path setting, only one study on complex paths would be needed, and other scholars could directly call it, significantly reducing the research threshold of additive manufacturing process simulation for complex paths. Unfortunately, according to the existing literature research, no relevant work was found, and moreover, most of the surveyed literatures even avoided mentioning the mathematical expression form or setting code of path setting. Summary of the Invention

[0010] The purpose of the present invention is to provide a scanning path solving method and system for additive manufacturing based on a two-step deduction method, which realizes the simplification and generalization of scanning path planning.

[0011] A scanning path solving method for additive manufacturing based on a two-step deduction method includes the following steps:

[0012] Obtain the layer slices of a three-dimensional object, and plan the scanning path of the layer slices using the two-step deduction method according to the set scanning method, where the two-step deduction method obtains the scanning path by solving the real-time position of the activation source;

[0013] The steps of the two-step deduction method for solving the real-time position of the activation source include:

[0014] Determine the current track number ch ;

[0015] Based on the current track number ch , calculate the moving displacement of the activation source in the current ch track ;

[0016] Based on the moving displacement of the activation source in the current ch track , combined with the initial position of the current ch track , obtain the real-time position of the activation source.

[0017] Furthermore, the steps of determining the current track number ch include:

[0018] Determine the scanning path type and scanning speed of the activation source, and calculate the total moving duration of the activation source in the nth track on the layer slice t n ;

[0019] Based on the total moving duration of the nth track t n , calculate the time period of the current track number ch during the scanning process, and determine the current track number according to the time period ch .

[0020] Furthermore, the calculation process of the total moving duration of the nth track t n includes:

[0021] Based on the scanning path type of the activation source and the layer slice, determine the total length of the nth track of the activation source on the layer slice L n ;

[0022] Based on the total length of the nth track L n and the scanning speed, calculate the total moving duration of the activation source in the nth track t n , where the calculation expression of the total moving duration of the nth track t n is:

[0023] ,

[0024] In the formula, v is the scanning speed.

[0025] Furthermore, the step of calculating the current track number ch of the time period of the scanning process includes:

[0026] Based on the total moving duration t n of the nth track, calculate the total time ch required to complete the first 1 to -1 tracks:

[0027] ,

[0028] Based on the total moving duration t n of the nth track, calculate the total time still required to be spent on the layer slice when the current track is completed:

[0029] ,

[0030] Based on the and , obtain the time period ch of the current track number during the scanning process: .

[0031] Furthermore, the step of determining the current track number ch according to the time period includes:

[0032] According to the total scanning time on the layer slice not exceeding the time to scan the last track, that is:

[0033] ,

[0034] In the formula, is the total time for the activation source to move in the current layer slice, che is the last track number;

[0035] Adopt sequential search to test the track number , and there is always satisfying:

[0036] ,

[0037] In the formula, is the test track number;

[0038] Determine the current track number ch to be: .

[0039] Further, the calculation of the activation source's movement displacement in the current ch track includes the following steps: :

[0040] Calculate the movement time of the activation source in the current ch track: t ch : ,

[0041] wherein, is the total movement time of the activation source in the current layer slice, and the total time for completing the first 1 to ch -1 tracks ;

[0042] Based on the definition of displacement-velocity vector integration and combined with the movement time of the activation source in the current ch track t ch , calculate the movement displacement of the activation source in the current ch track , where the calculation expression of the movement displacement is:

[0043] ,

[0044] wherein, is the unit vector in the scanning direction at t time, and is the scanning speed at t time.

[0045] Further, the scanning method 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.

[0046] Further, the determination process of the initial position of the current ch track is as follows:

[0047] 1) For unidirectional scanning:

[0048] Based on the fact that the initial position of the activation source in the current ch track is on the Y-axis, we get: ,

[0049] That is: ,

[0050] wherein, is the initial coordinate, d is the scanning pitch, and is the starting y coordinate of the activation source;

[0051] 2) For bidirectional scanning:

[0052] Alternately change according to the initial position of each track of the activation source on two boundaries parallel to the Y-axis to obtain:

[0053] ,

[0054] That is: ,

[0055] In the formula, a, b is the length and width of the layer slice, L n is the total length of the nth track of the activation source on the layer slice;

[0056] 3) For 45° unidirectional scanning:

[0057] Divide the layer slice into 3 regions and calculate L n in each region to obtain:

[0058] ,

[0059] In the formula, is the moving length of the activation source for the ch th track, is the intercept of the ch th track with the x axis;

[0060] According to L n , calculate the initial position of each track in the 3 regions:

[0061] ,

[0062] That is: ;

[0063] 4) For 45° bidirectional scanning:

[0064] Divide the layer slice into 3 regions and calculate L n in each region to obtain:

[0065] ,

[0066] According to L n , calculate the initial position of each track in the 3 regions: ,

[0067] That is: ;

[0068] 5) For variable-speed 45° one-way scanning:

[0069] Divide the layer slice into 3 regions, and calculate each region L n , to obtain:

[0070] ,

[0071] According to L n , calculate the initial position of each pass in the 3 regions: ,

[0072] That is:

[0073] ;

[0074] 6) For square single-layer vase printing scanning:

[0075] According to the movement of the activation source on the square boundary, the initial position of each pass is the four vertex coordinates of the square, that is:

[0076] ,

[0077] In the formula, , , and are the coordinates of the four vertices.

[0078] The calculation expression for the real-time position of the activation source is:

[0079] ,

[0080] In the formula, is the real-time position of the activation source.

[0081] The present invention also provides a scanning path solving system for additive manufacturing based on a two-step deduction method, including:

[0082] Option layer: used to set the scanning form;

[0083] General layer: used to plan the scanning path of the layer slice by using the two-step deduction method according to the scanning form set by the option layer, wherein the two-step deduction method obtains the scanning path by solving the real-time position of the activation source;

[0084] The steps of the two-step deduction method for solving the real-time position of the activation source include:

[0085] Determine the current pass sequence number ch ;

[0086] Based on the current track ordinal number ch , calculate the displacement of the activation source during the movement in the current ch track ;

[0087] Based on the displacement of the activation source during the movement in the current ch track , combined with the initial position of the current ch track , obtain the real-time position of the activation source.

[0088] Compared with the prior art, the present invention has the following beneficial effects:

[0089] (1) According to the basic principle of the two-step deduction method, the present invention transforms the planning of complex scanning paths into a standardized two-step solution process. Specifically, by solving the moving distance of the current track and combining it with the starting position of the current track, the real-time position of the activation source is obtained, realizing the simplification and generalization of scanning path planning.

[0090] (2) Through the two-step deduction method, the present invention can effectively solve the problem of setting complex scanning paths, that is, the problem of solving the position of the activation source, and unify it into a set of standardized procedures for solution, and can solve any complex scanning path.

[0091] (3) The present invention designs a modular form of a general layer and an option layer for path setting. The option layer solves the important parameters of different scanning methods for different scanning paths, and the general layer solves the path according to the principle of the two-step deduction method, providing an efficient and standardized path setting tool for the field, and laying a foundation for the practical engineering application of complex path setting. The present invention also verifies the generality and flexibility of the two-step deduction method under different path conditions through six typical scanning strategies, including one-way scanning, two-way scanning, 45° one-way scanning, 45° two-way scanning, variable-speed 45° one-way scanning, and single-layer vase path printing.

[0092] (4) The method proposed by the present invention for scanning path planning using the two-step deduction method provides a new possibility for constructing a digital twin model of additive manufacturing, and further promotes the process innovation and digital transformation in the field of additive manufacturing. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] Figure 1 is a schematic diagram of the derivation and verification process of the method of the present invention;

[0094] Figure 2 is the single-zone straight scanning path in the prior art of the present invention. Among them, (a) is the experimental one-way scanning, (b) is the simulation one-way scanning, (c) is the experimental two-way reciprocating scanning, and (d) is the simulation two-way reciprocating scanning;

[0095] Figure 3The single - zone corner scanning path in the prior art of the present invention. Among them, (a) in the figure is the 45 - degree unidirectional multi - track experiment, (b) in the figure is the 45 - degree reciprocating multi - track experiment, (c) in the figure is the imitation of the 45 - degree reciprocating multi - track direction, (d) in the figure is the 67 - degree reciprocating multi - track experiment, (e) in the figure is the 67 - degree reciprocating multi - track simulation;

[0096] Figure 4 The single - zone complex scanning path in the prior art of the present invention. Among them, (a) in the figure is the experimental spiral, (b) in the figure is the simulated spiral, (c) in the figure is the experimental fractal path, (d) in the figure is the simulated fractal path;

[0097] Figure 5 The multi - zone scanning path in the prior art of the present invention. Among them, (a) in the figure is the experimental strip, (b) in the figure is the simulated strip, (c) in the figure is the experimental chessboard, (d) in the figure is the simulated chessboard, (e) in the figure is the hexagon;

[0098] Figure 6 The schematic diagram of the two - step deduction method principle of the present invention;

[0099] Figure 7 The flowchart of the solution process of the two - step deduction method of the present invention;

[0100] Figure 8 The corresponding relationship between the mathematical foundation of the two - step deduction method and the menu - based model of the present invention;

[0101] Figure 9 The schematic diagram of the unidirectional scanning method of the present invention;

[0102] Figure 10 The schematic diagram of the bidirectional scanning method of the present invention;

[0103] Figure 11 The schematic diagram of the 45° unidirectional scanning method of the present invention;

[0104] Figure 12 The schematic diagram of the 45° bidirectional scanning method of the present invention;

[0105] Figure 13 The schematic diagram of the variable - speed 45° unidirectional scanning method of the present invention;

[0106] Figure 14 The schematic diagram of the printing of a single - layer vase in a grid of the present invention. Detailed implementation manners

[0107] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and the detailed implementation manners and specific operation processes are given, but the protection scope of the present invention is not limited to the following embodiments.

[0108] For various common scanning methods, the machining trajectory is not clearly described in experiments and simulations, lacking a general path setting framework, which hinders the wide application of research results in simulations. The two-step deduction method describes the scanning path of the additive manufacturing activation source (fusion source) in any form in a clearer, more general and concise way, and clarifies the common principle of scanning path loading and setting.

[0109] This embodiment provides a scanning path solving method based on the two-step deduction method for additive manufacturing. This method proposes a "menu model", with a "general layer" as a general functional module and an "option layer" as a drop-down module, making complex path settings easier. Through the specific analysis of six typical scanning strategies, the feasibility and generality of the two-step deduction method are proved, enabling flexible setting of scanning paths in simulations, and helping additive manufacturing process simulations and digital twins to perform complex process optimization predictions. Specifically:

[0110] I. Two-step deduction method model derivation

[0111] The problem of scanning path setting in additive manufacturing is essentially to solve the problem of transient loading of the activation source, which can be mathematically described as solving the real-time position of the activation source . However, the real-time position of the activation source cannot be directly called and needs to be determined according to known information, specifically including: (1) The current layer ordinal number ly : Since the printing process of each layer is generally set in one analysis step, the current analysis step is the current layer ordinal number; (2) The scanning speed v of the activation source (fusion source): This value is a preset value. For some variable-speed processes, ; (3) The total time for the activation source to move in the current layer ( ): The system can perform cumulative calculations according to the increment step. (4) The known scanning method, so the total length of the nth path can be solved according to the geometric relationship of the scanning method .

[0112] Table 1 Symbol index table

[0113]

[0114] According to the above process analysis of known information, There is a corresponding relationship with , and this relationship needs to be solved, and then is obtained through conversion. However, the difficulty lies in being unable to determine the current scanning path ordinal number ( ch ). The "two-step deduction method" can solve the above problem of which path, and on this basis, solve the and corresponding relationship.

[0115] According to Figure 6According to the principle shown above, the "two-step deduction method" assumes that any complex additive manufacturing path planning problem is carried out in two steps: first, move the activation source from the origin to the initial position of the current pass , and second, move from the initial position of the current pass to the final activation source, and the displacement experienced is denoted as . Through the "two-step deduction method", the complete scanning process can be divided into the pass ordinal numbers that have been scanned (1 to ch -1), and the pass ordinal number that is being scanned ch .

[0116] According to the above analysis, first solve ch . Solving ch requires knowing the total moving time of the activation source in the nth pass . Considering that can be solved and is known, then it can be solved according to Equation (1.1):

[0117]

[0118] where The solution example of will be given in the second part of this article. According to the processing principle of the "two-step deduction method" above, the total time spent on the completed part (corresponding pass ordinal numbers: 1 to ch -1) is:

[0119]

[0120] When the current pass is scanned and completed, the total time spent on the current layer will be

[0121]

[0122] Any ch pass scanning process corresponds to a time period:

[0123]

[0124] Considering that the total scanning time of the current layer will not exceed the time to scan the last pass, that is:

[0125]

[0126] Therefore, try to sequentially search for the test pass ordinal number , and there is always that satisfies:

[0127]

[0128] At this time, the current scanning pass ordinal number is , and on this basis, Solution. According to the basic principle of the "two-step deduction method", it can be mathematically described as that the activation source first reaches the starting point of the current channel ), and then the displacement experienced from this starting point to the current real-time position , then is:

[0129]

[0130] Among them, gives the specific mathematical form according to the specific geometric characteristics, while According to the definition of displacement-velocity vector integral, Equation (1.9) can be obtained. Considering the conventional and common cases of uniform and straight paths, Equation (1.9) also gives a simplified form

[0131]

[0132] The moving time of the activation source in the current channel ch in Equation (1.8), according to and (Equation 1.2) definition, can be obtained:

[0133]

[0134] Figure 7 is the flow chart of the solution process of the "two-step deduction method" obtained after sorting out the above derivation. This figure shows that the "two-step deduction method" can effectively solve the complicated scanning path setting problem, that is, the problem of solving the activation source position, and unify it into a set of standardized procedures for solution. The key of this method is to use the starting point of the current channel ch as the intermediate point, thereby dividing any scanning path into the steady-state problem of the completed part and the real-time dynamic problem of the uncompleted channels. The time (Equation 1.2) spent on the completed part can be conveniently solved from the steady-state problem, so that the time (Equation 1.9) that the uncompleted channels have experienced can be obtained. Thus, theoretically, any complex scanning path can be solved. In addition, Figure 7 The algorithm is implemented by means of an array. During the generation of the array, the time of each channel, the starting coordinates of each channel, the velocity direction of each channel, the velocity value of each channel, and the power value of each channel are obtained as the corresponding arrays through direct input, interactive input or automatic program calculation. The number of elements of the above arrays is consistent with the number of scanning channels.

[0135] In addition, Figure 8 summarizes the general solution equations in the "two-step deduction method" and the important parameters that vary for different scanning paths, which need to be solved according to the actual situation. According to the programming thinking, the general solution equations can be regarded as the "general layer", and the important parameters can be regarded as the "option layer", based on which Figure 8In the "menu model", the general layer corresponds to the function tab, while the selection layer corresponds to any option in the drop-down menu. If encapsulated into a program plug-in, it can directly call the complex path results in the simulation, greatly simplifying the complex path setting. Moreover, with the rise of digital twin research, this program plug-in can help establish an additive manufacturing digital twin machine, making the scanning path setting in the simulation process "menu-based". In the next section, several typical and simple cases will be selected to show how to solve the parameters according to the actual situation.

[0136] II. Practical Case Application of the Two-step Deduction Method (General Formula Becomes a Special Case)

[0137] To verify the feasibility and universality of the "menu model" of the two-step deduction method, six cases are introduced in detail in this section. Unidirectional scanning and bidirectional scanning are mainly used to describe the machining trajectories in the simulation of single-zone straightness. 45° unidirectional scanning, 45° bidirectional scanning, and variable-speed 45° unidirectional scanning describe the single-zone corner simulation process in detail. The square single-layer vase scanning describes the single-zone complex machining trajectory in detail. The specific mathematical expressions and their derivation processes of the six scanning strategies further explain the "menu model" of the two-step deduction method.

[0138] Considering that the general solution equations (i.e., the "general layer") in the "two-step deduction method" have been solved and summarized in detail above, the general layer expressions are the same for different scanning strategies, while the solution of the important parameters (i.e., the "option layer") varies with different scanning strategies. Therefore, only the important parameters in the option layer are solved in this section.

[0139] 2.1 Unidirectional Scanning

[0140] As Figure 9 is a schematic diagram of the unidirectional scanning method. Assume the grid length mm, mm, the scanning pitch , the starting coordinate of the activation source is (0, 0.05), and the scanning speed is , and it scans unidirectionally from the starting point.

[0141] From Figure 9 , it can be seen that the activation source moves an equal distance in each pass. Therefore, it can be obtained that:

[0142]

[0143] From the general layer formula (1.6), it can be seen that there is a unique . Based on this, can be obtained.

[0144] From Figure 9 , it can be seen that the unit vector Calculate the moving displacement of the activation source in the current channel ch , from the general formula (1.8), we can get:

[0145]

[0146] Let the initial position of the ch-th channel be . Since the starting coordinates of the activation source are (0, 0.05) and the scanning pitch , and the initial position of the activation source in each channel is on the Y-axis, we can get .

[0147] Substitute , into the expression of , we can get:

[0148]

[0149] In summary, we can get:

[0150] .

[0151] 2.2 Bidirectional scanning

[0152] As Figure 10 shows the schematic diagram of the bidirectional scanning method. Assume the grid length mm, mm, the scanning pitch , the starting coordinates of the activation source are (0, 0.05), and the scanning speed is , and it scans back and forth from the starting point.

[0153] It can be seen that in the multi-channel reciprocating scanning of the grid, the distance moved by the activation source in each channel is equal. Therefore, we can get:

[0154]

[0155] From the general formula (1.6), it can be known that there is a unique . Based on this, we can obtain .

[0156] From Figure 10 , it can be seen that the scanning direction alternates parallel to the X-axis. We can get the unit vector in the scanning direction . Calculate the moving displacement of the activation source in the current channel ch , from the general formula (1.8), we can get:

[0157]

[0158] Let the initial position of the ch-th channel be . Since the starting coordinates of the activation source are (0, 0.05) and the scanning pitch , the initial position of each activation source changes alternately on two boundary lines parallel to the Y-axis, and we can obtain . Substitute , into , and we can get:

[0159]

[0160] In summary, we can get:

[0161] .

[0162] 2.3 45° Unidirectional Scanning

[0163] As Figure 11 shows, it is a schematic diagram of the 45° unidirectional scanning method. Assume the grid length is mm, mm, the scanning pitch is , the starting coordinate of the laser heat source is (0, 0.05), and the scanning speed is , and it scans unidirectionally at a 45° angle from the starting point.

[0164] For the 45° unidirectional scanning of the grid, the moving distance of the activation source in each pass is unequal, and the total length of each pass changes with the change of the scanning pass number ch. Let , , where: d is the offset distance of each path on the coordinate axis, is the intercept of the ch-th pass on the x-axis.

[0165] As Figure 11 shows, the grid scanning area can be divided into 3 regions, and the length of the scanning pass in each region can be calculated as:

[0166] , and after sorting, we can get:

[0167]

[0168] From the general layer formula (1.6), it can be known that there is a unique , and based on this, can be obtained.

[0169] From Figure 11 , it can be known that the included angle between the scanning direction and the x axis is -45°, and the unit vector in the scanning direction can be obtained. Calculate the displacement of the activation source moving in the current ch-th pass. From the general layer formula (1.8), we can get:

[0170]

[0171] Let the initial position of the $ch$-th path be . The square scanning area is divided into three regions, and the initial position of each path in each region is obtained separately.

[0172] Substitute , into the expression of , and we can get:

[0173]

[0174] Substitute , into the expression of and after arrangement, we can get:

[0175]

[0176] To sum up, we can get:

[0177]

[0178] Among them, .

[0179] 2.4 45° Bidirectional Scanning

[0180] As Figure 12 shows, it is a schematic diagram of the 45° bidirectional scanning method. Assume that the side length of the square is mm, mm, the scanning pitch is , the starting coordinate of the laser heat source is (0, 0.05), and the scanning speed is . It scans unidirectionally at an angle of 45° starting from the starting point.

[0181] For the 45° bidirectional scanning of the square, the moving distance of the activation source in each path is not equal, and the total length of each path changes with the change of the scanning path number $ch$. Let , , where: $d$ is the offset distance of each path on the coordinate axis, is the intercept of the $ch$-th path on the $x$-axis.

[0182] As Figure 12 shows, the square scanning area can be divided into three regions, and the length of the scanning path in each region is calculated as:

[0183] , and after arrangement, we can get:

[0184]

[0185] From the general layer type (1.6), there exists a unique , and based on this, we can obtain .

[0186] It can be seen from Figure 12 that the angle between the scanning direction and the x-axis alternates between -45° and 135°, and the unit vector in the scanning direction can be obtained . Calculate the moving displacement of the activation source in the current channel ch . From the general layer formula (1.8), we can get:

[0187]

[0188] Let the initial position of the ch-th channel be . The square scanning area is divided into 3 regions, and the initial position of each channel in each region is obtained separately.

[0189] Substitute , into the expression of , and we can get:

[0190]

[0191] Substitute , into the expression of and after arrangement, we can get:

[0192]

[0193] In summary, we can get: 45° bidirectional scanning

[0194]

[0195] Among them, .

[0196] 2.5 Variable-speed 45° unidirectional scanning

[0197] As Figure 13 shows, it is a schematic diagram of the variable-speed 45° unidirectional scanning method. Assume that the square length is mm, mm, the scanning pitch is , the starting coordinate of the laser heat source is (0, 0.05), and the scanning speed is . Starting from the starting point, it scans unidirectionally at an angle of 45°. The variable-speed 45° unidirectional scanning method is described by the two-step deduction method. Assume that the square area is divided into 3 regions, and the specific variable speeds in regions 1 and 3 are: and , represents the speed of each channel.

[0198] For variable-speed 45° bidirectional scanning, the distance that the activation source moves in each channel is not equal, and the total length of each channel changes with the change of the scanning channel number ch. Let , , where: d is the offset distance of each path on the coordinate axis, is the intercept of the ch-th path with the x-axis.

[0199] As Figure 13 shown, the square scanning area can be divided into 3 zones, and the length of the scanning path in each zone is calculated as: Length =

[0200] , and after arrangement, we get:

[0201]

[0202] Since the specific variable speeds in zones 1 and 3 are: and , we can obtain:

[0203]

[0204] From the general layer formula (1.6), it can be known that there is a unique , and based on this, we can obtain .

[0205] From Figure 13 , it can be known that the angle between the scanning direction and the x-axis is -45°, and the unit vector in the scanning direction can be obtained. Calculate the moving displacement of the activation source in the current ch-th path. Substituting Equation (2.14) into the general layer formula (1.8), we get:

[0206]

[0207] Let the initial position of the ch-th path be . The square scanning area is divided into 3 zones, and the initial position of each path in each zone is obtained separately.

[0208] Substitute , into the expression of , and we get:

[0209] , substitute , into the expression of and after arrangement, we get:

[0210]

[0211] In summary, we can obtain: Variable speed 45° one-way scanning

[0212]

[0213] Among them, .

[0214] 2.6 Square single-layer vase printing

[0215] As Figure 14 shown in the schematic diagram of square single-layer vase printing, assuming the square length mm, mm, the starting coordinate of the laser heat source is (0, 0), and the scanning speed is . Starting from the starting point, scanning is performed in a rectangular frame manner. For square single-layer vase printing, the activation source moves on the boundary, and the total length of each scan can be obtained .

[0216]

[0217] From the general layer formula (1.6), it can be known that there is a unique . Based on this, can be obtained.

[0218] From Figure 14 it can be known that the scanning direction of square single-layer vase printing rotates 90 degrees clockwise for each pass, and the unit vector in the scanning direction can be obtained. Calculate the displacement of the activation source moving in the current ch-th pass. From the general layer formula (1.8), we can get:

[0219]

[0220] Let the initial position of the ch-th pass be . Since the starting coordinate of the activation source is (0, 0) and the activation source moves on the boundary, the initial position of each pass is the four vertex coordinates of the square, so we can get:

[0221]

[0222] To sum up, we can get:

[0223]

[0224] To sum up, in the above-mentioned commonly used simplified cases in the research, the menu software implemented by QT software, by selecting which scanning strategy on the menu.

[0225] This paper proposes a brand-new "two-step deduction method" for the scanning path setting in additive manufacturing simulation. This method transforms the simulation setting of complex scanning paths into a standardized two-step solution process, realizing the simplification and generalization of scanning path planning, and providing a brand-new solution for the simulation research in the field of additive manufacturing. The main conclusions of the research are as follows:

[0226] 1. This study designed a "menu-style model" to modularize path settings in the form of a "general layer" and an "option layer". This design can be directly applied to the development of simulation software plugins, providing an efficient and standardized path setting tool, laying a foundation for the practical engineering application of complex path settings.

[0227] 2. By analyzing six typical scanning strategies, including one-way scanning, two-way scanning, 45° one-way scanning, 45° two-way scanning, variable-speed 45° one-way scanning, and single-layer vase path printing, the generality and flexibility of the "two-step deduction method" under different path conditions were verified.

[0228] 3. The "two-step deduction method" solves the key problem of lacking a unified mathematical description and code implementation for complex paths, promoting the integration of scanning paths and simulation processes. With the rise of digital twin technology, the proposed method provides new possibilities for constructing digital twin models of additive manufacturing, further promoting process innovation and digital transformation in the field of additive manufacturing.

[0229] Although the preferred embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications to these embodiments once they know the basic creative concept. Therefore, the appended claims are intended to be construed as including the preferred embodiments and all changes and modifications falling within the scope of the present invention.

[0230] 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 equivalent technologies, 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 channel number ch, calculate the displacement of the activation source in the current channel ch Based on the activation source moving displacement in the current channel Combined with the current channel initial position Get the real-time location of the activation source; The step of determining the current channel number ch comprises: Determine the scanning path type and scanning speed of the activation source, and calculate the total time t of the activation source moving on the layer slice nth time n Based on the total duration t of the nth track movement n , calculating the time period of the scanning process of the current channel number ch, and determining the current channel number ch according to the time period; The total moving time of the nth track is t n The calculation process includes: Based on the scanning path type and layer slice of the activation source, determine the total length L of the nth path of the activation source on the layer slice. n ; Based on the total length L of the nth track n and scanning speed, calculate the total time t of the activation source moving in the nth channel n , where the total moving time of the nth track is t n The calculation expression is: Where v is the scanning speed; The step of calculating the time period of the current channel number ch scanning process comprises: Based on the total moving time t of the nth track n , calculate the total time t to complete the first 1 to ch-1 tracks old : Based on the total moving time t of the nth track n , calculate the total time t that needs to be spent on the layer slice when the current pass is completed cur : Based on the old and t cur , get the time period of the current channel number ch scanning process: The step of determining the current channel sequence number ch according to the time period comprises: The total scanning time on the layer slice does not exceed the time of scanning the last track, that is: Where, t total is the total time of the activation source movement in the current layer slice, che is the last ordinal number; Use sequential search to test the channel number ch * ≤che, there is always ch * satisfy: In the formula, ch * is the test track number; Determine the current channel number ch as: ch = ch * ; The calculation activation source moves the displacement in the current channel The steps include: Calculate the moving time t of the activation source in the current channel ch : Where, t total is the total time for the activation source to move in the current slice, and the total time t to complete the first 1 to ch-1 channels old ; Based on the displacement-velocity vector integral definition, combined with the moving time t in the current channel ch , calculate the displacement of the activation source in the current channel The displacement The calculation expression is: In the formula, is the unit vector in the scanning direction at time t, and v(t) is the scanning speed at time t; The calculation expression of the real-time position of the activation source is: In the formula, 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: 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.

3. The scanning path solving method based on two-step deductive method for additive manufacturing according to claim 2, characterized in that: The current channel initial position The determination process is: 1) For one-way scanning: According to the initial position of the activation source in the current channel All on the Y axis, we get: That is: In the formula, is the initial coordinate, d is the scanning distance, and y0 is the starting y coordinate of the activation source; 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: Where a and b are the length and width of the slice, 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 L in each region n ,get: Where, L ch is the moving length of the activation source of channel ch, m ch is the intercept of the chth track with the x-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 L in each region 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 L in each region 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.

4. A solution system for a scanning path solution method based on a two-step deductive method for additive manufacturing according to any one of claims 1 to 3, 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 channel number ch, calculate the displacement of the activation source in the current channel ch Based on the activation source moving displacement in the current channel Combined with the current channel initial position Get the real-time location of the activation source.

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