Mathematical methods for tracks analysis and a system for melt pool dynamics in additive manufacturing

Abstract

The present invention relates to a comprehensive framework for real-time quality monitoring, control, and optimization in additive manufacturing (AM) processes, notably Laser Powder Bed Fusion (LPBF). The system combines high-speed imaging, sophisticated mathematical modeling, and machine learning techniques to analyze track geometric attributes and melt pool characteristics, including width, height, depth, wetting angles, and hatch spacing. Novel dimensionless wetting shape factors are introduced to characterize track profiles, and equations for acute and obtuse contact angles are derived, with additional exploration of the interplay between powder layer thickness and track dimensions through quadratic equations describing hyperbolic relationships.

Description

[0001] DESCRIPTION

[0002] MATHEMATICAL METHODS FOR TRACKS ANALYSIS AND A SYSTEM FOR MELT POOL DYNAMICS IN ADDITIVE MANUFACTURING Technical Field of the Invention

[0003] The present invention relates to an additive manufacturing (AM), focusing on developing in-situ melt pool and layer thickness and hatch spacing measurement devices, real-time quality monitoring, and adaptive control systems.

[0004] The present invention particularly relates to in AM and laser powder bed fusion (LPBF) processes, with potential extensions to related fields such as laser cladding and welding, enhancing precision and control over manufacturing quality.

[0005] State of the Art

[0006] Additive manufacturing (AM), or 3D printing technology, is fundamentally transforming production processes. This technology enables the production of complex geometries and customized products, while understanding melt pool dynamics and trace analysis is crucial for optimizing AM processes.

[0007] The melt pool is a key element in AM, directly affecting material properties and part quality. Proper control of melt pool dynamics facilitates better layer adhesion, reducing defects and enhancing mechanical properties.

[0008] Mathematical modeling plays a significant role in analyzing track geometry in AM. Current techniques often rely on simplified geometric models to estimate key parameters such as width, height and depth. Traditional approaches typically assume idealized shapes, such as perfect parabolas, which fail to capture the real-world complexities of track formation influenced by varying process parameters.

[0009] Trace analysis examines the traces of the energy source during the printing process, where mathematical models evaluate the effects of parameters such as speed, power, and material feed rate on trace geometry and surface quality.

[0010] Numerous studies have demonstrated the applicability of mathematical methods in predicting melt pool dynamics. For instance, researchers utilize Finite Element Analysis (FEA) to model the thermal behavior of different materials, yielding significant insights into optimal processing conditions. Numerical methods, including the Finite Element Method (FEM) and Computational Fluid Dynamics (CFD), have increasingly been used to model melt pool behavior. These simulations provide valuable insights into temperature distribution and solidification rates. However, their effectiveness is limited by computational demands and the necessity for precise boundary conditions that are not always achievable in practical settings.

[0011] Some researchers have begun applying statistical modeling techniques to explore relationships between process parameters and track characteristics. While these models can yield useful correlations, they often neglect the underlying physics that govern melt pool dynamics, resulting in less comprehensive insights.

[0012] One significant challenge in melt pool dynamics is the lack of in-situ measurement capabilities. Most existing systems rely on post-process evaluations, which do not capture the dynamic behavior of the melt pool during manufacturing. Advances in sensor technologies, such as high-speed imaging and thermal sensors, are essential for facilitating real-time monitoring.

[0013] In the state of the art, there is a need for a system that aims to an sophisticated system for track analysis, process control, and optimization in AM and enhance AM process optimization, improve part quality, and provide deeper insights into the fundamental physics of track formation in AM by leveraging cutting-edge mathematical-analytical modeling, sensor technologies, and control engineering principles.

[0014] As a result, due to the negativity described above and the inadequacy of existing solutions on the subject, it has become necessary to make a development in the relevant technical field.

[0015] Objects of the Invention

[0016] The present invention relates to an advanced track analysis and control system to enhance additive manufacturing processes through real-time monitoring, prediction, and optimization. Thus, it will overcome the limitations of existing quality control methods by integrating sophisticated mathematical models, advanced sensor technology and machine learning algorithms into the system.

[0017] Another object of the present invention is to enable provide a comprehensive mathematical framework that includes s incorporates acute and obtuse contact angles by explaining the complex relationships between the track parameters. This framework aims to increase the predictive capabilities of the system by providing dimensionless wetting shape factors while providing detailed characterization of the track profiles. Thus, it provides a deeper understanding by examining the interactions between the powder layer thickness, laser energy absorption and track dimensions with hyperbolic modeling.

[0018] Another object of the present invention is to enable develop an integrated control system that combines a mathematical foundation with state-of-the-art sensor technology and machine learning. Thus, real-time data on track formation is collected using high-resolution cameras and advanced imaging systems, while thermal sensors enable monitoring of temperature gradients and material phase transitions.

[0019] Another object of the present invention is to enable simulate and account for realistic additive manufacturing conditions. Thus, the control algorithm predictions and control decisions closely reflect the actual behavior of materials during the manufacturing process.

[0020] Another object of the present invention is to enable the deep learning component of the system, a convolutional neural network, predicts track characteristics based on input parameters and real-time sensor data, enabling proactive adjustments to process parameters.

[0021] Another object of the present invention is to enable the volumetric changes and surface tension effects affecting the track geometry by incorporating the interface energy balance and phase change dynamics factors of the system into the predictive models. Another object of the present invention is to enable provide an advanced track analysis and control system that enhances additive manufacturing technology. It features an intuitive user interface for engineers to specify desired part characteristics and material specifications, while the control algorithm autonomously optimizes process parameters such as laser power, scan speed, and powder feed rate throughout manufacturing. Another object of the present invention is to enable improve part quality, reduce defects, and expand the range of feasible materials and geometries. Thus, real-time sensing, and adaptive machine learning, the invention addresses critical challenges in track control and quality assurance, making it a transformative solution for various industries, including aerospace and medical device manufacturing.

[0022] Description of the Figures

[0023] Figure 1 illustrates track analysis and control system.

[0024] Figure 2 powder layer and track properties: acute wetting angle 0 < 90°

[0025] Figure 3 powder layer and track properties: obtuse wetting angle 0 > 90°

[0026] Figure 4 tracks used to measure the relationship between the normalized enthalpy and depth.

[0027] Figure 5 Fitted circles, wetting angles, and parabolas for acute and obtuse angles Reference Numerals:

[0028] 1 : Acoustic sensors

[0029] 2: Photonic sensors

[0030] 3: X-ray measurement system

[0031] 4: Laser energy absorption sensors

[0032] 5: Device chamber

[0033] 6: Denudation zone

[0034] 7: Track width

[0035] 8: Track reinforcement area

[0036] 9: Track penetration area

[0037] 10: Build plate

[0038] 11: Contact or wetting angle

[0039] 12: Track depth

[0040] 13: Track height

[0041] 14: Powder layer thickness

[0042] 15: Gas flow 16: Scanning direction

[0043] 17: Spot size

[0044] 18: Image Analysis

[0045] 19: Real-time analysis

[0046] 20: Algorithms

[0047] 21: Computer Equipment

[0048] Description of the Invention

[0049] The present invention relates to an advanced track analysis and control system to enhance additive manufacturing processes through real-time monitoring, prediction, and optimization. By integrating sophisticated mathematical models, sensor technology, and machine learning algorithms (20), this system overcomes the limitations of traditional quality control methods, ensuring precision and reliability. The present invention is a comprehensive mathematical framework designed to elucidate the complex relationships between key track parameters such as track width (7), track height (13), track depth (12), hatch space, and wetting angles. This framework incorporates acute and obtuse contact angles and introduces novel dimensionless wetting shape factors that detail track profiles. These shape factors are represented as:

[0050] <

[0051]

[0052] The area of a track segment can be computed using these shape factors with the following equation:

[0053]

[0054] <

[0055] These equations establish the relationship between powder layer thickness (14), track dimensions, and laser energy absorption, predicting how laser parameters influence track profiles. For example, the contact angle theta (0) is expressed as:

[0056]

[0057] Furthermore, the absorptivity of the material depends on its properties and laser parameters, scaling with both the normalized enthalpy and track depth (12). The equation governs the quadratic relationship between powder layer thickness (14) and track width (7) (W):

[0058] >

[0059]

[0060] The following equation represents the steady-state hatch (Ks««), which is highly reliable and accurate:

[0061]

[0062] This method is based on the steady-state height and does not depend on depth, which can be erroneous due to insufficient parabola fitting over the depth. This model predicts a hatch spacing of 0.71 times the width in most cases, indicating that the maximum hatch spacing should be 0.71 of the width to achieve complete penetration and ensure a fully dense structure.

[0063] The mathematical models presented form the backbone of the system's predictive capabilities, enabling precise control over additive manufacturing processes and improving overall efficiency and quality.

[0064] The control system integrates this mathematical foundation with state-of-the-art sensor technology and machine learning. High-resolution cameras and advanced imaging systems capture real-time data on track formation, while thermal sensors monitor temperature gradients and material phase transitions. A sophisticated deep learning network processes this multi-modal data stream, which performs edge detection and boundary point analysis to accurately determine and track geometrical aspects in liquid or solid phases and wetting characteristics.

[0065] The present invention is to simulate and account for realistic additive manufacturing conditions. The control algorithm addresses material interactions, such as the adsorption of molten material components on the substrate surface and mass transfer effects between different phases. This holistic approach ensures that predictions and control decisions closely reflect the actual behavior of materials during the manufacturing process.

[0066] The present invention incorporates these factors into its predictive models to anticipate and compensate for volumetric changes and surface tension effects that influence track geometry. The control algorithm autonomously determines and adjusts optimal process parameters throughout the manufacturing process, such as laser power, scan speed, and powder feed rate.

[0067] This advanced track analysis and control system represents a significant advancement in additive manufacturing technology. It promises to dramatically improve part quality, reduce defects, and expand the range of materials and geometries feasible for additive manufacturing. By combining advanced mathematical-analytical modeling, real-time sensing, and adaptive machine learning, the invention addresses the challenges of track control and quality assurance, making it a transformative solution for industries ranging from aerospace to medical device manufacturing.

[0068] The present invention is an advanced track analysis and control system for additive manufacturing, welding, and cladding and includes material pretreatment equipment, process analysis equipment, track formation equipment and computer equipment (21) with deep learning capabilities. Computer equipment (21) that a database in which all process data is recorded.

[0069] The material pretreatment equipment simulates using powders of different sizes and properties to replicate the material's behavior in dense configurations.

[0070] The process analysis equipment includes sensors for real-time material characterization, such as acoustic sensors (1) for material density and viscosity, photonic sensors for chemical composition analysis, X-ray measurement systems (3) for crystal structure and elemental composition, and laser energy absorption sensors (4) for normalized enthalpy measurement.

[0071] The track formation equipment forms track on a substrate under controlled conditions and includes a temperature-controlled device chamber (5), high-resolution imaging devices for capturing track geometry, and sensors for measuring powder layer thickness (14), liquid layer thickness, and solidified track dimensions. Device chamber (5) that the controlled environment where the additive manufacturing process occurs. The computer equipment (21) analyzes track characteristics using deep learning methods, performing edge detection, training convolutional neural networks with boundary points, selecting target boundary points based on prediction errors, and calculating derivatives to determine track characteristics, including wetting angles. Analyses track features using deep learning methods with computer equipment (21), performs edge detection on track images to obtain an edge map, trains a convolutional neural network using a preset number of boundary points to create a predictive model, selects target boundary points based on the difference between predicted and actual coordinates, calculates derivatives at target boundary points to determine track characteristics including contact angles for powder, liquid and solidified material interfaces, volume of solidified material track, powder consumption and powder area. The present invention features a deep learning convolutional neural network trained on a diverse dataset of track formations under various conditions. This network predicts track characteristics based on input parameters and real-time sensor data, enabling proactive adjustments to process parameters. The system also includes an adaptive feedback control mechanism loop that continuously refines its predictive models based on observed outcomes, improving accuracy and responsiveness over time.

[0072] The present invention includes feedback control mechanism. The feedback control mechanism that includes continuously monitoring track formation parameters, compares measured track characteristics with desired outcomes, adjusts process parameters in real-time to optimize track formation, including laser power, scan speed, powder feed rate, substrate temperature, and inert gas flow (15) rate.

[0073] The feedback control mechanism method comprises the process steps of:

[0074] • Continuously monitoring track formation parameters,

[0075] • Comparing measured track characteristics with desired outcomes by deep learning

[0076] • Adjust process parameters in real-time to optimize track formation, including laser power, scan speed, powder feed rate, substrate temperature, and inert gas flow (15) rate. The system also includes an adaptive feedback loop that continuously refines its predictive models based on observed outcomes, improving accuracy and responsiveness over time.

[0077] The process monitoring equipment, CCD camera, allows capturing high-resolution images of the process and the laser system (16) provides energy to melt the powder with controllable scanning direction (16) and spot size (17).

[0078] The operational process and analysis method of the analysis and control system comprise the process steps of:

[0079] • Powder depositing of a layer of power with a thickness (14) on the build plate (10),

[0080] • Creating a melt pool by scanning the powder bed and a laser by realization of laser melting,

[0081] • Realization of track formation,

[0082] • Real-time analysis (19) with data collected through sensors, • Realization of deep learning analysis with deep learning algorithms (20),

[0083] • Realization of adaptive control with laser results,

[0084] • Display of real-time visualizations of process parameters and quality measurements in the user interface,

[0085] • Recording all process data in the database.

[0086] By scanning the powder bed and performing laser melting to form the melt pool, the basic parameters of laser scanning direction (16), laser spot size (17) and gas flow (15) for melt pool protection.

[0087] Realization of track formation, which is one of the operational process and analysis method process steps of the analysis and control system, includes the following process steps of:

[0088] • Measuring the track width (7) with track formation equipment,

[0089] • Analysing the track reinforcement area (8) on top of the powder bed with deep learning, • Assessing the track penetration area (9) into the previous layers with deep learning,

[0090] • Calculating the contact or wetting angle (11 ) with deep learning,

[0091] • Measuring the track depth (12) and track height (13),

[0092] Real-time analysis (19) with data collected through sensors, which is one of the operational process and analysis method process steps of the analysis and control system, includes the following process steps of:

[0093] • Monitoring of the denudation zone (6) around the melt pool with deep learning, • Sensors continuously collect data on material properties and process conditions,

[0094] • Capturing and processing high-resolution images in real time with CCD camera.

[0095] Denudation zone (6) is the area around the melt pool where powder particles are displaced due to vapor-driven flow.

[0096] Realization of deep learning analysis with deep learning algorithms (20), which is one of the operational process and analysis method process steps of the analysis and control system, includes the following process steps of:

[0097] • Obtaining high-resolution images with CCD camera of tracks formed on a substrate,

[0098] • Preprocessing the images with deep learning to reduce noise and apply Gaussian smoothing,

[0099] • Performing edge detection using a deep learning method to obtain an edge map,

[0100] • Training a deep learning convolutional neural network with deep learning a preset number of boundary points,

[0101] • Selecting target boundary points based on prediction errors with deep learning, • Determining track characteristics based on the derivatives at target boundary points with deep learning,

[0102] • Measuring laser energy absorption, powder layer thickness (14), liquid layer thickness, and solidified track dimensions, • Calculating the volume of solidified material track and powder consumption with deep learning and determining the relationship between track and powder areas.

Claims

CLAIMS1. An advanced track analysis and control system for additive manufacturing, welding, and cladding, characterized by comprising:• Material pretreatment equipment that simulates using powders of different sizes and properties to replicate the material's behavior in dense configurations,• Process analysis equipment that includes sensors for real-time material characterization, such as acoustic sensors (1) for material density and viscosity, photonic sensors (2) for chemical composition analysis, X-ray measurement systems (3) for crystal structure and elemental composition, and laser energy absorption sensors (4) for normalized enthalpy measurement,• Track formation equipment that forms tracks on a substrate under controlled conditions and includes a temperature-controlled device chamber (5), high-resolution imaging devices for capturing track geometry, and sensors for measuring powder layer thickness (14), liquid layer thickness, and solidified track dimensions, • Computer equipment (21) that analyzes track characteristics using deep learning methods, performing edge detection, training convolutional neural networks with boundary points, selecting target boundary points based on prediction errors, and calculating derivatives to determine track characteristics, including wetting angles.

2. An advanced track analysis and control system for additive manufacturing, welding, and cladding according to Claim 1, characterized by comprising, computer equipment (21) that a database in which all process data is recorded.

3. The operational process and analysis method of the analysis and control system, characterized by comprising:Powder depositing of a layer of power with a thickness (14) on the build plate (10),• Creating a melt pool by scanning the powder bed and a laser by realization of laser melting,• Realization of track formation,• Real-time analysis (19) with data collected through sensors, • Realization of deep learning analysis with deep learning algorithms (20),• Realization of adaptive control with laser results,• Display of real-time visualizations of process parameters and quality measurements in the user interface,• Recording all process data in the database.

4. An operational process and analysis method according to Claim 3, characterized by comprising; realization of track formation, characterized by comprising;• Measuring the track width (7) with track formation equipment,• Analysing the track reinforcement area (8) on top of the powder bed with deep learning,• Assessing the track penetration area (9) into the previous layers with deep learning,• Calculating the contact or wetting angle (11 ) with deep learning, • Measuring the track depth (12) and track height (13),5. An operational process and analysis method according to Claim 3, characterized by comprising; real-time analysis (19) with data collected through sensors, characterized by comprising;• Monitoring of the denudation zone (6) around the melt pool with deep learning,• Sensors continuously collect data on material properties and process conditions,• Capturing and processing high-resolution images in real time with CCD camera.

6. An operational process and analysis method according to Claim 3, characterized by comprising; realization of deep learning analysis with deep learning algorithms (20), characterized by comprising;• Obtaining high-resolution images with CCD camera of tracks formed on a substrate,• Preprocessing the images with deep learning to reduce noise and apply Gaussian smoothing,• Performing edge detection using a deep learning method to obtain an edge map,• Training a deep learning convolutional neural network with deep learning a preset number of boundary points,• Selecting target boundary points based on prediction errors with deep learning,• Determining track characteristics based on the derivatives at target boundary points with deep learning,• Measuring laser energy absorption, powder layer thickness (14), liquid layer thickness, and solidified track dimensions, • Calculating the volume of solidified material track and powder consumption with deep learning and determining the relationship between track and powder areas.

Images