A method for accurately reconstructing the surface morphology of the molten pool during scanning laser machining and its application

Abstract

A method for accurately reconstructing the surface morphology of a molten pool during a scanning laser processing process belongs to the technical field of methods for reconstructing the surface morphology of a molten pool. The method aims to solve the problem of difficulty in reconstructing the morphology of a molten pool under complex laser processing conditions. The present invention establishes a molten pool image acquisition device; sets the frame rate of the molten pool image acquisition device and the scanning parameters of the laser, turns on the device for scanning laser processing, and acquires the molten pool image of the laser spot position during the scanning laser processing process; performs image processing on the acquired molten pool image of the laser spot position according to a time series; uses the molten pool image of the laser spot position after image processing to locate the laser spot position, and extracts the coordinates of the center of the laser spot at each moment; reconstructs the morphology of the scanning laser irradiation area of ​​the molten pool surface based on the extracted center coordinates of the laser spot, and completes the local laser spot path fitting and the reconstruction of the molten pool surface morphology of the entire deposition path. The present invention is used for reconstructing the surface morphology of a molten pool during a scanning laser processing process.

Description

Technical Field

[0001] The present invention belongs to the technical field of material processing, and in particular relates to a method for accurately reconstructing the surface topography of a molten pool in a scanning laser processing process and an application thereof. Background Art

[0002] In the field of laser processing, ensuring a stable and controllable processing process requires obtaining the surface morphology of the molten pool during the laser processing process, and combining it with appropriate control strategies to form closed-loop control and achieve automation. However, factors such as high temperature, smoke, high-speed laser motion, and random jitter make accurate monitoring of the laser molten pool challenging. Obtaining more accurate molten pool surface morphology information including height, concavity, and shape through three-dimensional reconstruction is crucial for real-time monitoring of the dynamic changes of the molten pool and evaluation of processing quality, which helps to optimize the processing technology and improve processing efficiency and quality. However, overcoming the instability of data acquisition caused by smoke interference and violent fluctuations in the molten pool, and ensuring the accuracy and stability of three-dimensional morphology reconstruction, is one of the current difficulties.

[0003] Currently, the following methods are used to reconstruct the morphology of the melt pool:

[0004] 1) Active vision-based structured light method: An imaging screen is used to collect a surface dot array of laser light reflected from the melt pool surface, and a dedicated algorithm is designed to convert it into the three-dimensional topography of the melt pool surface. The problems with this method are: ① It requires a relatively quiet melt pool, meaning that there cannot be significant fluctuations, otherwise the melt pool mirror surface is destroyed and the surface dot array of laser light spots obtained by the imaging screen is incomplete, thus limiting its main application to TIG welding; ② The active vision method has poor transferability; and ③ The relative position of the structured light and the camera must be strictly accurate.

[0005] 2) Shape recovery from shadows: This method uses shadow clues in a single image to recover the relative heights or surface normals of each point on the surface, thereby obtaining the three-dimensional shape of the molten pool. The problems with this method are: ① When the algorithm was first designed, the point light source was required to be infinitely far away from the object being measured. Therefore, when it is applied to molten pool shape recovery, there are algorithm errors. When the welding environment changes, the adaptive adjustment of the algorithm is large; ② Actual reflections are diverse, and it is difficult to determine a suitable reflection model; ③ Since it also relies on transmitting light to the molten pool and then processing the collected reflected light, it has high requirements for the flatness of the molten pool, and its main application areas are also limited.

[0006] 3) Binocular stereo vision method: Using two cameras or dual optical paths to simulate the welder's eyes, the three-dimensional shape of the weld and molten pool is estimated and then restored. The problems with this method are: ① The two cameras collect data simultaneously, making data alignment difficult. Even if the camera models are the same, there are triggering and storage delays, making it difficult to ensure that the binocular vision captures information about the molten pool at the same moment; ② Binocular vision has high hardware requirements. This is due to the large amount of image information and the large number of features, and the real-time performance is also deteriorated.

[0007] Scanning laser head equipment offers exceptional flexibility, high efficiency, and a compact structure. Leveraging its technological advantages, it has rapidly gained widespread adoption in laser processing lines. However, due to the highly dynamic nature of the processing process and significant melt pool fluctuations, complex interference conditions present a pressing challenge in laser processing applications: establishing an accurate, real-time scanning laser melt pool surface topography reconstruction model. Summary of the Invention

[0008] The problem to be solved by the present invention is the difficulty in reconstructing the morphology of the molten pool under complex laser processing conditions. A method for accurately reconstructing the surface morphology of the molten pool during scanning laser processing and its application are proposed.

[0009] To achieve the above object, the present invention is implemented through the following technical solutions:

[0010] A method for accurately reconstructing the surface topography of a molten pool during scanning laser machining comprises the following steps:

[0011] S1. Establish a molten pool image acquisition device;

[0012] S2. Setting the frame rate of the molten pool image acquisition device and the laser scanning parameters, starting the device for scanning laser processing, and acquiring the molten pool image at the laser spot position during the scanning laser processing process;

[0013] S3, performing image processing on the molten pool image at the laser spot position acquired in step S2 according to a time series;

[0014] S4, using the molten pool image of the laser spot position after image processing in step S3 to locate the laser spot position, and extracting the coordinates of the laser spot center at each moment;

[0015] S5. Reconstruct the morphology of the molten pool surface scanning laser irradiation area based on the center coordinates of the laser spot extracted in step S4, and complete the local laser spot path fitting and the reconstruction of the molten pool surface morphology of the entire deposition channel.

[0016] Furthermore, the molten pool image acquisition device of step S1 includes an additive substrate or welding base material, a formed part of an additive part or welding part, an additive or welding molten pool, a scanning laser beam acting on the molten pool, a CCD camera, and a solidification deposition path profile acquisition device. The formed part of the additive part or welding part is generated on the upper surface of the additive substrate or welding base material, the solidification deposition path profile acquisition device is arranged above the solidification deposition path of the formed part of the additive part or welding part, the CCD camera is arranged in a position facing the laser, and is used to shoot the dynamic laser spot in the molten pool, and the scanning laser beam acting on the molten pool is arranged vertically above the additive or welding molten pool.

[0017] Furthermore, the specific implementation method of step S2 includes the following steps:

[0018] S2.1. Set the laser scanning frequency to 10-300 Hz, the scanning amplitude to 1-5 mm, and the scanning pattern to one of the following: circular, linear, figure-8, and horizontal figure-8;

[0019] S2.2. Adjust the CCD camera field of view and light intensity until the laser spot is clearly visible in the center of the field of view. Then set the CCD camera frame rate to 6 to 100 times the scanning frequency to collect time series images of the additive process.

[0020] Furthermore, the specific implementation method of step S3 includes the following steps:

[0021] S3.1. Crop the region of interest (ROI) in the molten pool image at the laser spot position;

[0022] S3.2, thresholding, convolution filtering, and Laplace transform are performed on the region of interest (ROI) in the molten pool image at the laser spot position;

[0023] S3.3. Based on structured light triangulation or phase profilometry, the coordinate information of the region of interest (ROI) in the molten pool image of the laser spot position is converted into actual width and height.

[0024] Furthermore, the specific implementation method of performing object recognition and center pixel coordinate extraction on the laser spot in the molten pool in step S4 includes the following steps:

[0025] S4.1. Frame the light spot, melt pool reflection, and laser plume in the melt pool image sequence after image processing in step S3, and record the pixel coordinates, width, and height of the corresponding frame starting point;

[0026] S4.2. Preprocess the raw data by random cropping, random scaling, and random splicing of images;

[0027] S4.3. Select the YOLO V5 model for object recognition. Set the network layer width and depth to the default values ​​of 0.50-0.70 and 0.20-0.55 respectively. Do not adjust the attention mechanism.

[0028] S4.4. Tune the YOLO V5 model hyperparameters, with batch size of 4-128, learning rate of 0.01-0.6, and iterations of 2000-8000.

[0029] S4.5, perform YOLO V5 model training;

[0030] S4.6. Use the best-trained YOLO V5 model to predict and identify the laser spot position. Read the corner coordinates, width, and height of the target box and convert them to the coordinates of the laser spot center.

[0031] Furthermore, the specific implementation method of step S5 includes performing local path fitting on the coordinates of the laser spot trajectory points in the molten pool obtained in step S4, and modeling the entire deposition path morphology of the laser irradiation area on the surface of the molten pool; the method for fitting the laser spot path in the molten pool is the least squares method, and the method for reconstructing the surface morphology of the molten pool is three-dimensional point cloud surface reconstruction; the specific implementation method of step S5 includes the following steps:

[0032] S5.1. Select the coordinates of the center trajectory of the laser spot with a motion cycle length of 1 to 5 laser spots;

[0033] S5.2. According to the molten pool morphology, the fitting curve model is selected as the cylindrical curve model;

[0034] S5.3. The error is equal to the distance from the data point to the fitting curve, that is, the fitting curve error function is defined as where h i is a point on the fitting curve, j i is the actual data point;

[0035] S5.4, use gradient descent method to iteratively obtain Then, the equation of the approximation curve is fitted to obtain the fitting path of the laser spot in the molten pool within 1 to 5 cycles, that is, the molten pool fitting equation of this period;

[0036] S5.5. Select the coordinates of the center trajectory points of the spot during the entire scanning laser processing process, perform point cloud acquisition, filtering, and surface reconstruction, and visualize the isosurface to obtain the three-dimensional shape of the entire sedimentary layer.

[0037] Furthermore, step S3.2 uses image filtering, image segmentation, image transformation and image enhancement operations to process the molten pool image at the laser spot position.

[0038] Furthermore, step S4.3 uses the permutation, combination, fusion and cascade of manual annotation, YOLO series, RCNN, Faster R-CNN, Mask R-CNN, FPN, RetinaNet, SSD, EfficientDet and other algorithms to locate the molten pool image of the laser spot position and extract the coordinates of the laser spot center at each moment.

[0039] The invention discloses an application of a method for accurately reconstructing the surface topography of a molten pool during a scanning laser processing process, which is realized by relying on the method for accurately reconstructing the surface topography of a molten pool during a scanning laser processing process, and is used for molten pool modeling of welding, molten pool modeling of wire-feed additive manufacturing, and molten pool modeling of powder-feed additive manufacturing.

[0040] Beneficial effects of the present invention:

[0041] The present invention provides a method for accurately reconstructing the surface topography of a molten pool during scanning laser machining, which monitors the molten pool, achieves hysteresis-free detection, and avoids long time delays.

[0042] The present invention provides a method for accurately reconstructing the surface topography of a molten pool during a scanning laser machining process. Reconstructing the topography of the molten pool surface in the area irradiated by the scanning laser only requires high-speed video of the keyhole, without the need for other equipment.

[0043] The present invention describes a method for accurately reconstructing the surface morphology of a molten pool during a scanning laser processing process. Through a molten pool image acquisition device and the method described herein, multiple keyhole features can be extracted, including keyhole opening size, opening roundness, and keyhole light intensity, thereby accurately constructing the surface morphology of the molten pool during a scanning laser processing process. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 Schematic diagram of the structure of the molten pool image acquisition device of the present invention;

[0045] Figure 2 This is a flow chart of a method for accurately reconstructing the surface topography of a molten pool during a scanning laser machining process according to the present invention. DETAILED DESCRIPTION

[0046] In order to make the objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only intended to explain the present invention and are not intended to limit the present invention. That is, the specific embodiments described herein are only some embodiments of the present invention, not all embodiments. Generally, the components of the specific embodiments of the present invention described and illustrated in the drawings herein can be arranged and designed in various different configurations, and the present invention can also have other embodiments.

[0047] Therefore, the following detailed description of the specific embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but is merely representative of selected specific embodiments of the present invention. All other specific embodiments obtained by those skilled in the art based on the specific embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0048] In order to further understand the content, features and effects of the present invention, the following specific embodiments are given as examples, and the attached Figure 1 -Attached Figure 2 The detailed instructions are as follows: Specific implementation method one:

[0050] A method for accurately reconstructing the surface topography of a molten pool during scanning laser machining comprises the following steps:

[0051] S1. Establish a molten pool image acquisition device;

[0052] Furthermore, the molten pool image acquisition device of step S1 includes an additive substrate or welding parent material 1, an additive part or welded part formed portion 2, an additive or welded molten pool 3, a scanning laser beam 4 acting on the molten pool, a CCD camera 5, and a solidification deposition path profile acquisition device 6. The additive part or welded part formed portion 2 is generated on the upper surface of the additive substrate or welded parent material 1. The solidification deposition path profile acquisition device 6 is arranged above the solidification deposition path of the additive part or welded part formed portion 2. The CCD camera 5 is arranged in a position facing the laser to capture the dynamic laser spot in the molten pool. The scanning laser beam 4 acting on the molten pool is arranged vertically above the additive or welded molten pool 3.

[0053] S2. Setting the frame rate of the molten pool image acquisition device and the laser scanning parameters, starting the device for scanning laser processing, and acquiring the molten pool image at the laser spot position during the scanning laser processing process;

[0054] Furthermore, the specific implementation method of step S2 includes the following steps:

[0055] S2.1. Set the laser scanning frequency to 10-300 Hz, the scanning amplitude to 1-5 mm, and the scanning pattern to one of the following: circular, linear, figure-8, and horizontal figure-8;

[0056] S2.2. Adjust the field of view and light intensity of CCD camera 5 until the laser spot is clearly visible in the center of the field of view. Then, set the frame rate of CCD camera 5 to 6 to 100 times the scanning frequency to capture time series images of the additive process.

[0057] S3, performing image processing on the molten pool image at the laser spot position acquired in step S2 according to a time series;

[0058] Furthermore, the specific implementation method of step S3 includes the following steps:

[0059] S3.1. Crop the region of interest (ROI) in the molten pool image at the laser spot position;

[0060] S3.2, thresholding, convolution filtering, and Laplace transform are performed on the region of interest (ROI) in the molten pool image at the laser spot position;

[0061] S3.3. Convert the coordinate information of the region of interest (ROI) in the molten pool image at the laser spot position into actual width and height based on structured light triangulation or phase profilometry;

[0062] S4, using the molten pool image of the laser spot position after image processing in step S3 to locate the laser spot position, and extracting the coordinates of the laser spot center at each moment;

[0063] Furthermore, the specific implementation method of performing object recognition and center pixel coordinate extraction on the laser spot in the molten pool in step S4 includes the following steps:

[0064] S4.1. Frame the light spot, melt pool reflection, and laser plume in the melt pool image sequence after image processing in step S3, and record the pixel coordinates, width, and height of the corresponding frame starting point;

[0065] S4.2. Preprocess the raw data by random cropping, random scaling, and random splicing of images;

[0066] S4.3. Select the YOLO V5 model for object recognition. Set the network layer width and depth to the default values ​​of 0.50-0.70 and 0.20-0.55 respectively. Do not adjust the attention mechanism.

[0067] S4.4. Tune the YOLO V5 model hyperparameters, with batch size of 4-128, learning rate of 0.01-0.6, and iterations of 2000-8000.

[0068] S4.5, perform YOLO V5 model training;

[0069] S4.6. Use the best-trained YOLO V5 model to predict and identify the laser spot position. Read the corner coordinates, width, and height of the target box and convert them to the coordinates of the laser spot center.

[0070] S5, reconstructing the morphology of the molten pool surface scanning laser irradiation area based on the center coordinates of the laser spot extracted in step S4, completing the local laser spot path fitting and the reconstruction of the molten pool surface morphology of the entire deposition track;

[0071] Furthermore, the specific implementation method of step S5 includes performing local path fitting on the coordinates of the laser spot trajectory points in the molten pool obtained in step S4, and modeling the entire deposition path morphology of the laser irradiation area on the surface of the molten pool; the method for fitting the laser spot path in the molten pool is the least squares method, and the method for reconstructing the surface morphology of the molten pool is three-dimensional point cloud surface reconstruction; the specific implementation method of step S5 includes the following steps:

[0072] S5.1. Select the coordinates of the center trajectory of the laser spot with a motion cycle length of 1 to 5 laser spots;

[0073] S5.2. According to the molten pool morphology, the fitting curve model is selected as the cylindrical curve model;

[0074] S5.3. The error is equal to the distance from the data point to the fitting curve, that is, the fitting curve error function is defined as where h i is a point on the fitting curve, j i is the actual data point;

[0075] S5.4, use gradient descent method to iteratively obtain Then, the equation of the approximation curve is fitted to obtain the fitting path of the laser spot in the molten pool within 1 to 5 cycles, that is, the molten pool fitting equation of this period;

[0076] S5.5. Select the coordinates of the center trajectory points of the spot during the entire scanning laser processing process, perform point cloud acquisition, filtering, and surface reconstruction, and visualize the isosurface to obtain the three-dimensional shape of the entire sedimentary layer.

[0077] Furthermore, step S3.2 uses image filtering, image segmentation, image transformation and image enhancement operations to process the molten pool image at the laser spot position.

[0078] Furthermore, step S4.3 uses the permutation, combination, fusion and cascade of manual annotation, YOLO series, RCNN, Faster R-CNN, Mask R-CNN, FPN, RetinaNet, SSD, EfficientDet and other algorithms to locate the molten pool image of the laser spot position and extract the coordinates of the laser spot center at each moment. Specific implementation method two:

[0080] The application of a method for accurately reconstructing the surface morphology of a molten pool during a scanning laser processing process is based on the method for accurately reconstructing the surface morphology of a molten pool during a scanning laser processing process described in the first specific embodiment, and is used for molten pool modeling of welding, molten pool modeling of wire-feed additive manufacturing, and molten pool modeling of powder-feed additive manufacturing.

[0081] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus comprising the element.

[0082] Although the present application has been described above with reference to specific embodiments, various modifications may be made thereto and components may be substituted with equivalents without departing from the scope of the present application. In particular, as long as there are no structural conflicts, the various features of the embodiments disclosed herein may be combined with each other in any manner, and the omission of an exhaustive description of these combinations in this specification is solely for the sake of space and resource conservation. Therefore, the present application is not limited to the specific embodiments disclosed herein, but includes all technical solutions within the scope of the claims.

Claims

1. A method for accurately reconstructing the surface topography of a molten pool during scanning laser machining, characterized in that: The steps include: S1. Establish a molten pool image acquisition device; S2. Setting the frame rate of the molten pool image acquisition device and the laser scanning parameters, starting the device for scanning laser processing, and acquiring the molten pool image at the laser spot position during the scanning laser processing process; S3, performing image processing on the molten pool image at the laser spot position acquired in step S2 according to a time series; S4, using the molten pool image of the laser spot position after image processing in step S3 to locate the laser spot position, and extracting the coordinates of the laser spot center at each moment; S5, reconstructing the morphology of the molten pool surface scanning laser irradiation area based on the center coordinates of the laser spot extracted in step S4, completing the local laser spot path fitting and the reconstruction of the molten pool surface morphology of the entire deposition track; The specific implementation method of step S5 includes performing local path fitting on the coordinates of the laser spot trajectory points in the molten pool obtained in step S4, and modeling the entire deposition path morphology of the laser irradiation area on the surface of the molten pool; the method for fitting the laser spot path in the molten pool is the least squares method, and the method for reconstructing the surface morphology of the molten pool is three-dimensional point cloud surface reconstruction; the specific implementation method of step S5 includes the following steps: S5.

1. Select the coordinates of the center trajectory of the laser spot with a motion cycle length of 1 to 5 laser spots; S5.

2. According to the molten pool morphology, the fitting curve model is selected as the cylindrical curve model; S5.

3. The error is equal to the distance from the data point to the fitting curve, that is, the fitting curve error function is defined as where h i is a point on the fitting curve, j i is the actual data point; S5.4, use gradient descent method to iteratively obtain Then, the equation of the approximation curve is fitted to obtain the fitting path of the laser spot in the molten pool within 1 to 5 cycles, that is, the molten pool fitting equation; S5.

5. Select the coordinates of the center trajectory points of the spot during the entire scanning laser processing process, perform point cloud acquisition, filtering, and surface reconstruction, and visualize the isosurface to obtain the three-dimensional shape of the entire sedimentary layer.

2. The method for accurately reconstructing the surface topography of a molten pool during scanning laser processing according to claim 1, characterized in that: The molten pool image acquisition device of step S1 includes an additive substrate or welding parent material (1), a formed portion of an additive part or welding part (2), an additive or welding molten pool (3), a scanning laser beam (4) acting on the molten pool, a CCD camera (5), and a solidification deposition path profile acquisition device (6). The formed portion (2) of the additive part or welding part is generated on the upper surface of the additive substrate or welding parent material (1). The solidification deposition path profile acquisition device (6) is arranged above the solidification deposition path of the formed portion (2) of the additive part or welding part. The CCD camera (5) is arranged in a position facing the laser and is used to capture the dynamic laser spot in the molten pool. The scanning laser beam (4) acting on the molten pool is vertically arranged above the additive or welding molten pool (3).

3. The method for accurately reconstructing the surface topography of a molten pool during scanning laser machining according to claim 2, characterized in that: The specific implementation method of step S2 includes the following steps: S2.

1. Set the laser scanning frequency to 10-300 Hz, the scanning amplitude to 1-5 mm, and the scanning pattern to one of the following: circular, linear, figure-8, and horizontal figure-8; S2.

2. Adjust the field of view and light intensity of the CCD camera (5) until the laser spot is clearly displayed at the center of the field of view, and then set the frame rate of the CCD camera (5) to 6 to 100 times the scanning frequency to collect time series images of the additive process.

4. The method for accurately reconstructing the surface topography of a molten pool during scanning laser machining according to claim 3, characterized in that: The specific implementation method of step S3 includes the following steps: S3.

1. Crop the region of interest (ROI) in the molten pool image at the laser spot position; S3.2, thresholding, convolution filtering, and Laplace transform are performed on the region of interest (ROI) in the molten pool image at the laser spot position; S3.

3. Based on structured light triangulation or phase profilometry, the coordinate information of the region of interest (ROI) in the molten pool image of the laser spot position is converted into actual width and height.

5. The method for accurately reconstructing the surface topography of a molten pool during scanning laser processing according to claim 4, characterized in that: The specific implementation method of performing object recognition and center pixel coordinate extraction on the laser spot in the molten pool in step S4 includes the following steps: S4.

1. Frame the light spot, melt pool reflection, and laser plume in the melt pool image sequence after image processing in step S3, and record the pixel coordinates, width, and height of the corresponding frame starting point; S4.

2. Preprocess the raw data by random cropping, random scaling, and random splicing of images; S4.

3. Select the YOLO V5 model for object recognition. Set the network layer width and depth to the default values ​​of 0.50-0.70 and 0.20-0.55 respectively. Do not adjust the attention mechanism. S4.

4. Tune the YOLO V5 model hyperparameters, with batch size of 4-128, learning rate of 0.01-0.6, and iterations of 2000-8000. S4.5, perform YOLO V5 model training; S4.

6. Use the best-trained YOLO V5 model to predict and identify the laser spot position. Read the corner coordinates, width, and height of the target box and convert them to the coordinates of the laser spot center.

6. The method for accurately reconstructing the surface topography of a molten pool during scanning laser machining according to claim 4, characterized in that: Step S3.2 uses image filtering, image segmentation, image transformation and image enhancement operations to process the molten pool image at the laser spot position.

7. The method for accurately reconstructing the surface topography of a molten pool during scanning laser machining according to claim 5, characterized in that: In step S4.3, the permutation, combination, fusion, and cascade of manual annotation, YOLO series, RCNN, Faster R-CNN, Mask R-CNN, FPN, RetinaNet, SSD, and EfficientDet algorithms are used to locate the molten pool image of the laser spot position and extract the coordinates of the laser spot center at each moment.

8. An application of a method for accurately reconstructing the surface topography of a molten pool during scanning laser processing, which is realized by the method for accurately reconstructing the surface topography of a molten pool during scanning laser processing according to any one of claims 1 to 7, characterized in that: Used for weld pool modeling, wire-feed additive manufacturing melt pool modeling, and powder-feed additive manufacturing melt pool modeling.

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