Method for additive manufacturing and corresponding system, device, medium and product

Abstract

The present invention provides a method and system for additive manufacturing, as well as corresponding computer devices, storage media, and computer program products. According to the present invention, thermal images are used to monitor deposition width errors in real time as a printhead prints a layer of material. Based on this information, a feedback signal is generated, if necessary, to determine compensation parameters for the printhead to use during subsequent printing. By using thermal images to monitor material deposition width errors and determining compensation parameters for subsequent depositions when the deposition width error exceeds an error threshold, the present invention can reduce deposition inaccuracies and improve printing accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of additive manufacturing, and more particularly to a method and system for additive manufacturing, as well as corresponding computer equipment, computer-readable storage media, and computer program products. Background Art

[0002] Additive Manufacturing (AM) systems are widely used due to their high degree of customization and minimal waste. To improve the manufacturing accuracy of AM systems, monitoring and feedback control systems have been introduced.

[0003] Currently, most existing monitoring and control systems are built on statistical models and are used to improve the AM process within a parameter adjustment framework that does not address the issues of instability or dynamic behavior in high-speed, high-acceleration AM systems. Two representative high-speed, high-acceleration AM systems are fused deposition modeling (FDM) and directed energy deposition (DED). FDM and DED are further characterized by a strong coupling between the mechanical motion system and the deposition process, making the design of controllers more challenging.

[0004] Several monitoring and control solutions have been proposed in the prior art. For example, Insight (Stratasys) models fused deposition modeling 3D printers to provide thermal monitoring and control. This software only adjusts the temperature of the chamber and nozzle. Furthermore, PrintRite3D (Sigma Labs) uses sensors and real-time analytics to monitor and control the laser melting process. It focuses on melt pool geometry and therefore controls the melting state without regard to geometric accuracy.

[0005] However, existing solutions have drawbacks. For example, existing monitoring efforts rarely attempt to extract temporal information about deposition trajectories from thermal images. Furthermore, control systems lack the ability to handle deposition inaccuracies stemming from dynamic features such as motion and high-frequency components of deposition (e.g., corners and vibrations). Summary of the Invention

[0006] The present application aims to propose a solution that can solve or alleviate at least part of the problems of the above-mentioned prior art.

[0007] According to a first aspect of the present invention, there is provided a method for additive manufacturing, wherein a print head is configured to move along a predetermined movement trajectory to print a material layer on a work platform, the predetermined movement trajectory being a function of time, the method comprising:

[0008] During printing of the material layer, obtaining a thermal image portion of interest of a thermal image captured at a capture time point within a printing period corresponding to the predetermined movement trajectory, the thermal image portion of interest comprising temperature information of a corresponding sub-printing segment printed along a corresponding trajectory segment of the predetermined movement trajectory on the working platform within a printing sub-period ending at the capture time point;

[0009] generating a first relationship between an actual deposited width of material and time during the printing sub-period from the thermal image portion of interest;

[0010] determining a third relationship between a deposition width error of the material and time within the printing sub-period based on a second relationship between an ideal deposition width of the material and time within the printing sub-period and the first relationship, wherein for any time within the printing sub-period, the deposition width error of the material at the time is equal to a difference between an actual deposition width of the material at the time and an ideal deposition width of the material at the time;

[0011] determining, based on the third relationship, whether the printing sub-period includes a printing time point at which a deposition width error of the material exceeds an error threshold;

[0012] If the result of the determination is positive, determining a compensation relationship associated with the printing sub-period, the compensation relationship representing a relationship between a compensation feed speed of the material input to the print head and time within an associated compensation period determined based on the printing sub-period,

[0013] The compensation relationship is used for printing by the print head along a trajectory segment of interest after the printing sub-interval, and the trajectory segment of interest is at least partially identical to or at least partially similar to the corresponding trajectory segment.

[0014] In one embodiment, when the angle at a corner point of the trajectory segment of interest is exactly the same as the angle at a corner point of the corresponding trajectory segment or differs by less than a first angle threshold, the trajectory segment of interest is at least partially identical to the corresponding trajectory segment. The first angle threshold can be appropriately determined according to the circumstances, for example, 0.1 degrees, 0.2 degrees, 1 degree, etc. In one embodiment, when the angle at a corner point of the trajectory segment of interest is less than a second angle threshold, the trajectory segment of interest is at least partially similar to the corresponding trajectory segment. The second angle threshold can be appropriately determined according to the circumstances, for example, 2 degrees, 3 degrees, 5 degrees, etc. The second angle threshold can be greater than the first angle threshold. For a trajectory or trajectory segment, the angle at its corner point can be calculated or determined in various ways, including methods in the prior art.

[0015] In one embodiment, the trajectory segment of interest includes: a trajectory segment of the predetermined movement trajectory, or a trajectory segment of another movement trajectory for the print head that is different from the predetermined movement trajectory.

[0016] In one embodiment, the thermal image includes a thermal image in which at least four corner points exist or can be detected.

[0017] In one embodiment, the thermal image is captured by a thermal imager fixedly mounted relative to the nozzles of the print head, and the method includes: acquiring the thermal image; detecting corner points in the thermal image; selecting four corner points from the detected corner points; determining, based on the four selected corner points, the physical position of the nozzle of the print head along the predetermined movement trajectory corresponding to the position of the nozzle of the print head in the thermal image; and determining the corresponding printing time point corresponding to the time when the nozzle of the print head was at the physical position along the predetermined movement trajectory as the capture time point of the thermal image by the thermal imager. Here, the thermal image also includes an additional thermal image portion corresponding to the nozzle of the print head, and the thermal image portion of interest of the thermal image is obtained by removing the additional thermal image portion from the thermal image.

[0018] In one embodiment, generating a first relationship between the actual width of material deposited during the printing sub-period and time from the thermal image portion of interest includes: connecting pixels indicating the same temperature in the thermal image portion of interest to obtain a plurality of isotherms, each indicating a corresponding temperature; identifying two isotherms from the plurality of isotherms indicating a threshold temperature; and, for any time within the printing sub-period, extracting distance information corresponding to the time between the two isotherms as the actual width of material deposited at that time, thereby generating the first relationship between the actual width of material deposited during the printing sub-period and time. In one embodiment, the threshold temperature is determined based on a temperature indicated by a corner point in the thermal image portion of interest (corner point temperature).

[0019] In one embodiment, the two isotherms include a first isotherm located on a first side of a linear extension portion corresponding to the predetermined movement trajectory in the thermal image portion of interest and a second isotherm located on a second side of the linear extension portion opposite to the first side, wherein for any time within the printing sub-period, extracting the distance information corresponding to the time between the two isotherms as the actual deposition width of the material at the time includes: dividing the area between the two isotherms into a first area portion located on the first side of the linear extension portion and a second area portion located on the second side of the linear extension portion; for any time within the printing sub-period, extracting the first distance information corresponding to the time between the first isotherm and the linear extension portion from the first area portion as the first deposition width, extracting the second distance information corresponding to the time between the second isotherm and the linear extension portion from the second area portion as the second deposition width, and calculating the sum of the first deposition width and the second deposition width as the actual deposition width of the material at the time.

[0020] In one embodiment, the sub-printing period starts at a first starting time point Δt0 and ends at a first ending time point Δt1 which is the capturing time point, and the associated compensation period starts at a second starting time point before the first starting time point. and ends at a second end time point after the first end time point Determining the compensation relationship includes the following steps:

[0021] The relationship between the deposition inaccuracy rate of the material and time in the printing sub-period ΔE(t sub ):

[0022] ΔE(t sub )=K e Δw(t sub ),

[0023] Among them, t sub ∈[Δt0,Δt1],K e represents the specified deposition correction gain, Δw(t sub ) represents a third relationship between a deposition width error of the material and time within the printing sub-period;

[0024] The relationship between the output compensation volume of the material output from the nozzle of the print head and time ΔE is determined according to the following formula: r (t sub ):

[0025]

[0026] Where τ is the specified time constant;

[0027] Specify multiple discrete control time points Δt within the associated compensation period i , where i∈[0,n], n is an integer greater than 1, for each control time point Δt i , the corresponding compensated feed speed of the material input to the print head is expressed as ΔV i , each control time point Δt i and its corresponding compensation feed speed ΔV i Represented as P i ,Right now And the compensation relationship is calculated based on the following formula

[0028]

[0029] stΔV min ≤ΔV i ≤ΔV max ,

[0030]

[0031] in, N i (Δt) is the basis function, is the filtered basis function, by using G(s) to N i (Δt) is filtered, G(s) is a transfer function representing the relationship between the volume of the material input to the print head and the volume of the material output from the nozzle of the print head,

[0032] represents a relationship between a desired output compensation rate of material output from the nozzles of the print head during the associated compensation period and time,

[0033] Δv e (Δt) represents the relationship between the ideal output compensation speed of the material output from the nozzle of the print head during the associated compensation period and time, and ΔE r (t sub ) has a linear relationship, and ΔE r (t sub ) is determined based on the linear relationship,

[0034] ΔV min and ΔV max Represents ΔV i The minimum and maximum allowed values.

[0035] In one embodiment, Δv e (Δt) is equal to ΔE r (tsub ) is multiplied by a coefficient, which can be a constant, for example, determined by experiment.

[0036] In one embodiment, K e Depends on the temperature indicated by the corner point in the thermal image portion of interest (corner point temperature).

[0037] In one embodiment, the first starting time point Δt0 and the second starting time point The time interval between the first end time point Δt1 and the second end time point The time interval between.

[0038] In one embodiment, the plurality of discrete control time points are spaced apart at fixed time intervals.The control time points may not necessarily correspond to printing time points.

[0039] In one embodiment, the method of the present invention further comprises: performing a pre-processing process before printing the material layer. The pre-processing process comprises:

[0040] identifying whether the printing period includes the following smoothing-required time span: each printing time point within a single smoothing-required time span is evaluated as not satisfying an elongated deposition condition, that is, for each printing time point within the single smoothing-required time span, a corresponding position of the nozzle of the print head along the predetermined movement trajectory is evaluated as being unable to deposit material along a normal direction of the predetermined movement trajectory within a working plane defined by the working platform, the evaluation being based on a predetermined curvature of the predetermined movement trajectory at the printing time point, a moving speed of the print head at the printing time point, and an output volume of material outputted from the nozzle of the print head at the printing time point;

[0041] If the recognition result is positive, a smoothing process is performed for each identified time span to be smoothed, the smoothing process comprising:

[0042] For each printing time point within the time span to be smoothed: specifying an effective curvature for the printing time point, determining an additional curvature at the printing time point based on the specified effective curvature, and calculating an additional rotation angle corresponding to the additional curvature at the printing time point, wherein the effective curvature specified for the printing time point is a maximum allowable curvature value that satisfies the elongated deposition condition at the printing time point assuming that the predetermined curvature of the predetermined movement trajectory at the printing time point is replaced by the specified effective curvature;

[0043] Determine the sum of the additional rotation angles calculated for each printing time point within the time span to be smoothed as the additional rotation angle to be allocated;

[0044] Allocating the additional rotation angle to be allocated to a plurality of future sampling time points after the end time point of the time span to be smoothed and a plurality of past sampling time points before the start time point of the time span to be smoothed, wherein the plurality of future sampling time points are obtained at fixed sampling intervals from the end time point, and the plurality of past sampling time points are obtained at fixed sampling intervals from the start time point, wherein the allocation is such that the additional rotation angle allocated to each sampling time point has the same sign as the additional rotation angle to be allocated,

[0045] wherein, for each of the plurality of future sampling time points and the plurality of past sampling time points, an effective curvature at the sampling time point is determined based on an additional rotation angle assigned to the sampling time point,

[0046] For any printing time point within the identified time span requiring smoothing, its effective curvature is the specified effective curvature; for any printing time point outside the identified time span requiring smoothing and not used as a sampling time point, the predetermined curvature of the predetermined movement trajectory at that point is its effective curvature.

[0047] According to the second relationship between the ideal deposition width of the material and time during the printing period, for any printing time point t during the printing period, the ideal deposition width of the material at that time is expressed as 2w d (t), where:

[0048]

[0049] φ eff (t) = κ eff (t)v(t)T s ,

[0050]

[0051] Wherein, w0(t) represents the theoretical deposition width at the position of the nozzle of the print head along the predetermined movement trajectory at the printing time point t, assuming that the material is deposited along the normal direction of the predetermined movement trajectory within the working plane defined by the working platform, φ eff (t) is the effective rotation angle of the predetermined moving trajectory at the printing time point t, κ eff (t) is the effective curvature of the predetermined movement trajectory at the printing time point t, v(t) represents the movement speed of the nozzle of the print head at the printing time point t, x(t) and y(t) are functions representing the predetermined movement trajectory with time as a variable, T s represents the sampling interval.

[0052] In one embodiment, for any printing time point used as a sampling time point, its effective curvature is equal to the sum of the predetermined curvature of the predetermined movement trajectory at the printing time point and the additional curvature at the printing time point, and the additional curvature at the printing time point corresponds to the additional rotation angle assigned to the printing time point.

[0053] In one embodiment, when multiple time spans requiring smoothing are identified, smoothing is performed sequentially on the multiple time spans requiring smoothing in chronological order. For example, smoothing may be performed sequentially on the multiple time spans requiring smoothing, starting with the earliest time span requiring smoothing.

[0054] In one embodiment, the material layer has a constant height h, and for any printing time point t within the printing period, it is evaluated as not meeting the elongated deposition condition when it does not satisfy the following formula:

[0055]

[0056] Wherein, κ(t) represents the predetermined curvature of the predetermined movement trajectory at the printing time point t, E(t) represents the output volume of the material output from the nozzle of the print head at the printing time point t,

[0057] in,

[0058] In one embodiment, for any printing time point t within a single time span to be smoothed, s , for which the effective curvature is specified as κ eff (t s ), the additional curvature calculated is κ φ (t s ),have:

[0059]

[0060] The additional rotation angle to be allocated is expressed as ΔΦ, which is:

[0061]

[0062] Among them, t v Indicates the printing time point t s The time period corresponding to the time span to be smoothed.

[0063] In one embodiment, the sum of the additional rotation angles allocated to the multiple future sampling time points is equal to half of the additional rotation angle to be allocated, and the sum of the additional rotation angles allocated to the multiple past sampling time points is equal to half of the additional rotation angle to be allocated.

[0064] In one embodiment, the multiple future sampling time points include N f future sampling time points,

[0065]

[0066] t f，j =t v，1 +jT s ,

[0067] The additional rotation angle assigned to each future sampling time point is determined based on the following equation:

[0068] φ f (t f，j+1 )=φ f (t f，j )-dφ f (t f，j ),

[0069]

[0070] dφ f (t f，j )=(κ(t f，j )+κ φ (t f，j ))v(t f，j )T s ,

[0071]

[0072]

[0073] Among them, t v，1 Indicates t v The end time point, N f is an integer greater than 1, j∈[1,N f ], t f Indicates the N f A set of future sampling time points, t f，j Denotes the set t f The jth element in Indicates that there is an assumption that there is a sampling time point later than Distance t v，1 Far T s A distant future The additional rotation angle φ assigned to the future distant point is f (t f，1 ) indicates the N f The sum of the additional rotation angles at future sampling time points, φf (t f，j ) represents the time points to be allocated to the jth future sampling time point to the Nth future sampling time point f The sum of the additional rotation angles at future sampling time points, when φ f (t f，1 ) is positive, φ f (t f，j ) is positive and changes with the variable t f，j Monotonically decreasing, when φ f (t f，1 ) is negative, φ f (t f，j ) is negative and varies with the variable t f，j Monotonically increasing, dφ f (t f，j ) represents the time allocated to the future sampling point t f，j The additional rotation angle, κ(t f，j ) represents the predetermined moving trajectory at the future sampling time point t f，j The predetermined curvature at φ (t f，j ) represents the future sampling time point t f，j The additional curvature at represents the future sampling time point t f，j The maximum allowed value of the additional curvature at represents the future sampling time point t f，j The additional curvature candidate at v(t f，j ) represents the nozzle of the print head at the future sampling time point t f，j The moving speed at f，j ) represents the future sampling time point t f，j The output volume of material output from the nozzle of the print head.

[0074] In one embodiment, the plurality of past sampling time points includes N p past sampling time points,

[0075]

[0076] t p，k =t v，0 -kT s ,

[0077] The additional rotation angle assigned to each past sampling time point is determined based on the following formula:

[0078] φ p (t p，k+1 )=φ p (t p，k )-dφ p (tp，k ),

[0079]

[0080] dφ p (t p，k )=(κ(t p，k )+κ φ (t p，k ))v(t p，k )T s ,

[0081]

[0082] Among them, t v，0 Indicates t v The starting time point, N p is an integer greater than 1, k∈[1,N p ], t p Indicates the N p A set of past sampling time points, t p，k Denotes the set t p The kth element in Indicates that there is an assumption that there is a sampling time point in the past Distance t v，0 Far T s A distant point in the past The additional rotation angle φ assigned to the past distant point in the case p (t p，1 ) indicates the N p The sum of the additional rotation angles at past sampling time points, φ p (t p，k ) represents the time points to be assigned to the kth past sampling time point to the Nth past sampling time point p The sum of the additional rotation angles of the past sampling time points, when φ p (t p，1 ) is positive, φ p (t p，k ) is positive and changes with the variable t p，k Monotonically decreasing, when φ p (t p，1 ) is negative, φ p (t p，k ) is negative and varies with the variable t p，k Monotonically increasing, dφ p (t p，k ) represents the time allocated to the past sampling point t p，k The additional rotation angle, κ(t p，k ) represents the predetermined movement trajectory at the past sampling time point t p，kThe predetermined curvature at φ (t p，k ) represents the past sampling time point t p，k The additional curvature at represents the past sampling time point t p，k The maximum allowed value of the additional curvature at represents the past sampling time point t p，k The additional curvature candidate at v(t p，k ) represents the nozzle of the print head at the past sampling time point t p，k The moving speed at p，k ) represents the sampling time point t in the past p，k The output volume of material output from the nozzle of the print head.

[0083] In one embodiment, for each identified time span to be smoothed, a previous printing time point adjacent to its start time point and before the start time point and a subsequent printing time point adjacent to its end time point and after the end time point meet the elongated deposition condition.

[0084] According to a second aspect of the present invention, there is provided a system for additive manufacturing, comprising a processor configured to execute computer instructions to cause the method of the first aspect to be performed.

[0085] According to a third aspect of the present invention, a computer device is provided, comprising a memory and a processor, wherein the memory stores computer instructions, and when the computer instructions are executed by the processor, the method of the first aspect is executed.

[0086] According to a fourth aspect of the present invention, there is provided a non-transitory computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, cause the method of the first aspect to be performed.

[0087] According to a fifth aspect of the present invention, there is provided a computer program product comprising computer instructions, which, when executed by a processor, cause the method of the first aspect to be performed.

[0088] The solution of the present invention creatively proposes to use thermal images to monitor the deposition width error of materials and determine a compensation relationship for subsequent deposition when the deposition width error exceeds an error threshold, which can make up for at least some of the shortcomings of the existing technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Non-limiting and non-exhaustive embodiments of the present invention are described, by way of example, with reference to the following drawings, in which:

[0090] Figure 1Schematic illustration of an example of width calculation for an elongated deposition path;

[0091] Figure 2 Schematically shows a flow chart of deposition direction assignment for avoiding violation of the elongated deposition condition;

[0092] Figure 3 Schematic illustration of the main deposition directions before and after processing the violation of the elongated deposition condition in the high curvature region;

[0093] Figure 4(a) to Figure 4(c) The effective thermal image, its corner detection results and its alignment and positioning relative to the trajectory of the nozzle of the print head are respectively shown;

[0094] FIG4( d ) schematically illustrates the alignment of multiple in-situ thermal images;

[0095] Figure 5(a) to Figure 5(c) The generation of input compensation velocity is schematically illustrated;

[0096] Figure 6 Schematic showing the experimental hardware setup used, including the FDM deposition nozzle with a thermal imager;

[0097] FIG7( a ) schematically illustrates a printing trajectory for a part, which includes multiple corner points at different angles;

[0098] FIG7( b ) schematically illustrates a printed part formed based on a 20-layer test track that follows the printing track in FIG7( a );

[0099] FIG8( a ) and FIG8 ( b ) respectively show images of printing results without and with the proposed compensation corner points;

[0100] FIG9(a) and FIG9(b) schematically show the printing results of the corner points without and with the proposed compensation, respectively. E analyze;

[0101] Figure 10 Schematic diagram of a surface profile measurement setup using a two-dimensional laser profiler for a printed part involved in the printing in FIG9( a ) and FIG9 ( b );

[0102] FIG11( a ) and FIG11 ( b ) schematically illustrate printed parts without and with the proposed compensation, respectively;

[0103] Figures 11(c) and 11(d) schematically illustrate the deposition profile error measurement results of the printed parts in Figures 11(a) and 11(b), respectively. DETAILED DESCRIPTION

[0104] Overview

[0105] To address the shortcomings of existing technologies, this application proposes a thermal image-based deposition trajectory monitoring and compensation scheme for additive manufacturing, aiming to mitigate deposition inaccuracies. This scheme uses thermal images to monitor deposition width errors in real time as the printhead prints a layer of material. This information is used to generate feedback signals, when necessary, to determine compensation parameters for the printhead to use during subsequent printing. This scheme employs a low-order analytical model that describes the print path boundaries and deposition direction. Real-time captured thermal images are analyzed using this model to generate dynamic time-domain compensation signals. This model has been validated to reduce deposition inaccuracies using an FDM printer.

[0106] 1. Introduction

[0107] Additive manufacturing (AM) is increasingly being used in aerospace, automotive, and medical applications (see Ref. [1]) due to its flexibility and convenience in the manufacture of rapid prototyping (see Ref. [2]) and systems with complex internal structures (see Ref. [3]). Despite its rapid growth, modern AM still suffers from the following problems: low accuracy, low product and process stability, lack of feedback, and insufficient data utilization (see Ref. [4] and Ref. [5]). Among the seven categories of AM (see Ref. [1]), FDM and DED are two widely used representative classifications (see Ref. [6]). Both FDM and DED processes are characterized by a strong coupling of the mechanical motion system and the deposition process (see Ref. [7] and Ref. [8]). The motion coupling causes FDM and DED to have poor accuracy compared to other methods (see Ref. [6]-Ref. [8]) and poses challenges to AM control systems. In order to improve printing accuracy, an increased level of monitoring and advanced feedback control methods are required for FDM and DED systems (see Ref. [2]).

[0108] Among various monitoring methods (e.g., acoustics, vibration, etc.), thermal monitoring plays a vital role in AM processes, especially in FDM and DED processes with unique heating and cooling cycles. In the FDM process, the filament is heated to a liquid state, deposited from a nozzle, and then solidified in an environment (see reference [9]). In the DED process, the material is first melted or fused by a high energy source (e.g., laser, plasma, etc.), followed by a solidification or secondary process (see reference

[10] ). The temperature distribution of the deposited material in FDM and DED processes contains real-time printing performance and deposition conditions, which is significantly responsible for possible printing defects (e.g., porosity, expansion) and printing geometric accuracy. In addition, thermal monitoring systems have additional benefits due to their non-contact nature and rich spatial / temporal information (see references

[11] -

[13] ). In order to utilize this information, various print quality monitoring methods for AM processes have been proposed. Tlegenov et al. (see reference

[11] ) established a dynamic model for minimizing nozzle clogging by monitoring nozzle temperature. Zhang et al. (see reference

[12] ) used in-situ monitoring of the surface temperature of printed parts to predict the printed geometry. Khanzadeh et al. (see references

[13] and

[14] ) applied thermal monitoring to the melt pool for predicting internal structural anomalies (e.g., porosity and microcracks). In bioprinting, thermal images of printed layers are also used to analyze thermal phase change processes (see reference

[15] ). Caltanissetta et al. (see reference

[16] ) proposed a method for automatically detecting temperature nonuniformity in printed parts via thermal video imaging. Mazzarisi et al. (see reference

[17] ) analyzed the relationship between thermal gradients and the metallographic structure and microhardness of the produced parts. Chandrasekar et al. (see reference

[18] ) linked the thermal characteristics of printed parts to their resulting shape and microstructure through similarity analysis. In addition, artificial intelligence (AI) algorithms have also been widely used in thermal image processing. Li et al. (see reference

[19] ) introduced a deep convolutional neural network model for feature extraction of thermal images. Li et al. (see Ref.

[20] ) proposed a surface roughness prediction model based on extruder temperature and some other printing parameters using machine learning. Tian et al. (see Ref.

[21] ) combined real-time captured thermal images with deep learning for in-situ porosity detection. However, existing work rarely attempts to extract temporal information of deposition trajectories from thermal images, especially in FDM and DED, where relatively long time-varying temperature histories are readily available.

[0109] Dynamic control of deposition progress and motion using information from monitoring systems is critical to the printing process (see Ref.

[22] ). The benefits of thermal images, namely their rich dynamic, spatial, and temporal information, make them an attractive candidate for control system feedback (see Ref.

[23] ). Wang et al. (see Ref.

[24] and Ref.

[25] ) used thermal imaging to construct regression models for surface temperature prediction and real-time layer printing time control. Li et al. (see Ref.

[26] ) applied thermal monitoring to deposited filaments for printing speed and temperature control. Caltanissetta et al. (see Ref.

[27] ) proposed a data-driven defect elimination scheme using in-situ thermal monitoring. Salehi and Brandt (see Ref.

[28] ) used a proportional, integral, and derivative (PID) controller to adjust the printer's laser power according to the temperature of the melt pool. Farshidianfar et al. (see Ref.

[29] ) provided a closed-loop controller to manipulate microstructures in a powder bed fusion process based on in-situ thermal images. However, most existing control methods using thermal images only adjust printing parameters; they lack the ability to control dynamic features during deposition. These dynamic features typically arise from high-frequency components of motion and deposition (e.g., corners, vibrations), resulting in deposition inaccuracies common in FDM and DED with motion / deposition coupling.

[0110] To fill the gap in dynamic feature monitoring and control during AM processes, this application constructs a real-time thermal monitoring and feedback control system to optimize deposition trajectories. Specifically, this application involves at least the following aspects:

[0111] · Analytical modeling of the dynamic relationship between deposition / motion trajectories and printed path geometry;

[0112] Establishing an automated alignment strategy for in-situ thermal images and their connection to the deposition trajectory time domain signal; and

[0113] • Develop a method to generate deposition compensation trajectories that accounts for both real-time deposition inaccuracies and deposition dynamics.

[0114] The rest of this application is as follows. Section 2 proposes a model for print width calculation and discusses a method for extracting the actual deposition width from thermal images. The error between the ideal deposition width and the actual deposition width is calculated and used as a feedback signal to generate a corresponding compensation signal for generating a compensation trajectory. Section 3 shows the experimental details about the hardware and software, as well as the experimental procedure. The comparison of two-dimensional and three-dimensional printed parts before and after compensation is illustrated, and the improvement of deposition inaccuracy is evaluated. Conclusions are then drawn in Section 4.

[0115] 2. In-situ monitoring and sedimentation inaccuracy compensation methods

[0116] 2.1 Printing Path Geometry Modeling and Critical Slender Deposition Condition

[0117] Considering an FDM or DED process with a moving print head, assuming that the print head moves along a given trajectory (x(t), y(t)) in a single layer, the output volume of the material output from the nozzle of the print head is E(t). Here, "output volume" can also be called "output amount", which can refer to the flow rate, volume, height, etc. of the material output from the nozzle of the print head, depending on the specific situation. The height of the printed layer is assumed to be determined by the distance from layer to layer and is defined as h. The velocity v(t) of the print head and the unit vector e(t) representing the time-varying printing direction are defined as

[0118]

[0119] The print direction e(t) is constant when the trajectory is straight and time-varying for curved print paths. Using these variables, the exact boundaries of the print path for arbitrary curves can be established based on the law of conservation of mass, including the left boundary (x l (t), y l (t)) and the right boundary (x r (t), y r (t)). In order to be able to subsequently dynamically manipulate the deposition process, a general time-varying flow rate E(t) is assumed.

[0120] For deposition along a straight line, the total deposited material Q from time t0 to t1 is given by:

[0121]

[0122] where w(t) is the half-width of the print path. It is also assumed that the steady-state initial flow rate and the ending flow rate are E0 and E1, respectively. Since equation (2) needs to be satisfied for all t, without considering the deposition delay and print height variation, the half-width of the print path w(t) is obtained as

[0123]

[0124] Note that for deposition along a straight line, when the flow rate and printing speed are constant, the half-width of the print path is constant.

[0125] For the more complex case, when the printed material is deposited along a curved path, a similar basic law can be derived based on the curvature κ given by:

[0126]

[0127] Where x′, y′ are the first-order curve derivatives of the movement trajectory of the print head nozzle along the x-axis and y-axis, respectively, and x″, y″ are the second-order curve derivatives of the movement trajectory of the print head nozzle along the x-axis and y-axis, respectively. Note that the curvature κ is positive for counterclockwise rotation in the movement direction of the print head nozzle and negative for clockwise movement in the same movement direction.

[0128] Figure 1 Schematic illustration of an example width calculation for an elongated deposition path. Figure 1 The middle curve in FIG shows the printing direction along the nozzle center path. The curve is the center line of the movement path of the nozzle of the print head, corresponding to the movement trajectory of the nozzle of the print head. Figure 1 As shown in , considering the deposition process at a specific time, S l and S r is the material deposition area on the left and right sides of the curve. For the curve segment with curvature κ<0, the right side is the inner side and the left side is the outer side, and S in =S r 、S out =S l For the curve segment with curvature κ>0, its right side is the outside and its left side is the inside, and S out =S r 、S in =S l , where S in 、S out Denote the material deposition area on the inside and outside, respectively. Assuming that the deposition process produces an elongated curve (i.e., at any position along the curve, the main deposited material is perpendicular to the curve, i.e., along the normal direction of the curve), the incremental deposition area on the left and right sides of the curve along the small curve length ds is calculated as

[0129]

[0130] Among them, w l is the left print half width, w r is the right print half-width, dα is the incremental change in print direction (positive values ​​indicate counterclockwise rotation, with the same sign as the curvature κ). It is assumed that material deposited on one side of the track along the print direction e(t) remains on that side, that is,

[0131]

[0132] Combining equations (5) to (7), the left print half width and the right print half width satisfy the following equations:

[0133]

[0134] The solutions to these two equations are

[0135]

[0136] For the sake of simplicity, some variables in equations (4) to (11) above omit the time-varying property, that is, the variable of time t is not reflected. These variables in equations (4) to (11) can be modified to reflect time t and still hold true. For example, κ, x′, y′, x″, y″, w in equations (4) to (11) l 、w r , E, v can be modified to κ(t), x′(t), x″(t), y′(t), y″(t), w l (t), w r (t), E(t), v(t).

[0137] Note that equations (8) and (9) have real solutions only when the following elongated deposition conditions are satisfied, i.e.,

[0138]

[0139] This elongated deposition condition indicates that the deposition progressed mainly along the vertical direction perpendicular to the centerline (e.g. Figure 1 The direction of the centerline (i.e., the normal to the centerline) is such that the deposition line is elongated, such as an elongated curve. However, this elongated deposition condition may not always hold, especially for additive manufacturing applications that utilize many corner segments. At the corners of the print path, the curvature will be very large, and the elongated deposition condition will be locally violated. This indicates that the print deposition direction is no longer perpendicular to the print direction, and additional mathematical processing is required to define its geometry.

[0140] 2.2 Establishment of deposition direction for high curvature areas

[0141] To alleviate the problem of violating the elongated deposition condition due to high curvature of the trajectory, the assumed deposition direction is modified to avoid possible crossing of the printing path boundary. In the normal region of the trajectory segment where the curvature is small (satisfying the elongated deposition condition defined and expressed by equation (12)), the deposition direction is perpendicular to the printing direction. However, when the curvature is large, an additional rotation angle φ(t) is introduced. Its corresponding increase in curvature κ φ (t) is defined as

[0142]

[0143] This rotation angle gives an additional degree of freedom to minimize the curvature for elongated deposition conditions. The effective curvature is defined as

[0144] κeff (t) = κ(t) + κ φ (t). (14)

[0145] Applying the effective curvature κ eff (t), the elongated deposition condition in equation (12) is modified to

[0146]

[0147] On the other hand, κ φ (or κ φ The design of the time variable t (t) is not completely free. Minimum changes to the normal region that adheres to the elongated deposition condition are desired. s0 and s1 are defined as the curve lengths sufficiently far from the region where increased curvature is desired, while t0 and t1 are the corresponding times. The deposition direction orientation with and without increased curvature should be the same, i.e., the following spatial and temporal relationships should be satisfied:

[0148]

[0149] This can be achieved by redistributing high curvature (κ) regions to their neighborhood, as long as the high curvature regions only consist of a small portion of the entire trajectory.

[0150] The detailed implementation of the above reallocation process is shown in Figure 2 The redistribution is an iterative process. First, we assume zero additional curvature (i.e., κ φ = 0), and evaluate S along the entire trajectory simultaneously c (t). Extract S c (t) is the time span that continuously shows an absolute value greater than 1. The first continuous time span that violates equation (12) is defined as t v , which is from t v，0 Start and at t v，1 Ends at t∈t v When the corresponding κ φ The value of (t) is designed to enforce the effective curvature κ eff (t) to satisfy equation (15). That is,

[0151]

[0152] Due to κ φ The rotation angle error caused by the introduction of (t) is defined as ΔΦ, which is given by the following equation:

[0153]

[0154] The rotation angle error can be referred to as the additional rotation angle to be allocated. This additional rotation angle is designed to be redistributed to t v neighborhood.

[0155] To maintain the symmetry of the path, the value ΔΦ is divided equally between the past time span and the future time span, satisfying

[0156]

[0157] Where ΔΦ f and ΔΦ p are the rotation angles introduced in the future time span and the past time span respectively. The past time span and the future time span are relative to t v In terms of.

[0158] In a discrete system with sampling time T s Execute ΔΦ f and ΔΦ p The distribution of , with a representation of a defined future time span and a representation of a defined past time span will be and t f The elements in (i.e., future sampling points) and t p The elements in (i.e., past sampling points) are defined as

[0159] t f，j =t v，1 +jT s ,

[0160] t p，j =t v，0 -jT s (20)

[0161] φ f (t f，j ) is defined as the f，j to The sum of the additional rotation angles, ΔΦ f The rest is used to f，j Start allocating until The additional rotation angle to complete the redistribution. f，1 arrive This sequence φ f (t f，j ) is strictly monotonically increasing or decreasing to reaches zero at ; the direction (monotonically increasing or decreasing) depends on the initial condition φ f (t f，1 ) sign. This process is performed by the following relationship:

[0162] φf (t f，j+1 )=φ f (t f，j )-dφ f (t f，j ) (twenty one)

[0163] Among them, dφ f (t f，j ) is composed of t f，j The additional rotation angle caused by the redistribution of curvature at , and for the set t f Each element in is kept as positive or kept as negative, that is, the additional rotation angles assigned to all future sampling points are either positive or negative. Following the relationship between curvature and rotation angle in equation (13), dφ f (t f，j ) is calculated as

[0164] dφ f (t f，j )=(κ(t f，j )+κ φ (t f，j ))v(t f，j )T s (twenty two)

[0165] Among them, κ φ (t f，j ) is composed of t f，j The additional curvature is caused by the redistribution of the rotation angle at . In order to determine the additional curvature κ φ (t f，j ), the method first calculates t f，j The maximum allowable value of the additional curvature that satisfies the elongated deposition condition It is given by:

[0166]

[0167] t f，j The corresponding curvature candidate at It is given by:

[0168]

[0169] The candidate is then verified to satisfy the maximum allowed value defined in Equation (23) (i.e., ). This verification further defines the t actually applied during the curvature redistribution process. f，j , with the following formula:

[0170]

[0171] Calculated t f，j , tf，j The corresponding effective rotation angle at is calculated as

[0172] φ eff (t f，j )=κ eff (t f，j )v(t f，j )T s (26)

[0173] Now, according to equations (21) and (22), calculate t f，j The additional rotation angle dφ redistributed at f (t f，j ) and at the next time t f，j+1 The remaining additional rotation angle φ awaiting reallocation f (t f，j+1 ). Repeat this operation until φ f (t f，j+1 )=0, indicating ΔΦ f In t f This also defines the discrete steps N required for the reallocation process. f .

[0174] The same reallocation method is applied to ΔΦ p In t p The redistribution of the samples in the past is carried out in a similar way in the opposite direction. f and t p When the redistribution is completed between the two, t v The violation of the elongated deposition condition at t has been fully resolved. Note that this redistribution process only resolves one continuous time span where the elongated deposition condition was violated; there are usually still multiple similar continuous time spans, which can be solved by redefining t for the next violation. v Repeat this recursive process until Indicates that the curvature smoothing process is completed. This process establishes the local deposition direction for any continuous trajectory.

[0175] The results of the above curvature smoothing method and the generated deposition direction are in Figure 3 is exemplified in . exist Figure 3In FIG, the movement trajectory of the nozzle of the print head is schematically shown by a dotted line, and the main deposition direction is schematically shown by a number of short solid lines transverse to the movement trajectory, wherein the upper figure shows the main deposition direction before processing the violation of the elongated deposition condition in the high curvature region, and the lower figure shows the main deposition direction after processing the violation of the elongated deposition condition in the high curvature region. It can be seen that the estimated boundary is expanded at the corner area with large curvature (κ) and low speed. In addition, due to the introduction of the effective curvature (κ eff ), where the corner areas are located, the main deposition directions are continuously distributed without crossing.

[0176] 2.3 Thermal Image Processing, Stitching, and Positioning

[0177] It is known that using thermal images as a monitoring tool has significant challenges in dealing with distortion. This challenge stems from the difficulty of calibrating thermal images with blurred boundaries due to heat flux (compared to traditional best-fit images). Similar to traditional best-fit images, thermal image distortion is decomposed into radial distortion and distortion due to tilted camera alignment. Radial distortion is an intrinsic parameter of the thermal imager; it is usually addressed by applying Zhang's method (see Ref.

[30] ), where a chessboard calibration image is used to identify the radial coefficient. Distortion due to tilted camera alignment is usually unavoidable in AM monitoring processes because thermal imagers can only monitor the heat-affected area from the side. This distortion can be addressed by a homography transformation. Define the two-dimensional generalized vector in the image coordinate system (for the thermal image captured by the thermal imager) and the ground coordinate system (for the movement trajectory of the nozzle of the print head) as and And define the homography matrix H that satisfies the following formula:

[0178]

[0179] Since the homography matrix H has 8 degrees of freedom (see reference

[31] ), at least four pairs of corresponding points (each pair of points consists of a point in the thermal image and a corresponding point in the movement trajectory of the nozzle of the print head) are required to obtain its solution. Because the FDM and DED methods contain a large number of dynamic features, the positions of the corner points in the thermal image and the corresponding corner points in the geometric printing trajectory are selected as pairs for H matrix calculation.

[0180] Conventional corner detection techniques (such as Haris) rely on significant gradient fluctuations in the image (see reference

[32] ), which are not suitable for thermal images with blurred edges due to heat flux. Because of the accumulation of heat at the print corners (usually caused by excessive deposition in the corners), feature extraction provides an alternative method for corner detection in thermal images. In this application, feature extraction in thermal images uses the Fast RCNN (with ResNet-50 as the backbone) model proposed by Ren et al. (see reference

[33] ), and combines the Feature Pyramid Network (FPN) proposed by Lin et al. (see reference

[34] ) to enhance the robustness of feature detection. The resulting detected feature boxes provide corner estimates of the thermal image. Considering that features close to the image edge may be incomplete, those points whose distance to the image edge is less than 5% of the image size are removed. These detected corners are used to calibrate the thermal image and locate the thermal image using the print track. The detected corners in the thermal image form a set P (0) , and the set of known physical points forms the set P (1) , as indicated by equation (27). Therefore, the homography transformation matrix H is calculated using the least squares method. Solving the H matrix requires at least four corner points in an image to provide sufficient information. Figure 4(a) to Figure 4(c)The figures show a valid thermal image, its corner detection results, and its alignment and positioning relative to the movement trajectory of the print head nozzles. Here, a valid thermal image can be understood as a thermal image captured by a thermal imager in which at least four corners are present or detectable. A thermal image captured by a thermal imager can be referred to as a "raw thermal image." Figure 4(a) shows a raw thermal image requiring further processing in an image coordinate system. This thermal image, captured by a thermal imager fixedly mounted relative to the print head nozzles, consists of two parts: an additional image portion corresponding to the print head nozzles, also known as the "nozzle area"—such as the portion of the thermal image within the dashed box; and a portion of the thermal image of interest, also known as the "information-rich area"—such as the portion of the thermal image outside the dashed box. Figure 4(b) shows the corner detection results in an image coordinate system after the thermal image in Figure 4(a) has been cropped to the information-rich area. This information-rich area is obtained by removing the nozzle area from the thermal image. The detected corners are indicated by cross-shaped asterisks. The image coordinate system has a width (w) axis and a height (h) axis (both in pixels). FIG4( c) shows the positioning result of the rich information area in FIG4( b) relative to the moving track in a ground coordinate system, see the area in the dotted box. The area in the dotted box in FIG4( c) can be referred to as the "monitoring area". The ground coordinate system has an x-axis and a y-axis (both in mm). As shown, there is a linear extension corresponding to the moving track (coinciding with the moving track - when the rich information area is aligned and positioned relative to the moving track as shown in FIG4( c)) in the rich information area, and the "corner point" should be understood as a point on the linear extension corresponding to the moving track in the rich information area that forms a corner. For the corner points detected in the thermal image shown in FIG4( b), there are corresponding corner points on the printed track shown in 4( c). Assume that the original thermal image in Figure 4(a) was acquired at a capture time point. The information-rich region in Figure 4(b) includes the temperature information of a corresponding sub-printing segment printed on the work platform along a corresponding trajectory segment of the movement trajectory within a printing sub-period ending at the capture time point. The monitoring region in Figure 4(c) includes the area within which the corresponding sub-printing segment is located. The intersection point of the leading edge of the monitoring region (in terms of the movement direction of the print head nozzle) and the movement trajectory (indicated as the "end position" in Figure 4(c)) corresponds to the capture time point. In other words, the end position shown in Figure 4(c) is the position of the print head nozzle on the movement trajectory at the capture time point.

[0181] Although the thermal imager is commanded to acquire thermal images at a fixed rate, the actual image capture time has slight fluctuations, so it is necessary to locate the thermal images captured by the thermal imager. The key to positioning is to know the actual time when the thermal image is captured. th The real capture time, recording time and unknown time fluctuation of thermal image are defined as tc (i), t r (i), t f (i) Satisfy

[0182] t c (i) = t r (i)+t f (i). (28)

[0183] Fluctuation t r (0) is relatively small, and therefore t r (0) is usually used to estimate t r (0).

[0184] Since the geometric relationship between the thermal imager and the nozzle of the print head is unchanged during the monitoring process, the nozzle position in the image coordinate system is manually marked in the first aligned thermal image (such as the thermal image in 4(a)) and is defined as For thermal images subsequent to the first aligned thermal image, it is not necessary to manually mark the nozzle position in them. th The nozzle position and monitoring area of ​​the thermal image are defined as and Recording time t r (i) Given i th Approximate nozzle position from thermal image and the expected monitoring area i th Corner points in thermal images and The corner points in the trajectory within are detected and they follow equation (27) to give the homography matrix H(i). Therefore, for i th Thermal image, the actual nozzle position in the ground coordinate system is given by:

[0185]

[0186] Calculated nozzle coordinates Combined with the trajectories x(t) and y(t) defined in equation (1), it is used to obtain the true capture time t c (i), which is given by:

[0187]

[0188] Among them, U(t r (i), δt) is t with a small time span δt r (i) neighborhood. For typical thermal images, δt should be within 10ms. Now we know i precisely thThe moment of thermal image capture indicates that the thermal image positioning is precisely aligned with the ground coordinate system. The resulting multiple in-situ thermal images are shown in Figure 4(d). Figure 4(d) also shows the stitching of multiple in-situ thermal images aligned and positioned relative to the movement trajectory.

[0189] 2.4. Sedimentation Information Extraction and Dynamic Sedimentation Compensation Methods

[0190] Reference Figure 5(a) to Figure 5(c) The compensation sequence generation process is described by way of example. Figure 5(a) to Figure 5(c) In FIG, the horizontal axis is time t (in s) and the vertical axis is width w (in mm).

[0191] For each localized thermal image, deposition information at each sampling time along the trajectory x(t), y(t) is extracted along the critical deposition direction derived in Section 2.2, as shown in Figure 5(a). Figure 5(a) can be obtained based on the localized thermal image. Specifically, by connecting pixels indicating the same temperature in the localized thermal image, multiple isotherms, each indicating a corresponding temperature, are obtained. These multiple isotherms are distributed in the thermal image and have a specific relative positional relationship within the thermal image. Due to the characteristics of additive manufacturing, isotherms indicating a certain temperature of the deposited material appear in pairs on either side of the linear extension of the movement trajectory in the thermal image. Accordingly, the two isotherms indicating a threshold temperature located on either side of the linear extension in the thermal image can be used to determine the deposition width of the material printed at the same printing time point, based on the fact that the material printed at the same printing time point has the same temperature. Based on the temporal alignment of the localized thermal image and the movement trajectory, the correspondence between the points on each isotherm and time can be obtained. Thus, the distance between the two isotherms indicating a threshold temperature on both sides of the linear extension in the thermal image at a certain time point can be regarded as the deposition width of the printed material at the corresponding time point. The threshold temperature can be determined based on the corner temperature in the corresponding thermal image. Referring to FIG5(a), the application of the threshold temperature T t The left and right deposition half widths w are extracted from the contours (isotherms) of l (T t , t) and w r (T t , t). Define the desired print path half width as w d (t), which is given by:

[0192]

[0193] Among them, φ eff (t) is the effective rotation angle defined in equation (26), and w0 is the theoretical width of the straight printing path. Accordingly, the error Δw in the deposition width is defined as

[0194] Δw=w l (T t , t)+w r (T t , t)-2w d (t), (32)

[0195] Define ∈ as the maximum allowable deposition inaccuracy; a deposition region satisfying |Δw| ≥ ∈ indicates a significant deposition inaccuracy that needs to be compensated. Δt0 and Δt1 are defined as the continuous deposition inaccuracy time span t, respectively. o The extracted width (actual deposition width) and perfect width (ideal deposition width) within the continuous deposition inaccuracy time span collected from Figure 5(a) are shown as solid lines and dashed lines in Figure 5(b), respectively. Based on the deposition inaccuracy Δw, the local deposition compensation rate is estimated as

[0196] ΔE(t)=K e (w l +w r -2w d ), (33)

[0197] Among them, K e is the experimentally obtained deposition correction gain.

[0198] In order to achieve the desired compensation results, the dynamics of the deposition process need to be taken into account. This stems from the fact that there is usually a delay between the deposition signal and the actual deposition process. The deposition compensation reference command is defined as ΔE(t) and the actual deposition change is ΔE r (t). Bellini et al. [see reference 33] studied this input-output, and this application uses a first-order linear time-invariant (LTI) system representation G(s) for its relationship, which is given by the following formula:

[0199]

[0200] Where s is the Laplace variable; τ is the time constant; ΔE r (s) and ΔE(s) is ΔE r (t) and the Laplace transform of ΔE(t). Its time domain representation is written as

[0201]

[0202] Taking into account the dynamics of deposition, the compensation time span is extended to The start and end times are respectively and The corresponding input deposition compensation velocity trajectory v er (Δt) using m th The Non-Uniform Rational Basis Spline (NURBS) of order is smoothed to

[0203]

[0204] in N i (Δt) is the basis function; is the control point, which defines the compensation velocity at a specific time, i.e., the pair of a specific time and the corresponding compensation velocity. To ensure a smooth transition in the case of uncompensated areas, the final input deposition velocity v ef (Δt) satisfies

[0205] v ef (Δt)=v e (Δt)-Δv er (Δt), (37)

[0206] Among them, v e (Δt) is the original input deposition rate.

[0207] According to the filtered B-spline (FBS) method proposed by Duan et al.

[35] , the transfer function G(s) in equation (34) is applied to N i (Δt) to obtain the filter basis function The following formula represents:

[0208]

[0209] in, yes The Laplace transform of , represents the filtered basis function, N i (s) is N i Laplace transform of (Δt).

[0210] Therefore, the desired output deposition compensation rate is calculated as

[0211]

[0212] Control Point is obtained by minimal optimization, where

[0213]

[0214] stΔV min ≤ΔV i ≤ΔV max ,

[0215]

[0216] Considering the original deposition rate and deposition dynamics, ΔV i The range of is limited by the minimum compensation speed and the maximum compensation speed. Figure 5(c) shows the desired input of the deposition compensation speed and perfect output Δv e Calculation results of (Δt).

[0217] Note: The generated input compensation speed over time (deposition compensation sequence) can be stored as a database and reused in subsequent printing for the same or similar trajectory segments. Such database application can save computing resources.

[0218] 3. Experimental Verification of the Proposed Method

[0219] 3.1. Experimental hardware setup

[0220] Figure 6 The experimental hardware setup is shown. A Flashforge Creator 3FDM printer was used for the experiments. A thermal imager (FLIR 3.5) was mounted on a lightweight fixture securely attached to the print nozzle and moved with the nozzle during printing. The thermal imager's mounting facilitated the capture of real-time deposition conditions. Printing parameters and thermal imager specifications are specified in Tables 1 and 2, respectively. Note that the thermal expansion of PLA in the target range is very small. A temperature drop of 200°C resulted in only a one-dimensional contraction of 0.0041%. Therefore, thermal expansion was omitted from the thermal images in this case.

[0221] Table 1

[0222]

[0223] Table 2

[0224]

[0225] Because FDM and DED processes typically feature abundant corners, the main test track includes corners at various angles, as illustrated in Figure 7(a). To further verify the effectiveness of enhancing deposition accuracy during layer-by-layer fabrication, a test part was designed using 20 layers of test tracks, as shown in Figure 7(b). Despite issues caused by flattening the print bed, a baseplate was added to provide a flat and solid foundation for the main track printing.

[0226] Thermal image processing and compensation trajectory generation

[0227] The first step in thermal image processing is corner detection. The images used for corner detection model training are carefully annotated with one category (corner) using a mature and effective image labeling method [see reference 37]. There are 69 annotated images in total with more than 200 features. The image dataset is packaged in the form of PASCAL VOC 2012 [see reference 38] and randomly divided into training and test sets with a ratio of 1:1. The initial learning rate is set to 0.01. The batch size of training is set to 2, and the epoch size is 15. The mean average precision (mAP) value of the model generated from each epoch is calculated according to the evaluation criteria. The mAP of the final trained model selected is 99.5%, demonstrating high accuracy and high precision.

[0228] The monitoring system begins capturing and processing thermal images after the main track printing begins. The thermal images are first labeled with the nozzle position and cropped to preserve information-rich areas. Using a pre-trained detection model, the real-time captured images are sent for corner feature detection. The time interval between each thermal image is set to 0.125 seconds. The hardware used for thermal image processing is an i5-12500H CPU and a single NVIDIA GeForce RTX 2050 GPU.

[0229] Using the corner points detected in the thermal image, the stitching and positioning and deposition width extraction processes mentioned in Sections 2.3 and 2.4 are performed. Note that, considering the accuracy of monitoring, only sufficiently new printed corner points whose temperature T p Meet 140℃≤T p The thermal images of ≤150℃ will be further processed. Based on the actual deposition width monitored, the deposition width error Δw is calculated according to equations (31) and (32). The expected path width w0 for the straight line in equation (31) is related to the feed deposition rate ratio α, and the relationship between them is obtained through experiments and is expressed as w0=3.44α+0.67.

[0230] Based on the deposition width error Δw, the local deposition inaccuracy rate ΔE(t) is calculated by equation (33). e It was determined experimentally to be K e =1+(150-T p ) / 15, where T p is the corner temperature. To generate the input deposition compensation speed from ΔE(t), the time constant τ in equation (34) for the deposition dynamics of the printer used is identified as 0.0873s. The minimum compensation speed and the maximum compensation speed in equation (40) have been set to ΔV respectively.min =-2mm / s and ΔV max = 4 mm / s. Time expansion for dynamic compensation (i.e., from to Δt0 and from Δt1 to The time intervals) are all set to 0.1 s, taking into account the identified deposition dynamics. The calculated input compensated deposition rate v ef (Δt) is sent to the printer for compensation.

[0231] Results

[0232] For preliminary compensation efficiency evaluation, a layer of part with and without compensation was printed along the designed trajectory mentioned in Section 3.1. A thermal image of the print trajectory without compensation was first collected and sent to the controller for compensation trajectory calculation, which was then sent to the printer for another printed part. Figures 8(a) and 8(b) illustrate the print results for different corners without and with compensation. It was observed that the print results without compensation suffered from over-deposition in the corners. The two-dimensional over-deposition index O at the corner area is E is defined as

[0233]

[0234] Among them, A o is the over-extrusion area, and A c is the area of ​​the perfect corner polyhedron in the corner. O before and after compensation E The analysis results are shown in Figures 9(a) and 9(b), where the "desired corner regions" are shown as regular polyhedrons at the corners, and "overdeposition regions" are shown to form around the corner regions. The average overdeposition index for this print decreased from 106.75% to 31.73%, indicating an increase in deposition accuracy.

[0235] After preliminary verification, test parts with and without compensation were printed, as shown in Figures 11(a) and 11(b). A Keyence LJ-V7300 2D laser profiler was used to obtain the outer surface profile of the printed parts using a z-axis sampling spacing of 0.5 mm. The measurement system setup is shown in Figure 10 With each point (x t ,y t )∈P t The corresponding deposition deviation e t After the measurement, it is obtained, where P t The set P represents the set of points in a particular layer that represent the desired outer surface contour. t The coordinates of each point (x t ,yt ) is obtained from the CAD file of the printed part. Deposition deviation e t and its corresponding (x t ,y t )Synthetic element (x t ,y t , e t )∈e t , where e t is the error set. In order to calculate the error set showing the difference between the expected contour and the measured contour, another point set P is defined m , P m The points (x m ,y m ) composition. Specific (x t ,y t ) at the deposition profile error e t It is therefore calculated as

[0236]

[0237] For each layer with sampled measurement profiles, the error set e is calculated t , and all e belonging to parts without compensation are illustrated in Figure 11(c) and Figure 11(d) respectively. t The result and all e belonging to the parts with compensation t After the monitoring and compensation system intervened, the maximum deviation (MAX) was reduced from 1.6805 mm to 0.2468 mm, and the mean value (RMS) was reduced from 0.4301 mm to 0.2017 mm, as shown in Table 3.

[0238] Table 3

[0239]

[0240]

[0241] 4. Conclusion

[0242] This application proposes a method for in-situ additive manufacturing deposition trajectory monitoring and compensation using thermal images as feedback signals. An analytical model is established to describe the dynamic relationship between the deposition / motion trajectory and the print path geometry. To resolve the conflicting elongated deposition conditions of the proposed model, the curvature of the motion trajectory is rearranged to help determine the deposition direction. Based on the established model, an in-situ monitoring and deposition trajectory compensation system is established. Real-time thermal images are collected as feedback signals and sent to the system for automatic time-dependent trajectory alignment before further processing. Alignment relies on the AI ​​thermal image corner detection method proposed in this application. After alignment, deposition information along the specified direction determined by the analytical model is extracted, and deposition inaccuracy is calculated accordingly. This deposition inaccuracy information is then processed by a deposition trajectory compensation generator. The compensation generator is designed to fully account for real-time deposition inaccuracies and deposition dynamics. The resulting compensated trajectory is sent to the printer to complete the feedback control process.

[0243] Experiments conducted using an FDM printer validated the effectiveness of the monitoring and control system in improving deposition inaccuracy. Two-dimensional and three-dimensional examples were printed with and without deposition compensation for deposition inaccuracy evaluation. In the two-dimensional example, the average overdeposition rate decreased from 106.75% to 31.73%. In the three-dimensional example, the maximum deposition deviation decreased from 1.6805mm to 0.2468mm, and the average value decreased from 0.4301mm to 0.2017mm. The results demonstrate improved deposition accuracy.

[0244] The present invention can be implemented as a computer device comprising a memory and a processor, wherein the memory stores computer instructions executable by the processor, and when executed by the processor, the computer instructions instruct the processor to perform the steps of the method of the present invention. The executable computer instructions can be embodied and implemented in the form of an application program. The computer device can be broadly defined as a server, a terminal, or any other electronic device with the necessary computing and / or processing capabilities. In one embodiment, the computer device may include a processor, memory, a network interface, a communication interface, etc. connected via a system bus. The processor of the computer device can be used to provide the necessary computing, processing, and / or control capabilities. The memory of the computer device can include a non-volatile storage medium and an internal memory. The non-volatile storage medium can store an operating system, a computer program, etc. in or on the non-volatile storage medium. The internal memory can provide an environment for the operation of the operating system and computer program in the non-volatile storage medium. The network interface and communication interface of the computer device can be used to connect to and communicate with external devices via a network. When the computer program is executed by the processor, the steps of the method of the present invention are performed.

[0245] The present invention can be implemented as a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, causes the steps of the method of the present invention to be performed. In one embodiment, the computer program is distributed across a plurality of network-coupled computer devices or processors so that the computer program is stored, accessed, and executed in a distributed manner by one or more computer devices or processors. A single method step / operation, or two or more method steps / operations, can be performed by a single computer device or processor or by two or more computer devices or processors. One or more method steps / operations can be performed by one or more computer devices or processors, and one or more other method steps / operations can be performed by one or more other computer devices or processors. One or more computer devices or processors can perform a single method step / operation, or perform two or more method steps / operations.

[0246] It will be understood by those skilled in the art that all or part of the steps of the present invention may be performed by instructing relevant hardware such as a computer device or a processor through a computer program, and the computer program may be stored in a non-transitory computer-readable storage medium, which causes the steps of the method of the present invention to be performed when the computer program is executed. Depending on the circumstances, any reference to memory, storage, database or other media herein may include non-volatile and / or volatile memory. Examples of non-volatile memory include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), flash memory, magnetic tape, floppy disk, magneto-optical data storage device, optical data storage device, hard disk, solid-state disk, etc. Examples of volatile memory include random access memory (RAM), external cache memory, etc.

[0247] Various documents are mentioned and cited above, the contents of each of which are hereby incorporated by reference in their entirety.

[0248] The various technical features described above can be combined arbitrarily. Although not all possible combinations of these technical features are described, any combination of these technical features should be considered to be covered by this specification as long as such combination does not conflict.

[0249] Although the present invention has been described in conjunction with the embodiments, it should be understood by those skilled in the art that the above description and the accompanying drawings are only exemplary and non-restrictive, and the present invention is not limited to the disclosed embodiments. Various modifications and variations are possible without departing from the spirit of the present invention.

[0250] Reference list:

[0251] [1]K.V.Wong,A.Hemandez,A Review of Additive Manufacturing,ISRNMechanical Engineering.2012(2012)1-10.https: / / doi.org / 10.5402 / 2012 / 208760.

[0252] [2]H.Bikas,P.Stavropoulos,G.Chtyssolouris,Additive manufacturingmethods and modeling approaches:A ctitical review,International Journal ofAdvanced Manufacturing Technology.83(2016)389-405.https: / / doi.org / 10.1007 / s00170-015-7576-2.

[0253] [3]I.Gibson,D.Rosen,B.Stucker,M.Khorasani,Additive ManufacturingTechnologies,n.d.

[0254] [4]H.Lhachemi,A.Malik,R.Shorten,Augmented Reality,Cyber-PhysicalSystems,and Feedback Control for A dditive Manufacturing:A Review,IEEEAccess.7(2019)50119-50135.https: / / doi.org / 10.1109 / A CCESS.2019.2907287.

[0255] [5]S.K.Everton,M.Hirsch,P.I.Stavroulakis,R.K.Leach,A.T.Clare,Reviewofin-situ process monitoring and in-situ metrology for metal additivemanufacturing。Mater Des.95(2016)431-445.https: / / doi.org / 10.1016 / j.matdes.2016.01.099.

[0256] [6]T.D.Ngo,A.Kashani,G.Imbalzano,K.T.Q.Nguyen,D.Hui,Additivemanufacturing(3D printing):A review of materials,methods,applications andchallenges,Compos B Eng.143(2018)172-196.https: / / doi.org / 10.1016 / j.comp ositesb.2018.02.012.

[0257] [7]R.B.Kristiawan,F.Imaduddin,D.Ariawan,Ubaidillah,Z.Arifin,A reviewon the fused deposition modeling(FDM)3D printing Filament processing,materials,and printing parameters,Open Engineering11(2021)639-649.https: / / doi.org / 10.1515 / eng-2021-0063.

[0258] [8]D.G.Ahn,Directed Energy Deposition(DED)Process:State of the Art,International Journal of Precision Engineering and Manufactring-GreenTechnology.8(2021)703-742.https: / / doi.org / 10.1007 / s40684-020-00302-7.

[0259] [9]Y.Fu,A.Downey,L.Yuan,A.Pratt,Y.Balogun,In situ monitoring forfused filament fabrication process:A review,Addit Manuf.38(2021).https: / / doi.org / 10.1016 / j.addma.2020.101749.

[0260]

[10] M.Lalegani Dezaki,A.Serjouei,A.Zolfagharian,M.Fotouhi,M.Moradi,M.K.A.Ariffin,M.B odaghi,A review on additive / subtractive hybridmanufacturing of directed energy deposition(DED)process,Advanced PowderMaterials.1(2022)100054.https: / / doi.org / 10.1016 / j.apmate.2022.100054.

[0261]

[11] Y.Tlegenov,W.F.Lu,G.S.Hong,A dynamic model for current-basednozzle condition monitoring in fused deposition modelling,Progress inAdditive Manufacturing.4(2019)211-223.https: / / doi.org / 10.1007 / s40964-019-00089-3.

[0262]

[12] H.Zhang,X.Zhao,In-situ thermal monitoring informed modeling andsimulation of process temperature during vat photopolymerization additivemanufacturing。Mater Today Proc.70(2022)237-241.https: / / doi.org / 10.1016 / j.matpr.2022.09.027.

[0263]

[13] M.Khanzadeh,S.Chowdhuty,M.A.Tschopp,H.R.Doude,M.Marufuzzaman,L.Bian,In-situ monitoring of melt pool images for poro sity prediction indirected energy deposition processes,IISE Trans.51(2019)437-455.https: / / doi.org / 10.1080 / 24725854.2017.1417656.

[0264]

[14] M.Khanzadeh,W.Tian,A.Yadollahi,H.R.Doude,M.A.Tschopp,L.Bian,Dualprocess monitoring of metal-based additive manufacturing usingtensordecomposition of thermal image streams,Addit Manuf.23(2018)443-456.https: / / doi.org / 10.1016 / j.addma.2018.08.014.

[0265]

[15] G.Ukpai,B.Rubinsky,A three-dimensional model for analysis andcontrol of phase change phenomena during 3D printing of biological tissue,Bioprinting.18(2020).https: / / doi.ort / 10.1016 / j.bprint.2020.e00077.

[0266]

[16] F.Caltanissetta,G.Dreifus,A.J.Hart.,B.M.Colosimo,In-situmonitoring of Material Extrusion processes via thermal videoimaging withapplication to Big Area Additive Manufacturing(B AANI),Addit Manuf.58(2022)102995.https: / / doi.org / 10.1016 / j.addma.2022.102995.

[0267]

[17] M.Mazzarisi,A.Angelastro,M.Latte,T.Colucci,F.Palano,S.L.Campanelli,Thermal monitoring of laser metal deposition strategies usinginfrared thermography,J Manuf Process.85(2023)594-611.https: / / doi.org / 10.1016 / j.jmapro.2022.11.067.

[0268]

[18] S.Chandrasekar,J.B.Coble,F.List,K.Catver,S.B eauchamp,A.Godfrey,V.Paquit,S.S.Babu,Similarity analysis for thermal signature comparison inmetal additive manufacturing,Mater Des.224(2022).https: / / doi.org / 10.1016 / j.matdes.2022.111261.

[0269]

[19] X.Li,S.Siahpour,J.Lee,Y.Wang,J.Shi,Deep leaming-based intelligentprocess monitoring of directed energy deposition in additive manufacturingwith thermal images,in:ElsevierB.V.,2020:pp.643-649.https: / / doi.org / 10.1016 / j.promfg.2020.05.093.

[0270]

[20] Z.Li,Z.Zhang,J.Shi,D.Wu,Prediction of surface roughness inextrusion-based additive manufacturing with machine leaming,RobotComput.Integr Manuf.57(2019)488-495.https: / / doi.org / 10.1016 / j.rcim.2019.01.004.

[0271]

[21] Q.Tian,S.Guo,E.Melder,L.Bian,W.Guo,Deep leaming-based data fusionmethod for in situ porosity detection in laser-based additive manufacturing,Joumal of Manufacturing Science and Engineering,Transactions of the ASME.143(2021).https: / / doi.org / 10.1115 / 1.4048957.

[0272]

[22] Y.AbouelNour,N.gupta,In-situ monitoring of sub-surface andintemal defects in additive manufacturing:A review,Mater Des.222(2022)111063.https: / / doi.org / 10.1016 / J.MA TDES.2022.111063.

[0273]

[23] M.Mani,B.Lane,A.Donmez,S.Feng,S.Moylan,R.Fesperman,MeasurementScience Needs for Real-time Control of Additive Manufacturing Powder BedFusion Processes,Gaithersburg,MD,2015.https: / / doi.org / 10.6028 / NIST.IR.8036.

[0274]

[24] F.Wang,F.Ju,K.Rowe,N.Hofmann,Real-time control for large scaleadditive manufacturing using thermal images,in:IEEE Intermational Conferenceon Automation Science and Engineering,IEEE,2019:pp.36-41.https: / / doi.org / 10.1109 / COASE.2019.8843264.

[0275]

[25] F.Wang,S.Fathizadan,F.Ju,K.Rowe,N.Hofmann,Print Surface ThemalModeling and Layer Time Control for Large-Scale Additive Manufacturing,IEEETransactions on Automation Science and Engineering.18(2021)244-254.https: / / doi.org / 10.1109 / TASE.2020.3001047.

[0276]

[26] N.Li,G.Link,J.Jelonnek,Rapid 3D microwave printing of continucascarbon fiberreinforced plastics,CIRP Annals.69(2020)221-224.https: / / doi.org / 10.1016 / j.cirp.2020.04.057.

[0277]

[27] F.Caltanissetta,G.Dreifus,A.J.Hart,B.M.Colosimo,In-situmonitoring of Material Extrusion processes via thermal videoimaging withapplication to Big Area Additive Manufacturing(BAAM),Addit Manuf.58(2022).https: / / doi.org / 10.1016 / j.addrna.2022.102995.

[0278]

[28] D.Salahi,M.Brandt,Melt pool temperature control using LabVIEW inNd:YAG laser blown powder cladding process,International Journal of AdvancedManufacturing Technology.29(2006)273-278.https: / / doi.org / 10.1007 / s00170-005-2514-3.

[0279]

[29] M.H.Farshidianfar,A.Khajepour,A.Gerlich,Real-time control ofmicrostructure in laser additive manufacturing,International Journal ofAdvanced Manufacturing Technology.82(2016)1173-1186.https: / / doi.org / 10.1007 / s00170-015-7423-5.

[0280]

[30] Z.Zhang,A Flexible New Technique for Camera Calibration,2000.https: / / doi.org / 10.1109 / 34.888718.

[0281]

[31] D.DeTone,T.Malisiewicz,A.Rabinovich,Deep Image HomographyEstimation,(2016).http: / / atxiv.org / abs / 1606.03798.

[0282]

[32] J.Chen,L.hui Zou,J.Zhang,L.hua Dou,The comparison and applicationo f comer detection algorithms,J Multimed.4(2009)435-441.https: / / doi.org / 10.4304 / jmm.4.6.435-441.

[0283]

[33] S.Ren,K.He,R.Girshick,J.Sun,Faster R-CNN:Towards Real-Time ObjectDetection with Region Proposal Networks,Adv Neural Inf Process Syst.28(2015).http: / / arxiv.org / abs / 1506.01497.

[0284]

[34] T.-Y.Lin,P.Dollár,R.Girshick,K.He,B.Hariharan,S.Belongie,FeaturePytamid Networks for Object Detection,Proceedings of the IEEE Conference onComputerVision and Pattern Recognition.(2017)2117-2125.http: / / arxiv.org / abs / 1612.03144.

[0285]

[35] A.Bellini,S. M.Bertoldi,Liquefier dynamics in fuseddeposition,J Manuf Sci Eng.126(2004)237-246.https: / / doi.org / 10.1115 / 1.1688377.

[0286]

[36] M.Dan,D.Yoon,C.E.Okwudire,A limited-preview filtered B-splineapproach to tracking control-With application to vibration-induced errorcompensation of a 3D printer,Mechatronics.56(2018)287-296.https: / / doi.org / 10.1016 / J.MECHATRONICS.2017.09.002.

[0287]

[37] Tzutalin,LabelImg,Git Code.(2015).https: / / github.com / tzutalin / labelImg(accessed March 13,2023).

[0288]

[38] The PASCAL Visual Object Classes Challenge 2012(VOC2012)Results|BibSonomy,(n.d.).https: / / www.bibsonomy.org / bibtex / 2af3e05b5f98957bd59f03f37fad407c5 / tgandor(accessed March13,20:3).

Claims

1. A method for additive manufacturing, wherein a print head is configured to move along a predetermined motion trajectory to print a material layer on a work platform, wherein the predetermined motion trajectory is a function of time, the method comprising: During printing of the material layer, obtaining a thermal image portion of interest of a thermal image captured at a capture time point within a printing period corresponding to the predetermined movement trajectory, the thermal image portion of interest comprising temperature information of a corresponding sub-printing segment printed along a corresponding trajectory segment of the predetermined movement trajectory on the working platform within a printing sub-period ending at the capture time point; generating a first relationship between an actual deposited width of material and time during the printing sub-period from the thermal image portion of interest; determining a third relationship between a deposition width error of the material and time within the printing sub-period based on a second relationship between an ideal deposition width of the material and time within the printing sub-period and the first relationship, wherein for any time within the printing sub-period, the deposition width error of the material at the time is equal to a difference between an actual deposition width of the material at the time and an ideal deposition width of the material at the time; determining, based on the third relationship, whether the printing sub-period includes a printing time point at which a deposition width error of the material exceeds an error threshold; If the result of the determination is positive, determining a compensation relationship associated with the printing sub-period, the compensation relationship representing a relationship between a compensation feed speed of the material input to the print head and time within an associated compensation period determined based on the printing sub-period, The compensation relationship is used for printing by the print head along a trajectory segment of interest after the printing sub-interval, and the trajectory segment of interest is at least partially identical to or at least partially similar to the corresponding trajectory segment.

2. The method according to claim 1, wherein The interesting trajectory segments include: a trajectory segment of the predetermined movement trajectory, or A trajectory section for a further movement trajectory of the print head that differs from the predetermined movement trajectory.

3. The method according to claim 1, wherein The thermal image includes a thermal image in which at least four corner points exist or can be detected.

4. The method according to claim 3, wherein: The thermal image is captured by a thermal imager fixedly mounted relative to the nozzles of the print head, the method comprising: acquiring the thermal image; detecting corner points in the thermal image; Select 4 corner points from the detected corner points; Determining, based on the selected four corner points, a physical position of the nozzle of the print head along the predetermined movement trajectory corresponding to the position of the nozzle of the print head in the thermal image; determining a corresponding printing time point corresponding to when the nozzle of the print head is at the physical position along the predetermined movement trajectory as the capture time point when the thermal imager captures the thermal image, The thermal image further includes an additional thermal image portion corresponding to the nozzles of the print head, and the thermal image portion of interest of the thermal image is obtained by removing the additional thermal image portion from the thermal image.

5. The method according to claim 4, wherein Generating a first relationship between an actual deposition width of material and time within the printing sub-period from the portion of the thermal image of interest comprises: connecting pixels indicating the same temperature in the portion of the thermal image of interest to obtain a plurality of isotherms each indicating a corresponding temperature; identifying two isotherms from the plurality of isotherms that indicate a threshold temperature; For any time within the printing sub-period, the distance information between the two isotherms corresponding to the time is extracted as the actual deposition width of the material at the time, thereby generating a first relationship between the actual deposition width of the material and time within the printing sub-period.

6. The method according to claim 5, wherein: The two isotherms include a first isotherm located on a first side of a linear extension corresponding to the predetermined movement trajectory in the portion of the thermal image of interest, and a second isotherm located on a second side of the linear extension opposite to the first side, wherein for any time within the printing sub-period, extracting distance information between the two isotherms corresponding to the time as the actual deposition width of the material at the time includes: dividing the region between the two isotherms into a first region portion located on the first side of the linear extension portion and a second region portion located on the second side of the linear extension portion; For any time within the printing sub-period, the first distance information corresponding to the time between the first isotherm and the linear extension is extracted from the first area portion as the first deposition width, and the second distance information corresponding to the time between the second isotherm and the linear extension is extracted from the second area portion as the second deposition width, and the sum of the first deposition width and the second deposition width is calculated as the actual deposition width of the material at that time.

7. The method according to claim 1, wherein The sub-printing period starts from a first starting time point Δt0 and ends at a first ending time point Δt1 which is the capturing time point, and the associated compensation period starts from a second starting time point before the first starting time point. and ends at a second end time point after the first end time point Determining the compensation relationship includes: The relationship between the deposition inaccuracy rate of the material and time in the printing sub-period ΔE(t sub ): ΔE(t sub )=K e Δw(t sub ), Among them, t sub ∈[Δt0,Δt1],K e represents the specified deposition correction gain, Δw(t sub ) represents a third relationship between a deposition width error of the material and time within the printing sub-period; The relationship between the output compensation volume of the material output from the nozzle of the print head and time ΔE is determined according to the following formula: r (t sub ): Where τ is the specified time constant; Specify multiple discrete control time points Δt within the associated compensation period i , where i∈[0,n], n is an integer greater than 1, for each control time point Δt i , the corresponding compensated feed speed of the material input to the print head is expressed as ΔV i , each control time point Δt i and its corresponding compensation feed speed ΔV i Represented as P i , that is, P i ={Δt i , ΔV i } T , and the compensation relationship is calculated based on the following formula s.t.ΔV min ≤V i ≤ΔV max , in, N i (Δt) is the basis function, is the filtered basis function, by using G(s) to N i (Δt) is filtered, G(s) is a transfer function representing the relationship between the volume of the material input to the print head and the volume of the material output from the nozzle of the print head, represents a relationship between a desired output compensation rate of material output from the nozzles of the print head during the associated compensation period and time, Δv e (Δt) represents the relationship between the ideal output compensation speed of the material output from the nozzle of the print head during the associated compensation period and time, and ΔE r (t sub ) has a linear relationship, and ΔE r (t sub ) is determined based on the linear relationship, ΔV min and ΔV max Represents ΔV i The minimum and maximum allowed values.

8. The method according to claim 7, wherein: K e Depends on the temperature indicated by the corner point in the thermal image portion of interest.

9. The method according to claim 7, wherein: The first starting time point Δt0 and the second starting time point The time interval between the first end time point Δt1 and the second end time point The time interval between.

10. The method according to claim 7, wherein: The plurality of discrete control time points are spaced apart at fixed time intervals.

11. The method according to any one of claims 1 to 10, further comprising: Before printing the material layer, a pre-processing process is performed, the pre-processing process comprising: identifying whether the printing period includes the following smoothing-required time span: each printing time point within a single smoothing-required time span is evaluated as not satisfying an elongated deposition condition, that is, for each printing time point within the single smoothing-required time span, a corresponding position of the nozzle of the print head along the predetermined movement trajectory is evaluated as being unable to deposit material along a normal direction of the predetermined movement trajectory within a working plane defined by the working platform, the evaluation being based on a predetermined curvature of the predetermined movement trajectory at the printing time point, a moving speed of the print head at the printing time point, and an output volume of material outputted from the nozzle of the print head at the printing time point; If the recognition result is positive, a smoothing process is performed for each identified time span to be smoothed, the smoothing process comprising: For each printing time point within the time span to be smoothed: specifying an effective curvature for the printing time point, determining an additional curvature at the printing time point based on the specified effective curvature, and calculating an additional rotation angle corresponding to the additional curvature at the printing time point, wherein the effective curvature specified for the printing time point is a maximum allowable curvature value that satisfies the elongated deposition condition at the printing time point assuming that the predetermined curvature of the predetermined movement trajectory at the printing time point is replaced by the specified effective curvature; Determine the sum of the additional rotation angles calculated for each printing time point within the time span to be smoothed as the additional rotation angle to be allocated; Allocating the additional rotation angle to be allocated to a plurality of future sampling time points after the end time point of the time span to be smoothed and a plurality of past sampling time points before the start time point of the time span to be smoothed, wherein the plurality of future sampling time points are obtained at fixed sampling intervals from the end time point, and the plurality of past sampling time points are obtained at fixed sampling intervals from the start time point, wherein the allocation is such that the additional rotation angle allocated to each sampling time point has the same sign as the additional rotation angle to be allocated, wherein, for each of the plurality of future sampling time points and the plurality of past sampling time points, an effective curvature at the sampling time point is determined based on an additional rotation angle assigned to the sampling time point, For any printing time point within the identified time span requiring smoothing, its effective curvature is the specified effective curvature; for any printing time point outside the identified time span requiring smoothing and not used as a sampling time point, the predetermined curvature of the predetermined movement trajectory at that point is its effective curvature. According to the second relationship between the ideal deposition width of the material and time during the printing period, for any printing time point t during the printing period, the ideal deposition width of the material at that time is expressed as 2w d (t), where: φ eff (t)=κ eff (t)v(t)T s , Wherein, w0(t) represents the theoretical deposition width at the position of the nozzle of the print head along the predetermined movement trajectory at the printing time point t, assuming that the material is deposited along the normal direction of the predetermined movement trajectory within the working plane defined by the working platform, φ eff (t) is the effective rotation angle of the predetermined moving trajectory at the printing time point t, κ eff (t) is the effective curvature of the predetermined movement trajectory at the printing time point t, v(t) represents the movement speed of the nozzle of the print head at the printing time point t, x(t) and y(t) are functions representing the predetermined movement trajectory with time as a variable, T s represents the sampling interval.

12. The method according to claim 11, wherein the material layer has a constant height h, and for any printing time point t within the printing period, when it does not satisfy the following formula, it is evaluated as not satisfying the elongated deposition condition: in, κ(t) represents the predetermined curvature of the predetermined movement trajectory at the printing time point t, E(t) represents the output volume of the material output from the nozzle of the print head at the printing time point t, in, 13. The method according to claim 12, wherein: For any printing time point t within a single time span to be smoothed s , for which the effective curvature is specified as κ eff (t s ), the additional curvature calculated is κ φ (t s ),have: The additional rotation angle to be allocated is expressed as ΔΦ, which is: Among them, t v Indicates the printing time point t s The time period corresponding to the time span to be smoothed.

14. The method according to claim 13, wherein The sum of the additional rotation angles allocated to the multiple future sampling time points is equal to half of the additional rotation angle to be allocated, and the sum of the additional rotation angles allocated to the multiple past sampling time points is equal to half of the additional rotation angle to be allocated.

15. The method according to claim 14, wherein The multiple future sampling time points include N f future sampling time points, t f，j =t v，1 +jT s , The additional rotation angle assigned to each future sampling time point is determined based on the following equation: f f (t f，j+1 )=φ f (t f，j )-dφ f (t f，j ), dφ f (t f，j )=(κ(t f，j )+κ φ (t f，j ))v(t f，j )T s , Among them, t v，1 Indicates t v The end time point, N f is an integer greater than 1, j∈[1,N f ], t f Indicates the N f A set of future sampling time points, t f，j Denotes the set t f The jth element in Indicates that there is an assumption that there is a sampling time point later than Distance t v，1 Far T s A distant future The additional rotation angle φ assigned to the future distant point is f (t f，1 ) indicates the N f The sum of the additional rotation angles at future sampling time points, φ f (t f，j ) represents the time points to be allocated to the jth future sampling time point to the Nth future sampling time point f The sum of the additional rotation angles at future sampling time points, when φ f (t f，1 ) is positive, φ f (t f，j ) is positive and changes with the variable t f，j Monotonically decreasing, when φ f (t f，1 ) is negative, φ f (t f，j ) is negative and varies with the variable t f，j Monotonically increasing, dφ f (t f，j ) represents the time allocated to the future sampling point t f，j The additional rotation angle, κ(t f，j ) represents the predetermined moving trajectory at the future sampling time point t f，j The predetermined curvature at φ (t f，j ) represents the future sampling time point t f，j The additional curvature at represents the future sampling time point t f，j The maximum allowed value of the additional curvature at represents the future sampling time point t f，j The additional curvature candidate at v(t f，j ) represents the nozzle of the print head at the future sampling time point t f，j The moving speed at the location, E(t f，j ) represents the future sampling time point t f，j The output volume of material output from the nozzle of the print head.

16. The method according to claim 14, wherein The plurality of past sampling time points include N p past sampling time points, t p，k =t v，0 -kT s , The additional rotation angle assigned to each past sampling time point is determined based on the following formula: f p (t p，k+1 )=φ p (t p，k )-dφ p (t p，k ), dφ p (t p，k )=(k(t p，k )+k φ (t p，k ))v(t p，k )T s , Among them, t v，0 Indicates t v The starting time point, N p is an integer greater than 1, k∈[1,N p ], t p Indicates the N p A set of past sampling time points, t p，k Denotes the set t p The kth element in Indicates that there is an assumption that there is a sampling time point in the past Distance t v，0 Far T s A distant point in the past The additional rotation angle φ assigned to the past distant point in the case p (t p，1 ) indicates the N p The sum of the additional rotation angles at past sampling time points, φ p (t p，k ) represents the time points to be assigned to the kth past sampling time point to the Nth past sampling time point p The sum of the additional rotation angles of the past sampling time points, when φ p (t p，1 ) is positive, φ p (t p，k ) is positive and changes with the variable t p，k Monotonically decreasing, when φ p (t p，1 ) is negative, φ p (t p，k ) is negative and varies with the variable t p，k Monotonically increasing, dφ p (t p，k ) represents the time allocated to the past sampling point t p，k The additional rotation angle, k(t p，k ) represents the predetermined movement trajectory at the past sampling time point t p，k The predetermined curvature at φ (t p，k ) represents the past sampling time point t p，k The additional curvature at represents the past sampling time point t p，k The maximum allowed value of the additional curvature at represents the past sampling time point t p，k The additional curvature candidate at v(t p，k ) represents the nozzle of the print head at the past sampling time point t p，k The moving speed at the location, E(t p，k ) represents the sampling time point t in the past p，k The output volume of material output from the nozzle of the print head.

17. The method according to claim 11, wherein For each identified time span to be smoothed, a previous printing time point adjacent to its start time point and before the start time point and a subsequent printing time point adjacent to its end time point and after the end time point meet the elongated deposition condition.

18. A system for additive manufacturing, comprising a processor configured to execute computer instructions to cause the method according to any one of claims 1 to 17 to be performed.

19. A computer device comprising a memory and a processor, the memory having computer instructions stored thereon, the computer instructions causing the method according to any one of claims 1 to 17 to be performed when executed by the processor.

20. A non-transitory computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, cause the method according to any one of claims 1 to 17 to be performed.

21. A computer program product comprising computer instructions which, when executed by a processor, cause the method according to any one of claims 1 to 17 to be performed.

Images