In an atmospheric plasma spray (APS) process, in-flight powder particle characteristics, such as the particle velocity and temperature, have significant influence on the coating formation. The nonlinear relationship between the input process parameters and in-flight particle characteristics is thus of paramount importance for coating properties design and quality control. It is also known that the ageing of torch electrodes affects this relationship. In recent years, machine learning algorithms have proven to be able to take into account such complex nonlinear interactions. This work illustrates the application of ensemble methods based on decision tree algorithms to evaluate and to predict in-flight particle temperature and velocity during an APS process considering torch electrodes ageing. Experiments were performed to record simultaneously the input process parameters, the in-flight powder particle characteristics and the electrodes usage time. Various spray durations were considered to emulate industrial coating spray production settings. Random forest and gradient boosting algorithms were used to rank and select the features for the APS process data recorded as the electrodes aged and the corresponding predictive models were compared. The time series aspect of the data will be examined.

Plasma spraying is a key industrial coating process that exhibits intricate nonlinear interactions among process parameters. This complexity makes accurate predictions of particle properties, which greatly affect process behavior, very challenging. Specifically, particle velocities and temperatures profoundly impact coating quality and process efficiency. Conventional methods often require empirical correlations and extensive parameter tuning due to their limited ability to capture the underlying physics within this intricate system. This study introduces Physics-Informed Neural Networks (PINNs) as a solution. By seamlessly integrating known physical laws and constraints directly into the model architecture, PINNs offer the potential to learn the underlying physics of the system. For comparison, Artificial Neural Networks (ANNs) are also developed. Computational Fluid Dynamics (CFD) simulations of a plasma generator and plasma jet model provide data to train both ANN and PINN models. The study reveals an improvement in particle velocity prediction through the proposed PINN model, demonstrating its capability to handle complex relationships. However, challenges arise in predicting particle temperature, warranting further investigation. The developed models can aid in optimizing the plasma spraying process by predicting essential particle properties and guiding necessary process adjustments to enhance coating quality.

The fluid and particle dynamics of a High-Velocity Oxygen-Fuel Thermal Spray torch are analyzed using computational and experimental techniques. Three-dimensional Computational Fluid Dynamics (CFD) results are presented for a curved aircap used for coating interior surfaces such as engine cylinder bores. The device analyzed is similar to the Metco Diamond Jet Rotating Wire (DJRW) torch. The feed gases are injected through an axisymmetric nozzle into the curved aircap. Premixed propylene and oxygen are introduced from an annulus in the nozzle, while cooling air is injected between the nozzle and the interior wall of the aircap. The combustion process is modeled using a single-step finite- rate chemistry model with a total of 9 gas species which includes dissociation of combustion products. A continually-fed steel wire passes through the center of the nozzle and melting occurs at a conical tip near the exit of the aircap. Wire melting is simulated computationally by injecting liquid steel particles into the flow field near the tip of the wire. Experimental particle velocity measurements during wire feed were also taken using a Laser Two-Focus (L2F) velocimeter system. Flow fields inside and outside the aircap are presented and particle velocity predictions are compared with experimental measurements outside of the aircap.

When describing the cold spray process, one of the most widely used concepts is the critical velocity. Current models predicting critical velocities take the temperature of the sprayed particles explicitly into account but not the surface temperature (substrate or already deposited layers) on which the particle impact. This surface temperature is expected to play an important role since the deformation process leading to particle bonding and coating formation takes place both on the particle and the substrate side. The aim of this work is to investigate the effect of the substrate temperature on the coating formation process. Experiments were performed using aluminum, zinc and tin powders as coating materials. These materials have a rather large difference in critical velocities that gives the possibility to cover a broad range of deposition velocity to critical velocity ratio using commercial low pressure cold spray system. The sample surface was heated and the temperature was varied from room temperature to a high fraction of the melting point of the coating material for all three materials. The change in temperature of the substrate during the deposition process was measured by means of a high speed IR camera. The coating formation was investigated as a function of (1) the measured surface temperature of the substrate during deposition, (2) the gun transverse speed and (3) the particle velocity. Both single particle impact samples and thick coatings were produced and characterized. Both the particle-substrate and interparticle bondings were evaluated by SEM and confocal microscopy

In cold spray (CS) additive manufacturing process, micrometer scale particles accelerated through a supersonic nozzle are targeted on a surface with velocities in the rage of 300-1500 m/s in solid state. The impact energy of the particles leads them to deform plastically with high shear energy near the impact interface and adhere to the surface metallurgically, mechanically, and chemically. Using CS, deposition of metals, metal matrix composites, and polymers are achieved with high adhesive/cohesive strength and low porosity. Sensitivity of the CS additive manufacturing process to the variabilities in the process parameters are still being understood. Among the process parameters, particle morphology can have significant implications on drag forces, and therefore, on the particle impact velocity. This in turn affects the deposition efficiency (DE) and the quality of products. In this work, a new approach is introduced for computing DE by incorporating particle sphericity and its variation into one-dimensional numerical models. Size, sphericity, and the variability of size and sphericity of aluminum, copper, titanium, and tantalum particles are measured from static optical microscope images. The data is used for predicting impact velocity, temperature, and DE. The model results are then compared with particle velocity measurements.

A numerical finite difference model has been developed to treat the transfer of heat and momentum between a gas environment and a particle injected into it. The model is based on an explicit solution scheme for the thermal field and explicit treatment of the momentum exchange. The latent heat associated with phase changes is simulated via a post-iterative heat accumulation scheme. Particle-gas heat transfer is represented by a heat transfer coefficient, which is a function of relative gas velocity. The validity of the model is confirmed via comparisons between predicted behaviour and previously-published experimental data for thermal histories and particle trajectories. Comparisons are also presented with predictions from previously-developed models. Results are then presented for the behaviour of hollow zirconia particles, with particular attention being paid to in-flight melting characteristics. It is shown that there is an optimum combination of particle size and wall thickness for the promotion of efficient melting, for a given gas flow and temperature field.

In cold gas spraying, successful bonding occurs when particle impact velocities exceed the critical velocity. The critical velocity formula depends on material properties and temperature upon impact, relying mainly on tabulated data of bulk material. However, rapid solidification of powder particles during gas atomization can result in strengths up to twice that of bulk materials, causing an underestimation of the critical velocity. Thus, a re-adjustment of the semi-empirical calibration constants could supply a more accurate prediction of the requested spray conditions for bonding. Using copper and aluminum as examples, experimentally determined particle strengths for various particle sizes were 43% and 81% higher than those of the corresponding soft bulk materials. Cold gas spraying was performed over a wide range of parameter sets, achieving deposition efficiencies ranging from 2% to 98%. Deposition efficiencies were plotted as functions of particle impact velocities and temperatures, as calculated by a fluid dynamic approach. By using deposition efficiencies of 50%, the critical velocities of the different powders and the corresponding semi-empirical constants were determined. Based on particle strengths, the results reveal slight material-dependent differences in the mechanical pre-factor. This allows for a more precise description of individual influences by particle strengths on critical velocities and thus coating properties. Nevertheless, the general description of the critical velocity based on bulk data with generalized empirical constants still proves to be a good approximation for predicting required parameter sets or interpreting achieved coating properties.

In this study, suspension plasma spraying is used to deposit pseudo eutectic alumina-yttria stabilized zirconia as a potential thermal barrier coating. Process variables including feed rate, powder size, and plasma gas composition were altered to determine the influence of spray parameters on the formation of phases in the composite coating. The most significant variable was found to be the auxiliary gas. The gas influences the formation of phases primarily through its effect on in-flight particle velocity.

Thermal spraying of dense titanium coatings in the air atmosphere was achieved by using a two-stage high velocity oxy-fuel process (HVOF) called the Warm Spray Process. In the process nitrogen gas is mixed with the combustion gas to lower the gas temperature. Gas dynamics modeling of the flow field of the gas in the spray apparatus as well as the acceleration and heating of titanium powder injected from the powder feed ports were conducted. Based on the obtained temperature history of a titanium powder particle, its oxidation during flight was also predicted by using a Wagner-type oxidation model. These results were compared with measured velocity and temperature of sprayed particles by DPV2000 and the properties of deposited coatings. Significant discrepancy in the temperature of sprayed particles was found between the calculation and measurement whereas the measured velocity was closer to the model calculation. The model prediction of oxygen content was in a good agreement with the analysis of actual coatings. Furthermore, properties of the sprayed coatings such as porosity, oxygen content were correlated with the particle velocities and temperatures. Nitrogen gas was highly effective in lowering the oxygen content, but excessive nitrogen addition caused the coating porosity to increase due to insufficient particle temperatures.

In Cold Gas Dynamic Spraying the nozzle is a key part that must be optimized to maximize the injected particle acceleration and improve the coating quality. In this study an axi-symmetric two-dimensional mathematical model is presented and used to predict the flow inside a commercial cold spray nozzle and the particle velocity at the nozzle exit. Comparisons between the model results and the measurements made show that the model allows predicting accurately the particle velocity in the cold spray jet even in the presence of shock waves. The study shows that the particle exit velocity depends on the type of propellant gas used and the stagnation temperature and pressure. Following this work, the design of nozzles for specific applications using this mathematical model can be considered.

The numerical forecast constitutes an interesting way for plasma spraying to minimize the number of experiments to achieved the optimum spraying conditions. Many computational codes have been developed to predict the properties of the plasma jet (velocity, temperature) and the particles behavior within (temperature, velocity, melting state). According to the particle injection orthogonally to the plasma jet, the models have to be 3D. However, such codes need several hours if not several days of calculations to obtain the results of one condition. This is the main drawback of the existing sophisticated codes. The computing time is not compatible with industrial needs. Various clever numerical methods were developed in the past to simulate 2-D parabolic gas flows for laminar boundary layers or jets. For example, the Genmix 2-D axi-symmetric algorithm developed by Spalding and Patankar, and known as the Bikini method requires a very low-cost memory and computing time. This algorithm makes it possible, when using the proper thermodynamics and transport properties of plasma gases and the whole equation of Boussinesq-Oseen-Basset and taking into account the thermophoresis and non continuity effect for small particle, to predict in a fast and rather realistic way, the velocity and temperature fields of the plasma jet.

Computational Fluid Dynamics (CFD) is used to model the Shock-wave Induced Spray Process (SISP). SISP utilizes the kinetic and thermal energy induced by a moving shock-wave to accelerate and heat powder particles, similar to Cold Gas-Dynamic Spraying (CGDS), where the particles impact the substrate and deform plastically to produce a coating. Individual powder particles reach the substrate at different velocities and temperatures depending on their location within the unsteady flow regime. The critical velocity correlated to particle impact temperature and a CFD model are used to predict whether a particle traveling within this unsteady flow regime will bond to the substrate upon impact or bounce off. This information is then used to predict if a coating can be formed under a specific set of spray conditions.

This article attempts to predict the temperature, state and velocity of Tribaloy 800 particles by means of numerical modeling. It aims to identify parameters that have a significant influence on the inflight particle characteristics for Argon/Hydrogen plasma sprayed Tribaloy 800, and to compare predicted air entrainment and particle residence times between Argon/Hydrogen and Argon/Helium plasma gas mixtures. The effect of spray parameters (primary-, secondary- carrier gas mass flows, current, spray distance and nozzle diameter) on the particle in-flight characteristics (velocity and temperature) and their interactions are studied by a two level fractional factorial experiment applied on the simulations. A comparison between argon Argon/Hydrogen and Argon/helium plasm gas mixtures is made in order to investigate whether the coating oxidation level can be reduced using Argon/Helium. Finally, the correlation between the modeled parameters and the application microstructure is studied. Paper includes a German-language abstract.

In thermal spray process, the in-flight particle characteristics such as particle size, velocity and temperature influence significantly their flight duration as well as their melting degree. Consequently, they influence the splat formation and ultimately the coating properties. Thus, the knowledge of the interactions between the process parameters and the in-flight particle characteristics is very important for optimizing the coating properties. Artificial Neural Network (ANN) concept was used to predict in-flight particle velocity and temperature considering the case of alumina (Al 2 O 3 -TiO 2 ) coatings. Databases of in-flight particle characteristics (diameter, velocity and temperature) versus spray process parameters (arc current intensity, hydrogen rate and plasma gas composition) were collected. ANN was trained with the database to establish the relationships linking the particle diameter and spray process parameters to particle velocity and temperature. Then, the established ANN relationships permitted to determine the inflight particle velocity and temperature versus their diameter for given spray process parameters. These velocity and temperature data were then used to determine the time for complete particle melting and the particle dwell-time before impact by an analytical model for given operating conditions.

In cold spraying a powder material is accelerated and heated in the gas flow of a supersonic nozzle to velocities and temperatures that are sufficient to obtain cohesion of the particles to a substrate due to plastic deformation. The deposition efficiency of the powder particles is significantly determined by their velocity and temperature. The particle velocity correlates with the kinetic energy of the particles and thereby with the amount of energy that is converted to plastic deformation and thermal heating. The initial particle temperature significantly influences the mechanical properties of the particle. Velocity and temperature of the particles have nonlinear dependence on the pressure and temperature of the gas at the nozzle entrance. Whereas the particle velocity can easily be measured during the process, the particle temperature is not directly accessible by experimental techniques. Generally information about the particle temperature can be obtained based on theoretical models. In this contribution a simulation model based on the reactingParcelFoam solver of OpenFOAM is presented and applied for an analysis of the cold spray process. The model combines a compressible description of the gas flow in the nozzle with a Lagrangian particle tracking. The predictions of the simulation model are verified based on an analytical description of the gas flow, the particle acceleration and heating in the nozzle. Based on experimental data the drag model according to Plessis and Masliyah is identified to be best suited for OpenFOAM modelling particle heating and acceleration in cold spraying.

In cold spraying, the high strain rate plastic deformation during particle impact leads to a local temperature rise at the particle/substrate interface. This gives rise to thermal softening and thus further strain and heat generation, finally resulting in adiabatic shear instabilities, which are necessary to supply sufficient heat for successful bonding of the particles. These adiabatic shear instabilities can only occur, if a critical impact velocity is exceeded. A further increase of the impact velocity beyond this critical velocity continuously increases the fraction of well-bonded interfaces up to 95%, thus improving mechanical performance of the coatings. However, at far too high impact velocities, the efficiency again decreases and then changes to erosion due to hydrodynamic penetration. This erosion velocity is approximately two to three times higher than the critical velocity. The optimum velocity range between critical and erosion velocity is defined as “window of deposition”. Both critical and erosion velocity depend on the spray material properties, but also on particle impact temperature and particle size. Furthermore, they are also influenced by the powder purity. This study demonstrates the previously mentioned effects by calculations and experimental investigations. The presented link between fluid dynamics and impact dynamics enables to predict optimum spray parameters as well as the process effectiveness and resulting coating properties for certain cold spray conditions. Following this strategy, it was possible to increase the ultimate cohesive strength of cold-sprayed copper coatings from 80 MPa to more than 400 MPa, using nitrogen as process gas. In the annealed state, the ductility of these coatings corresponds to annealed bulk material. The overall optimization strategy is applicable to a wide variety of other spray materials. These developments should boost several new cold spray applications.

The advantages of the solid state deposition process Cold Spray (CS) over conventional spray technologies go hand in hand with the requirement of high and well-predictable particle velocities. The acceleration of particles primarily takes place within the CS-nozzle while measurements of their velocity are conducted downstream of its exit. Despite their essential value, these observations are limited, in that only the result of the acceleration can be evaluated, not the actual driving mechanisms themselves. Previous work has indicated that there is no conclusive understanding of these mechanisms, especially in cases of increasing particle loading. This study therefore presents a transparent rectangular CS-nozzle design (made out of quartz) for a low stagnation pressure regime. A novelty to the field of thermal spray is the first report of particle in-flight measurements within the CS-nozzle using Particle Tracking Velocimetry (PTV) at varying particle loadings and pressure levels. It is found that particle velocities in the jet decrease with increasing particulate loading as the momentum exchange of the gas is enhanced, while in the subsonic flow region, the average velocity level increases due to particle-particle interactions with shallower axial velocity profiles. This effect is aggravated for higher working pressures, as energetic collisions cause increasing losses, depending on the number density of particles. This study forms the basis for a comprehensive nozzle-internal analysis.

The influence of arc root fluctuations in DC plasma spraying on the physical state of the particle jet is investigated by correlating individual in-flight particle temperature and velocity measurements with the instantaneous voltage difference between the electrodes. In-flight diagnostics with the DPV-2000 sensing device involves two-color pyrometry and time-of-flight technique for the determination of temperature and velocity. Synchronization of particle diagnostics with the torch voltage fluctuations is performed using an electronic circuit that generates a pulse when the voltage reaches some specific level; this pulse, that can be shifted by an arbitrary period of time, is used to trigger the acquisition of the pyrometric signals. Unlike what has been predicted by numerical modeling, time-dependent particle temperature and velocity due to power fluctuations induced by the arc movement can be very important. Periodic variations of the mean particle temperature and velocity, reaching ΔT = 600°C and Δv = 200m/s, are recorded during a voltage cycle. Moreover, very few particles are detected during some part of the cycle. The existence of quiet periods suggests that particles that are injected at some specific moments in the plasma are neither heated nor accelerated efficiently. To our knowledge, this is the first time large time-dependent effects of the arc root fluctuations on the particle state (temperature and velocity) are experimentally demonstrated with quantitative measurements.

Plasma-sprayed coatings are formed by the impact and accumulation of feedstock particles with random sizes, temperatures and velocities on the surface of a substrate. The simulation results obtained for a single particle are not able to represent the behaviour of the feedstock in the process. A statistical analysis is required to describe this stochastic behaviour and in this research, the Monte-Carlo method was used to simulate the particles in the plasma jet. Parcels of groups of particles based on the particle size distribution were employed to provide a simplified and mathematically tractable representation of real feedstock powders. The distributions of particle temperature, velocity and trajectory were directly linked to the particle size distribution and the injection conditions occurring in practice. The statistical approach enables the prediction of the mean value and standard deviation of particle temperature, particle velocity and deposition impact position. The influence of particle-injection velocity, injection position and plasma parameters on the quality of the coatings was studied. The research shows how statistical techniques can be used to control and optimise the plasma-spray process.

The resulting thermal and mechanical properties of atmospheric plasma sprayed coatings, are strongly dependent on the particle in-flight characteristics, which in turn depend on the spray gun variables. In industrial production the spray gun variables are set to constant values and closed loop controlled. However, calibrations of the variable levels are regularly performed and variations within specified tolerance limits allowed, which cause variations in the particle in-flight characteristics. The objective of this work was to investigate how these calibration variations affect the particle in-flight characteristics and the final coating properties. The investigation was performed using three-dimensional computational fluid dynamics simulations. The process model correspond to the SM-F-100 Connex gun, spraying ZrO 2 for thermal barrier coating applications. Particle in-flight characteristics were calculated using a stochastic discrete particle model. Validation of the model was performed using the optical DPV2000 system, and fair agreement was found. Voltage, arc current, primary, secondary and carrier gas flow rates were systematically varied one factor at a time and their separate effects on the particle in-flight characteristics evaluated. The most important variables influencing the particle characteristics were current and voltage. Final simulations considering extreme cases enabled determination of the particle characteristics limiting conditions due to tolerance variations. Coating microstructure evaluations of two of these extreme cases revealed that the total porosity could vary up to 4% due to tolerance variations.