Vector-level feedforward control of LPBF melt pool area using a physics-based thermal model

Lithium-ion batteries (LIBs) have found widespread application in energy storage due to their high energy density, low self-discharge and low maintenance characteristics. However, the stability and longevity of the batteries under extreme operating conditions is yet to be fully understood. Numerous experimental and simulation studies have been performed to elucidate the effect of temperature, current, depth of discharge, and the number of cycles [1,2,3] on the performance of LIBs. These studies show that the solid-electrolyte interface (SEI) layer and gas formation accelerate at high C-rates due to increased electrolyte decomposition [4,5]. Consequently, the cell's internal resistance increases, resulting in ever-increasing irreversible heat generation inside the cell [6]. This heat generation leads to high internal temperature and a corresponding reduction in cell capacity. The data of cell temperature for a wide range of ambient temperatures and cycling rates is limited because cell performance is typically reported at room temperature. The design of battery packs for electric vehicles(EVs) is also based on test data taken at room conditions. Given that the cell's capacity, specific energy, maximum power output is bound to depend on C-rate and ambient temperature, it is necessary to test and design battery packs based on these parameters.The thermal characteristics of a lithium-ion cell can be predicted using a physics-based thermal model or data-driven methods (DDM) relying on empirical data. Experimental determination of internal cell parameters required in physics-based thermal models is challenging and time-consuming for commercial cells. On the other hand, DDM requires only cell cycling data at specific operating conditions, thereby eliminating the need for internal parameter estimation. This model predicts the experimental input and output data pattern and fits the response surface to estimate the unknown output. In this study, surrogate modelling has been employed to estimate the surface temperature, capacity, energy, and average power of commercial lithium-ion cells for different discharge currents and ambient temperatures. Surrogate modelling, a popular data analysis and reduced-order modelling technique, aims to find a global minimum of a particular objective function using a few objective function evaluations [7]. The surrogate-based model divides experimental data into training and test data sets. The training data set is employed to train the algorithm. After that, the testing data set is used to validate the model's accuracy. Experiments were performed to develop a surrogate model, with the number of experiments decided using the design of experiments[8] for a current range of 0.5C to 3C-rate and ambient temperature range of 0°C to 45°C . The cycling of cells was performed using a high current battery cycler (Arbin), and the ambient temperature was maintained using a thermal chamber (Cincinnati). The surface temperature of commercial 18650 (NMC811) lithium-ion cells was recorded using T-type thermocouples and a National Instruments DAQ module. A polynomial response surface was fitted using surrogate modelling on experimentally obtained data. The response surface shown in figure 1. contains nine data points for the preliminary study, sub-divided into a set of seven training and two testing data. The prediction error sum of squares (PRESS) is currently bounded within 10% due to the limited training data set availability and is expected to be within a band of 1% after adding data from ongoing experiments. The estimation of temperature, capacity, and specific energy can be used to optimize and develop an improved thermal management system for electric vehicles that works under various operating conditions. References Waldmann, T., Wilka, M., Kasper, M., Fleischhammer, M., & Wohlfahrt-Mehrens, M. (2014). Journal of Power Sources, 262, 129-135.Guan, T., Sun, S., Yu, F., Gao, Y., Fan, P., Zuo, P., Du,C., & Yin, G. (2018). Electrochimica Acta, 279, 204-212.Simolka, M., Heger, J. F., Traub, N., Kaess, H., & Friedrich, K. A. (2020). Journal of The Electrochemical Society, 167(11), 110502.Xu, B., Diao, W., Wen, G., Choe, S. Y., Kim, J., & Pecht, M. (2021). Journal of Power Sources, 510, 230390.Rashid, M., & Gupta, A. (2017). Electrochimica Acta, 231, 171-184.Leng, F., Tan, C. M., & Pecht, M. (2015). Scientific reports, 5(1), 1-12.Queipo, N. V., Haftka, R. T., Shyy, W., Goel, T., Vaidyanathan, R., & Tucker, P. K. (2005). Progress in aerospace sciences, 41(1), 1-28.Li, W., Xiao, M., Peng, X., Garg, A., & Gao, L. (2019). Applied Thermal Engineering, 147, 90-100. Figure 1

Selective laser melting (SLM), a metal powder fusion additive manufacturing process, has the potential to manufacture complex components for aerospace and biomedical implants. Large-scale adaptation of these technologies is hampered due to the presence of defects such as porosity and part distortion. Nonuniform melt pool size is a major cause of these defects. The melt pool size changes due to heat from the previous powder bed tracks. In this work, the effect of heat sourced from neighbouring tracks was modelled and feedback control was designed. The objective of control is to regulate the melt pool cross-sectional area rejecting the effect of heat from neighbouring tracks within a layer of the powder bed. The SLM process’s thermal model was developed using the energy balance of lumped melt pool volume. The disturbing heat from neighbouring tracks was modelled as the initial temperature of the melt pool. Combining the thermal model with disturbance model resulted in a nonlinear model describing melt pool evolution. The PID, a classical feedback control approach, was used to minimize the effect of intertrack disturbance on the melt pool area. The controller was tuned for the desired melt pool area in a known environment. Simulation results revealed that the proposed controller regulated the desired melt pool area during the scan of multiple tracks of a powder layer within 16 milliseconds and within a length of 0.04 mm reducing laser power by 10% approximately in five tracks. This reduced the chance of pore formation. Hence, it enhances the quality of components manufactured using the SLM process, reducing defects.

Lithium sulfur batteries are a promising option for next-generation energy storage in electric transportation, and some companies have reported values over 400 Wh/kg (1). The push for more energy density within batteries can result in higher resistive batteries. For lithium sulfur batteries in particular, a study has shown that the cell resistance increases with increased capacity (2). As the energy stored within battery packs increase, the importance of thermal management for safety and performance also grows, which requires an accurate thermal model for design and control. A joint understanding of the thermal and electrochemical behavior is especially important in a system as nonlinear and complex as lithium sulfur batteries. However, the majority of lithium sulfur physics-based models are isothermal and do not consider thermal effects. To that end, we propose coupling a thermal and electrochemical model for lithium sulfur batteries.To describe the electrochemical behavior, our work utilizes physics-based models that give insight into the internal states of a battery, which describe phenomena that can contribute to decreased performance under certain conditions. The lithium sulfur model in this study is the one-dimensional physics-based model developed by Kumaresan et al. (3) that considers transport, kinetics, thermodynamics, and morphological changes within the lithium sulfur cell under isothermal conditions. The corresponding set of equations results in a numerically stiff system with variables evolving across many orders of magnitude. To alleviate the computational footprint while maintaining a high degree of accuracy, we have previously developed a mass-conserving lumped model through volume-averaging, called the Lithium Sulfur Tank-in-Series Model. The tank-in-series method was developed for lithium ion batteries (4) and adapted to the lithium sulfur system. The Lithium Sulfur Tank-in-Series model, with average quantities in each region, eliminates the spatial dependence for increased computational efficiency that expedites model use in estimation, control, and optimization.Mathematical thermal models have been developed for lithium sulfur batteries, including both 2D (5) and lumped models (6). These models are based on the general energy balance for batteries by Bernardi et al. (7) and include heat generation terms that are functions of thermodynamics, overpotentials, and material conductivities. The work by Stroe et al. (6) also detailed an experimental plan for determination of parameters, as well as their experimentally derived values. The results from the 2D model study (5) found that the temperature gradients within the cell were negligible, which indicates that a lumped model may capture the thermal behavior well.In this work, we extend mathematical modeling of lithium sulfur batteries by coupling the Tank-in-Series model with a thermal model based on the work by Stroe (6), which includes heat generation due to internal resistance and entropic contributions. Suitable approximations are made to estimate the various source terms within the thermal model. Coupling the thermal model with a more accurate predictive electrochemical model allows further insight into battery performance and future use in estimation and control. Acknowledgments The authors are thankful for financial support from the Advanced Battery Material Research (BMR) Program (Battery 500 Consortium). References A. Fotouhi, D. J. Auger, L. O’Neill, T. Cleaver, and S. Walus, Energies, 10 (2017).G. J. Offer and M. Wild, Lithium Sulfur Batteries, p. 149, John Wiley & Sons, New Jersey (2019).K. Kumaresan, Y. Mikhaylik, and R. E. White, J. Electrochem. Soc., 155, A576 (2008).A. Subramaniam et al., J. Electrochem. Soc., 167, 013534 (2020).D. Adair, K. Ismailov, Y. Massalin, and Z. Bakenov, Mod. Environ. Sci. Eng., 2, 246–250 (2016).D. I. Stroe, V. Knap, M. Swierczynski, and E. Schaltz, ECS Trans., 77, 467–476 (2017).D. Bernardi, E. Pawlikowski, and J. Newman, J. Electrochem. Soc., 132, 5 (1985).

Solidification microstructure control via melt pool geometry control is investigated in detail for the AlSi10Mg alloy in a laser melting process. Relationships between cell spacing and melting process parameters—beam power and velocity, are investigated. Single beads and multi-layer pad experiments are performed and analyzed for melt pool geometry and microstructure. Information from these experiments is used to achieve location-specific control of cell spacing in a single part using an EOS laser powder bed fusion machine. Along with experiments, thermal modeling is used to map the effect of melting parameters on solidification conditions. Optical microscopy and scanning electron microscopy are used to determine the melt pool dimensions and cell spacing, respectively. Results from the model and experiments show that cell spacing can be varied by controlling the cooling rate of the melt pool via beam power and travel speed for both single bead and multi-layer pad experiments. In addition, the relationship between melt pool area and cooling rate is used to demonstrate integrated melt pool geometry and microstructure control. This is also critical for process qualification using simple observable metrics such as melt pool size. This relationship is then used to demonstrate location-specific control of cell spacing in a single component.

Fusion-based additive manufacturing of metal is particularly challenging to simulate due to the broad range of length/time scales of multiphysics phenomena to bridge. Integrated Computational Materials Engineering (ICME) offers a promising route to accelerate the design of new materials, optimize manufacturing processes, and thus improve material properties and performance. ICME heavily relies on linking multiple modelling techniques relevant to distinct length/time scales and/or different physics. While a wide range of physics-based and predictive models exist, the efficient linking of these models remains challenging. In the context of additive manufacturing, interdependent phenomena across scales include: multicomponent alloys with complex phase diagrams, multiple phase transformations and temperature-dependent properties; complex thermal exchanges in the vicinity of the melt pool; and the development of nonequilibrium grain microstructures within this melt pool. A multiscale modeling strategy (i.e. micro and macro) has been developed to simulate powder-bed fusion of metallic alloys, which combines: (1) Temperaturedependent alloy properties and phase diagrams calculated by CalPhaD, (2) macroscale thermal and thermo-mechanical simulations of the material addition and fusion using finite elements (FE), (3) Phase-field (PF) simulations of the melt pool’s solidification at the microscopic scale, and (4) Simulations of the microscopic solidification of the melt pool using cellular automaton (CA). Realistic processing parameters are used in the methodology to simulate selective laser melting (SLM) of an Inconel 718 alloy. In the first step, three-dimensional thermal and thermo-mechanical frameworks were developed – using an in-house finite element code (IRIS) and a material library (MUESLI) implemented in C++ programming language – by considering these four factors: (1) Representing the thermal input from the scanning laser, (2) A material model to specify the temperature-dependent material property in the cyclic heating and cooling environment, (3) A physics-based method to explain the layer build-up process, and (4) A laser material interaction model to account for transient thermo-mechanical phenomena. Then, the thermal model was coupled with CalPhaD and PF methods to predict the formation of microstructures at the scale of the entire melt pool. In this part, the effect of temperature-dependent properties and the necessity of taking into account differences in properties between the powder bed and the dense material have been discussed. We perform an appropriately-converged PF solidification simulation at the scale of the entire melt pool using a two-dimensional longitudinal slice of the thermal field calculated through FE simulations. This calculation has over one billion grid points, yet is performed on a single cluster node with eight graphics processing units (GPUs). These microscale simulations, with a level of detail down to individual dendrites, offer new insight into the selection of grain texture via polycrystalline growth competition under realistic SLM conditions. Finally, comparisons between phase-field (PF) and cellular automaton (CA) simulations of polycrystalline growth in a two-dimensional melt pool under additive manufacturing (powder-bed fusion) relevant conditions have been performed. The generated grain structures from local (point-by-point) measurements and grain orientation distributions that were averaged over various simulations have been compared. We investigated how the melt pool aspect ratio and the CA spatial discretization level affected the selected grain texture. Our simulations demonstrate that only PF simulations are capable of capturing the fine-grained microscopic features related to transient growth conditions and solid-liquid interface stability, such as the initial planar growth stage before its cellular/dendritic destabilization or the early elimination of unfavorably oriented grains due to neighbor grain sidebranching. CA grid refinement can only partially address the resulting disagreement between PF and CA predictions. In addition, with some variability on the CA grid and melt pool shape, overall grain distributions averaged throughout the entire melt pools of several simulations appear to lead to a noticeably better agreement between PF and CA. This research offers a helpful step in that direction by quantitatively comparing both approaches at process-relevant length and time scales, even though more effort is still needed, especially to identify the appropriate selection of CA spatial discretization and its link to characteristic microstructural length scales.

The complex interaction between laser and material in Laser Wire Direct Energy Deposition (LW-DED) Additive Manufacturing (AM) benefits from process monitoring methods to ensure process stability and final part quality. Understanding the relationship between process parameters and melt pool geometrical characteristics can be used to effectively monitor and in-process control the process, as the melt pool geometrical characteristics serve as crucial indicators of process stability and quality.This study presents a novel in-situ monitoring approach for LW-DED, utilizing process images for melt pool segmentation, melt pool geometrical characteristics estimation, process stability assessment, and bead geometry prediction. The segmentation of melt pool objects was successfully accomplished using Convolutional Neural Networks (CNN)-based models, enabling the prediction of essential parameters such as melt pool area, height, width, center of area, and the center point of the bounding box enclosing the melt pool. Multiple models were compared regarding the accuracy and processing speed using a controlled central composite design and random experiments. We used an Inconel alloy 625 wire and two distinct substrate materials for deposition, a coaxial laser welding head with a 3 kW fiber laser, and an off-axis welding camera for monitoring.Among the CNN architectures evaluated, YOLOv8l demonstrated superior accuracy with mean Average Precision (mAP) values of 0.925 and 0.853 for Stainless Steel (SS) and low carbon steel (S355) substrates, respectively. Additionally, YOLOv8s exhibited a notable processing speed of over 114 frames per second, which indicates its suitability for real-time process control. Furthermore, the results indicate a significant correlation between process parameters and melt pool geometry variables. Notably, a clear correlation was established between melt pool characteristics and bead geometries obtained through microscopic examinations, including penetration depth and heat-affected zone. The analysis revealed a significant correlation for the bead area and width parameters. In relation to the bead height, while the correlation exhibited a lower magnitude compared to bead area and width, it remained responsive. In addition, the tensor masks derived from the developed models have proven to be highly effective in accurately predicting bead geometries.The results demonstrate the effectiveness of YOLO-based algorithms for detecting and segmenting the melt pool. Statistical analysis confirms the significance of stabilized process data and the accuracy of melt pool geometric models. We demonstrate that integrating advanced monitoring and control techniques using artificial intelligence methods like CNN can facilitate process stability and quality control.

A digital twin (DT), with the components of a physics-based model, a data-driven model, and a machine learning (ML) enabled efficient surrogate model, behaves as a virtual twin of the real-world physical process. In terms of Laser Powder Bed Fusion (L-PBF) based additive manufacturing (AM), a DT can predict the current and future states of the melt pool and the resulting defects corresponding to the input laser parameters, evolve itself by assimilating in-situ sensor data, and optimize the laser parameters to mitigate defect formation. In this paper, we present a deep neural operator enabled DT framework for closed-loop feedback control of the L-PBF process. This is accomplished by building a physics-based computational model to accurately represent the melt pool states, an efficient Fourier neural operator (FNO) based surrogate model to approximate the melt pool solution field, followed by a physics-based procedure to extract information from the computed melt pool simulation that can further be correlated to the defect quantities of interest (e.g., surface roughness). An optimization algorithm is then exercised to control laser input and minimize defects. On the other hand, the constructed DT also evolves with the physical twin via offline finetuning and online material calibration. For instance, the probabilistic distribution of laser absorptivity can be updated to match the real-time captured thermal image data. Finally, a probabilistic framework is adopted for uncertainty quantification. The developed DT is envisioned to guide the AM process and facilitate high-quality manufacturing in L-PBF-based metal AM.

3D spatial reconstruction of thermal characteristics in directed energy deposition through optical thermal imaging

Lithium sulfur (LiS) batteries are a promising option for next-generation energy storage due to their high energy density. Applications where weight is especially important like electric flight and electric vehicles have driven the study of this chemistry because the current technology cannot meet the higher energy density requirements. A recent study (1) estimated specific energy requirements for short-range aircraft to start at 750 Wh/kg, about 3 times the specific energy of lithium ion battery packs. Lithium sulfur batteries have a high theoretical specific energy of 2600 Wh/kg, with some companies reporting values over 400 Wh/kg (2). For these applications, the demand for packing more energy into a battery can lead to batteries with higher resistance. For lithium sulfur batteries in particular, the resistance is seen to increase with higher capacities per cell (3). As the required energy and subsequent size of the battery packs increase, the importance of heat dissipation for safety and performance also grows, which requires an accurate thermal model for design and control.A thermal study done by Stroe et al. (4) on lithium sulfur pouch cells detailed a lumped thermal model and experimental plan for determination of thermal parameters. However, the study assumed adiabatic conditions, meaning no external heat transfer was considered. For practical uses in a battery management system or battery pack sizing, adiabatic conditions no longer hold.Physics-based models enable a look into the internal states of the battery, which correspond to physical phenomena that can contribute to decreased performance under certain conditions. The physics-based models for lithium sulfur have focused on transport, kinetics, or morphology under isothermal operation. The mathematical model for lithium sulfur batteries developed by Kumaresan et al. (5) was the first one-dimensional physics-based model for lithium sulfur batteries. This discharge model was developed on porous electrode theory and considers transport, kinetics, thermodynamics, and morphological changes. The corresponding physics-based model results in a numerically stiff set of equations with variables evolving across many orders of magnitude. To alleviate the computational footprint and still maintain a high degree of accuracy, we have previously developed a mass-conserving lumped model through volume-averaging, called the Lithium Sulfur Tank-in-Series Model. This model, with average quantities in each region, eliminates the spatial dependence for increased computational efficiency that expedites model use in estimation, control, and optimization.In this work, the LiS tank-in-series model is coupled with a thermal model based on the work by Stroe (4). The thermal model includes heat generation due to internal resistance and entropic contributions. Suitable approximations are made to estimate the various source terms within the thermal model. Coupling the thermal model with a more accurate predictive model allows further insight into battery performance. Acknowledgments The authors are thankful for financial support from the Battery500 Consortium, BAE Systems, and the Joint Center for Aerospace Technology Innovation.

The growing number of commercially available machines for laser deposition welding show the growing acceptance and importance of this technology for industrial applications. Their increasing usage in research and production requires process stability and user-friendly handling. A commercially available DMG MORI LT 65 3D hybrid machine used in combination with a CCD-based coaxial temperature measurement system was utilized in this work to investigate what information relating to the intensity distribution of melt pool surfaces could be appropriate to draw conclusions about process conditions. In this study it is shown how the minimal required specific energy for a stable process can be determined, and it is indicated that the evolution of a plasma plume depends on thermal energy within the base material. An estimated melt pool area—calculated by the number of pixels (NOP) with intensities larger than a fixed, predefined threshold—builds the main measure in analysing images from the process camera. The melt pool area and its temporal variance can also serve as an indicator for an increased working distance.

An investigation on mechanical and microstructural properties of 316LSi parts fabricated by a robotized laser/wire direct metal deposition system

A physics-based dynamic electrothermal model is developed for the IGBT by coupling a temperature-dependent IGBT electrical model with dynamic thermal models for the IGBT silicon chip, packages, and heatsinks. The temperature-dependent IGBT electrical model describes the instantaneous electrical behavior in terms of the instantaneous temperature of the IGBT silicon chip surface. The instantaneous power dissipated in the IGBT is calculated using the electrical model and determines the instantaneous rate that heat is applied to the surface of the silicon chip thermal model. The thermal models determine the evolution of the temperature distribution within the thermal network and thus determine the instantaneous value of the silicon chip surface temperature used by the electrical model. The IGBT electrothermal model is implemented in the Saber circuit simulator and is connected to external circuits in the same way as the previously presented Saber IGBT model, except that it has an additional thermal terminal that is connected to the thermal network component models for the silicon chip, package, and heatsink. The IGBT dynamic electrothermal model and the thermal network component models are verified for the range of temperature and power dissipation levels (heating rates) that are important for power electronic systems. >

Additive manufacturing has the potential to revolutionize industrial hardware and unlock efficiency gains through the fabrication of geometries and architectures not possible by conventional processing. Wire Arc Additive manufacturing (WAAM) process is a class of directed energy deposition process enabling higher build rate and allowing custom wire feedstock allowing spatial variation of microstructure. The larger spot size and lower speed creates a larger melt pool, reducing residual stress and often time creating directional/columnar microstructure for Ni-superalloy. The use of flexible platform provides freedom in deposition strategy, which can accommodate complex substrates, including feature addition onto existing structures, non-flat layers, and repair methods. However, the certification of the final component needs to match the strength requirement. Hence, the quality of the component produced is stringently monitored to avoid buildup of residual stress, cracks, porosity and to reduce detrimental segregated phases commonly observed during alloy solidification. Simulation plays a huge role in predicting the melt pool dimension and can be used to optimize the process parameter. Similar development is also required to perform physics-based modeling of microstructural development in WAAM that can predict the microstructural features during solidification and can be used to optimize the process more effectively. To move toward this goal, Raytheon Technologies Research Center together with Siemens worked to create a set of computational tools to control the process parameters, enable on-line measurements and acquisition with feedback to the optimized process parameters, and eventually track material evolution through each step of the additive process. Computational fluid dynamics is used for accurate prediction and calibration of the thermal field during WAAM process. and phase field models for microstructure evolution as a function of processing parameters to establish a connection between additive parameters and the final microstructure. Here we report cellular automata (CA) model development to predict the dendritic microstructure evolution with surface and bulk nuclei for single track and multiple layers. The CA model was developed to account for secondary element addition and predict segregation, local melting, and latent heat release as well as prediction of Euler angles from orientation information and validated against experiments. This framework was utilized to tailor spatially-varying composition in a part by appropriately controlling the microstructure evolution during the additive process. Functionally graded Haynes 282 alloy with high Cr content at the surface was tested for oxidation and mechanical properties. An advanced physics-based reaction-diffusion model predicting the simultaneous creation of chromium oxide and alumina is developed and validated to extend life expectancy of the WAAM manufactured high temperature part. A machine-learning data-driven framework establishing the process-structure relationship from a dataset of real microstructure images and corresponding process history data has been developed and implemented in the NX Siemens design system. The digital twin configuration along with the tool path generation enabled prediction of WAAM component buildup time and the techno-economic analysis provided a favorable option for all 4 cases with 15-40% cost reduction.

The laser cladding process is based on the generation of a melt-pool in a substrate where a filler material is injected, generating a high quality clad with a minimum heat affected zone. This process is industrially used to generate coatings over wear or damaged surfaces, being an alternative to traditional deposition techniques. One of the most important aspects for its industrial application is to know the clad geometry in order to calculate the deposited layer thickness. This work presents a model in which, starting from the concentration of injected material and the melt-pool geometry, clad height is finally estimated. Both input variables are obtained by two previous validated models. On one hand, the melt pool is estimated by a thermal model based on the finite difference method, and on the other hand, concentration of injected material is provided by a particle concentration CFD model. This data is used in a mass balance over melt-pool area in order to estimate the deposited clad height.

A simple concept of characteristic thermal length is used to develop a physics-based compact thermal circuit model for the multi-gate field effective transistor (MuGFET) structure including the device channel, fins, source/drain/poly pads, metal contacts, poly wire and metal mires. The characteristic thermal lengths are used to represent various heat loss paths of heat conduction along each segment of the fins, channels and poly/metal wires. Extraction of thermal resistances and thermal lengths used to construct the model is achieved through numerical simulations of the 2D cross section for each segment. The circuit models are developed for single-fin and multi-fin MuGFET structures, and simulations of the thermal circuits are performed in SPICE to validate the model for each structure.