System for modeling and optimizing the process parameters in physical vapor deposition with regard to the grain size of titanium nitride

Abstract

A system for modeling and optimizing the process parameters of physical vapor deposition for determining the grain size of titanium nitride, wherein the system comprises the following: a vacuum coating chamber designed to hold a substrate and a titanium starting material for coating formation; a gas supply unit that is operationally connected to the vacuum coating chamber and is configured to regulate a nitrogen and an argon gas supply within predefined pressure ranges; a substrate holding unit located inside the vacuum coating chamber and mechanically coupled to a rotary drive unit configured to control the rotational movement of the substrate at variable speeds; a sensor unit with pressure sensors for measuring nitrogen and argon gas pressure and a rotary sensor element for measuring the rotational speed of the substrate holding unit; a data acquisition unit that is operationally connected to the sensor unit and configured to receive process parameter data in real time; a processing unit operationally coupled with the data acquisition unit, wherein the processing unit is configured to generate a predictive mathematical model that represents a relationship between the nitrogen gas pressure, the argon gas pressure, the rotational speed and a coating grain size parameter, wherein the predictive mathematical model includes a multivariate polynomial representation including interaction and higher-order terms; an optimization unit that is operationally coupled to the processing unit and configured to iteratively determine an optimal set of process parameters by evaluating candidate parameter sets against the predictive mathematical model using an evolutionary search procedure that includes selection, recombination, and perturbation operations; and a control unit that is operationally coupled with the gas supply unit and the rotary drive unit and is configured to adjust the nitrogen gas pressure, the argon gas pressure and the rotational speed according to the optimal set of process parameters, the system is configured to minimize the coating grain size by continuously updating the predictive mathematical model and applying optimized process parameters during operation.

Description

TECHNICAL FIELD

[0001] The present invention relates to the field of advanced manufacturing systems, in particular a device and an integrated machine architecture for modeling, monitoring, and optimizing PVD (physical vapor deposition) coating processes. More specifically, the invention relates to a computer-controlled PVD coating system for controlling the coating parameters for titanium nitride (TiN) thin films. The grain size is optimized using a hybrid framework integrated into the device, consisting of response surface methodology (RSM) and genetic algorithms (GA). BACKGROUND OF THE INVENTION

[0002] In high-speed machining environments, cutting tools are subjected to extreme thermal and mechanical stresses, often reaching temperatures exceeding 800 °C. This leads to rapid tool wear and performance degradation. Titanium nitride coatings applied by physical vapor deposition (PVD) are widely used to improve wear resistance and hardness. However, the effectiveness of such coatings depends critically on their microstructural properties, particularly grain size.

[0003] Existing PVD coating systems lack an integrated mechanism for real-time modeling and optimization of process parameters such as nitrogen and argon pressure and substrate rotation speed. Conventional optimization methods are either based on empirical estimates or require extensive experimentation, leading to higher costs and inefficiencies. As this study demonstrates, optimization using a combined response surface methodology (RSM) and genetic algorithms (GA) significantly improves the accuracy of particle size prediction and reduces the experimental effort.

[0004] Therefore, there is a need for a machine-integrated intelligent device that is capable of dynamically modeling, predicting and optimizing coating parameters in a closed control loop.

[0005] Physical vapor deposition (PVD) has become a cornerstone of modern manufacturing, particularly in applications involving cutting tools, aerospace components, biomedical implants, and microelectronic devices. Among the various coating materials, titanium nitride (TiN) has garnered significant attention due to its superior hardness, chemical stability, low coefficient of friction, and enhanced wear resistance. These properties make TiN coatings especially suitable for high-speed machining environments subject to extreme thermal and mechanical stresses. However, the functionality of TiN coatings is highly dependent on their microstructural properties, particularly grain size, which directly influences hardness, adhesion, and tribological behavior.In practice, achieving a uniform and optimized grain size remains a complex challenge due to the many variables in PVD processes.

[0006] Conventional PVD systems, including magnetron sputtering and cathode arc evaporation, rely heavily on manual parameter selection or empirically determined process windows. Key process parameters such as nitrogen and argon gas pressure, substrate temperature, preload, and turntable speed collectively influence nucleation rates, adatom mobility, and layer growth dynamics. In most industrial applications, these parameters are selected based on operator experience, historical data sets, or general manuals, which typically provide only approximate ranges rather than optimal values. Consequently, manufacturers often resort to iterative trials to achieve acceptable coating quality. This approach is not only time-consuming but also leads to increased operating costs, material waste, and inconsistencies in coating performance.

[0007] Previous approaches attempt to overcome these limitations through statistical and computational modeling techniques. One widely used approach is the Taguchi method, which employs orthogonal arrays to reduce the number of experiments required for process optimization. While Taguchi-based designs of experiments effectively identify dominant factors, they are inherently limited in their ability to capture nonlinear interactions between process variables. This limitation becomes relevant in PVD processes, where complex physicochemical interactions govern film formation. Consequently, Taguchi methods may fail to accurately predict optimal conditions when strong interactions or higher-order dependencies are present.

[0008] Another common approach is full factorial design of experiments, which systematically evaluates all possible combinations of process parameters. While this method provides comprehensive insights into parameter interactions, it is impractical for PVD systems with multiple variables and stages because the number of required experiments increases exponentially. This leads to excessive experimentation and makes the approach unsuitable for real-time or industrial optimization.

[0009] Response surface modeling (RSM) has established itself as an advanced statistical method for modeling and optimizing complex processes. RSM creates mathematical models, typically second-order polynomial equations, to approximate the relationship between input parameters and output variables. In the context of TiN coating, RSM enables the prediction of grain size based on process variables such as nitrogen pressure, argon pressure, and rotary table speed. As the referenced study demonstrates, RSM achieves high prediction accuracy. Validation results confirm prediction accuracies exceeding 96% and residual errors below 10 nm. Despite its advantages, RSM has inherent limitations, particularly its reliance on predefined experimental designs and its susceptibility to local optima.The method is primarily deterministic and may not be able to effectively search the global search space, especially if the response surface has multiple minima or complex nonlinearities.

[0010] To overcome the limitations of traditional statistical methods, artificial intelligence approaches have also been explored. Techniques such as artificial neural networks (ANNs), fuzzy logic systems, and adaptive neuro-fuzzy inference systems (ANFIS) have been employed to predict coating properties and optimize process parameters. Neural networks, in particular, are capable of modeling highly nonlinear relationships and achieving high predictive accuracy with a sufficiently large training dataset. However, these methods require large datasets for training, which are often difficult and costly to obtain in PVD processes. Furthermore, neural networks function as "black-box" models, which limits their interpretability and complicates the understanding of the underlying physical relationships between the parameters.This lack of transparency poses a challenge for industrial applications, where explainability and reliability are crucial.

[0011] Fuzzy logic approaches offer improved interpretability by incorporating linguistic rules and expert knowledge into the modeling process. However, the accuracy of fuzzy systems depends heavily on the quality of the rule definitions and membership functions, which are often subjective and require domain expertise. ANFIS also combines neural networks and fuzzy logic to improve predictive capability, but inherits the limitations of both approaches, including computational complexity and dependence on training data.

[0012] Genetic engineering (GA) methods are widely regarded as powerful optimization tools for solving complex, multivariable problems. Inspired by natural evolution, GAs utilize mechanisms such as selection, crossover, and mutation to iteratively search for optimal solutions. In the context of PVD coating, GAs can be used to identify optimal combinations of process parameters that minimize particle size or maximize coating performance. As the referenced study demonstrates, GAs achieved improved optimization results compared to the response surface modeling (RSM) method alone, reducing particle size by approximately 6% compared to experimental data. However, standalone GA implementations lack a predictive modeling framework; they rely on fitness functions that must be defined a priori. Without a precise underlying model, the effectiveness of GA optimization may be limited.

[0013] To leverage the strengths of both methods, hybrid approaches combining RSM and GAs have been proposed. In such systems, RSM provides a mathematical model that serves as a fitness function for GA optimization, thus enabling efficient exploration of the solution space. While this approach improves optimization accuracy and reduces experimental effort, existing implementations are typically limited to offline analyses using external software tools such as MATLAB or DesignExpert. These solutions are not integrated into the PVD plant itself, leading to a mismatch between modeling, optimization, and the actual process control.

[0014] Another significant limitation of existing solutions is their lack of real-time capability. Most current systems model and optimize based on pre-acquired experimental data, without considering dynamic fluctuations in process conditions. Factors such as gas flow variations, temperature instability, and equipment wear can lead to variability that is not captured in static models. Consequently, the optimized parameters may no longer be valid under altered operating conditions, resulting in suboptimal coating performance.

[0015] Furthermore, existing PVD systems lack integrated sensor and feedback mechanisms for continuous monitoring of coating properties. While methods such as atomic force microscopy (AFM) provide precise particle size measurements, these are typically performed offline after the coating process is complete. This prevents real-time adjustment of process parameters and limits the possibilities for adaptive control. The absence of closed-loop control leads to delayed responses to process deviations and reduces the overall efficiency of the system.

[0016] Furthermore, the computational methods used in existing solutions often require significant manual intervention, including data preprocessing, parameter optimization, and model validation. This increases implementation complexity and reduces scalability for industrial applications. The reliance on external computing platforms also leads to latency and limits the possibility of real-time optimization.

[0017] Despite significant advances in modeling and optimization techniques, existing solutions for PVD coating processes exhibit several drawbacks. These include the limited ability to capture complex nonlinear interactions, high experimental costs, reliance on large datasets, lack of interpretability, absence of real-time integration, and inadequate control. These limitations underscore the need for a unified, machine-integrated system that combines predictive modeling, intelligent optimization, and real-time process control to achieve consistent and optimized coating performance. SUMMARY OF THE INVENTION

[0018] The present invention discloses a system for modeling and optimizing the process parameters of a physical vapor deposition for determining the grain size of titanium nitride.

[0019] The present invention discloses a device integrated into a coating machine for optimizing PVD coatings, consisting of a processing unit for generating a quadratic response surface model and an optimization engine based on genetic techniques, wherein the system dynamically calculates optimal process parameters to minimize the TiN coating particle size.

[0020] The device comprises a sensor-based characterization system, a data acquisition interface, a mathematical modeling processor, and an optimization control unit coupled to a magnetron sputtering chamber. The system continuously receives real-time process data, generates predictive models, and iteratively adjusts operating parameters to achieve optimal coating properties.

[0021] The present invention aims to provide a system integrated into a device for modeling and optimizing the process parameters of PVD (Physical Vapor Deposition) coatings. The system is configured to accurately predict and minimize the grain size of titanium nitride (TiN) coatings using a unified computational and process control framework. The invention overcomes the limitations of conventional trial-and-error methods by integrating a predictive modeling mechanism into the coating system, thus enabling the systematic determination of optimal process conditions.

[0022] A further objective of the invention is the development of a machine-based architecture that integrates the Response Surface Method (RSM) for the mathematical representation of the relationship between coating process parameters and the resulting particle size. The model takes into account linear, interactive, and higher-order effects of variables such as nitrogen and argon gas pressure, as well as the rotational speed of the substrate turntable. The invention aims to ensure high predictive accuracy and reliability of the generated model, thereby reducing the dependence on extensive experimental trials.

[0023] A further objective of the invention is the integration of a genetic optimization unit into the device. This optimization unit is configured to iteratively determine optimal combinations of process parameters by evaluating a fitness function derived from the predictive model. The invention aims to enable global optimization of the coating process by overcoming the local minima associated with conventional statistical methods and thereby achieving improved coating properties.

[0024] A further objective of the invention is to provide a closed control loop within the PVD system, in which process parameters are continuously monitored in real time and dynamically adjusted based on the outputs generated by the modeling and optimization units. The invention aims to enable adaptive control of the coating process and thus ensure consistent coating quality even under varying operating conditions.

[0025] A further objective of the invention is the integration of sensor-based data acquisition mechanisms for the real-time measurement of process variables and coating properties, including gas pressures and substrate rotation speed, as well as interfaces for receiving particle size measurements from characterization systems. The invention aims to enable continuous, data-driven improvement of the predictive model and the optimization process.

[0026] A further objective of the invention is to reduce manufacturing costs, material waste, and processing times in PVD coating processes by minimizing the need for repeated trials and manual parameter adjustments. The invention also aims to improve the uniformity, repeatability, and overall performance of the coated components, particularly in high-stress applications such as cutting tools.

[0027] A further objective of the invention is to provide a scalable and automated solution that can be integrated into existing PVD coating systems without significant modifications, thus enabling broad industrial application. The invention also aims to improve the interpretability and transparency of the optimization process through the use of a structured mathematical model in conjunction with intelligent optimization techniques.

[0028] A further objective of the invention is to increase the efficiency of investigating coating parameters by combining deterministic modeling with stochastic optimization. This enables rapid convergence to optimal solutions within a reduced computation time. The invention further aims to provide a robust framework capable of handling nonlinear interactions and the process variability inherent in PVD coating systems.

[0029] Accordingly, the invention aims to provide a comprehensive, intelligent and machine-integrated solution for the modeling, optimization and control of PVD coating processes, thereby achieving superior coating performance and operational efficiency. BRIEF DESCRIPTION OF THE IMAGE

[0030] These and other features, aspects and advantages of the present invention will be better understood if the following detailed description is read with reference to the accompanying drawing, in which the same symbols represent the same parts: Fig. Figure 1 shows a block diagram of a system for modeling and optimizing the process parameters of physical vapor deposition for the grain size of titanium nitride.

[0031] Furthermore, those skilled in the art will recognize that the elements in the drawing are simplified and not necessarily drawn to scale. For example, the flowcharts illustrate the process by highlighting the main steps to facilitate understanding of the present disclosure. With regard to the construction of the device, one or more components may be represented in the drawing by conventional symbols. The drawing may show only those specific details relevant to understanding the embodiments of the present disclosure, so as not to clutter the drawing with details that are already apparent to those skilled in the art from the description contained herein. Detailed description of the invention

[0032] To facilitate understanding of the principles of the invention, reference is made below to the embodiment shown in the drawing, which is described using specific terms. It is understood, however, that this does not limit the scope of protection of the invention. Rather, modifications and further developments of the depicted system, as well as further applications of the inventive principles shown therein, are conceivable, insofar as they would normally occur to a person skilled in the art in the field of the invention.

[0033] It will be clear to those skilled in the art that the foregoing general description and the following detailed description are exemplary and explanatory of the invention and are not to be understood as a limitation of it.

[0034] References to “an aspect”, “another aspect”, or similar phrases in this description mean that a particular feature, structure, or property described in connection with the embodiment is included in at least one embodiment of the present disclosure. Therefore, phrases such as “in one embodiment”, “in another embodiment”, and similar expressions in this description may, but do not necessarily, all refer to the same embodiment.

[0035] The terms "includes," "comprehensive," or similar expressions denote non-exclusive inclusion. Thus, a procedure or method containing a list of steps does not only include those steps but may also include further steps not explicitly listed or inherent in the procedure or method. Likewise, the statement "includes..." for one or more devices, subsystems, elements, structures, or components, without further limitations, does not preclude the existence of other devices, subsystems, elements, structures, or components.

[0036] Unless otherwise defined, all technical and scientific terms used herein have the same meanings generally known to those skilled in the art in the field to which this invention belongs. The systems, methods, and examples described herein serve only for illustration and are not to be understood as limiting.

[0037] Embodiments of the present disclosure are described in detail below with reference to the attached drawing.

[0038] Fig.Figure 1 shows a block diagram of a system for modeling and optimizing the process parameters of physical vapor deposition (PVD) for determining the grain size of titanium nitride. The system 100 comprises: a vacuum coating chamber (102) for holding a substrate and a titanium starting material for coating formation; a gas supply unit (104) operationally connected to the vacuum coating chamber and configured to regulate nitrogen and argon supplies within predefined pressure ranges; a substrate holding unit (106) located inside the vacuum coating chamber and mechanically coupled to a rotary drive unit configured to control the rotational movement of the substrate at variable speeds; a sensor unit (108) with pressure sensors for measuring the nitrogen and argon gas pressure and a rotary sensor element for measuring the rotational speed of the substrate holding unit;a data acquisition unit (110) that is operationally connected to the sensor unit and configured to receive process parameter data in real time; a processing unit (112) that is operationally coupled to the data acquisition unit, wherein the processing unit is configured to generate a predictive mathematical model that represents a relationship between the nitrogen gas pressure, the argon gas pressure, the rotational speed and a coating particle size parameter, wherein the predictive mathematical model comprises a multivariate polynomial representation including interaction and higher-order terms;an optimization unit (114) operationally coupled to the processing unit and configured to iteratively determine an optimal set of process parameters by evaluating candidate parameter sets against the predictive mathematical model using an evolutionary search procedure that includes selection, recombination, and perturbation operations; and a control unit (116) operationally coupled to the gas supply unit and the rotary drive unit, the control unit being configured to adjust the nitrogen gas pressure, the argon gas pressure, and the rotational speed according to the optimal set of process parameters, the system being configured to minimize the coating grain size by continuously updating the predictive mathematical model and applying optimized process parameters during operation.

[0039] In one embodiment, the processing unit is further configured to perform statistical validation of the predictive mathematical model by calculating residual values ​​between the predicted and measured particle sizes and evaluating the statistical significance of individual model terms using analysis of variance. The processing unit selectively removes non-significant terms to improve model accuracy.

[0040] In one embodiment, the optimization unit is configured to encode each process parameter as a numerical sequence, combine multiple sequences into candidate solutions, and iteratively generate new candidate solutions by swapping segments between sequences and introducing controlled variations to explore a global search space.

[0041] In one embodiment, the optimization unit is further configured to apply constraints that correspond to predefined lower and upper limits of nitrogen gas pressure, argon gas pressure and rotational speed, so that candidate solutions outside the predefined limits are excluded from the evaluation.

[0042] In one embodiment, the sensor unit further comprises a temperature sensor element configured to monitor the substrate temperature within the vacuum coating chamber, wherein the processing unit incorporates temperature data into the predictive mathematical model to improve prediction accuracy.

[0043] In an embodiment further comprising a surface characterization interface configured to receive grain size measurement data from an external microscopy device, wherein the received grain size measurement data is used by the processing unit to update and recalibrate the predictive mathematical model.

[0044] In one embodiment, the processing unit is configured to generate a reduced polynomial model by eliminating interaction terms and higher-order terms that do not meet a predefined statistical significance threshold, thereby improving computational efficiency during optimization.

[0045] In one embodiment, the optimization unit is configured to determine a fitness value for each candidate parameter set based on the predicted grain size and iteratively refines the candidate parameter sets until a convergence condition is met, which corresponds to a minimum grain size threshold or a maximum number of iterations.

[0046] In one embodiment, the control unit is configured to implement a closed control loop by continuously receiving updated parameter values ​​from the optimization unit and dynamically adjusting the gas supply unit and the rotary drive unit during an ongoing coating process.

[0047] In one embodiment, the data acquisition unit is configured to store historical process data and corresponding particle size measurements, with the processing unit using the stored data to improve predictive capability through iterative refinement of the mathematical model.

[0048] The system components are implemented as physically identifiable hardware elements arranged to perform measurable and controllable operations within the coating system. This ensures that the claimed subject matter is fully realizable and not abstract. The vacuum coating chamber forms a sealed enclosure capable of withstanding negative pressure conditions. The gas supply unit comprises flow control valves, lines, and pressure regulators that physically modulate the nitrogen and argon supply. The substrate holder and the rotary drive unit are implemented by mechanical devices and motor-driven assemblies that impart controlled rotational movement to the substrate. The sensor unit includes discrete pressure transducers and rotation sensors that generate electrical signals corresponding to the actual physical conditions within the chamber.These signals are transmitted via conductive traces to the data acquisition unit, which contains hardware circuits for signal conditioning, conversion, and buffering of the measurement parameters. The processing unit is implemented as a dedicated electronic circuit that performs mathematical transformations of the acquired signals at the hardware level. The optimization unit comprises interconnected electronic components that iteratively evaluate parameter changes based on the physically acquired data.

[0049] The present invention relates to a system for modeling and optimizing the process parameters of physical vapor deposition (PVD) for controlling the grain size of titanium nitride. The system integrates process hardware with a computing architecture that enables predictive modeling, iterative optimization, and real-time control. It operates in a vacuum chamber in which a substrate is mounted on a rotatable holder and exposed to a titanium source under controlled nitrogen and argon supply. The gas supply unit regulates the partial pressures of the reaction and inert gases, while the rotary drive unit controls the substrate movement, thereby influencing the coating uniformity and microstructure development. During operation, the sensor unit continuously measures the nitrogen and argon pressure as well as the rotational speed and transmits the acquired signals to the data acquisition unit.This digitizes, filters, and timestamps the data for further processing.

[0050] The processing unit is configured to create a predictive mathematical model that represents the functional relationship between the process parameters and the resulting particle size of the deposited coating. First, the processing unit receives a dataset of measured parameter values ​​and the corresponding particle size values, obtained via a surface characterization interface. The processing unit normalizes the incoming data to eliminate scale differences and improve numerical stability during modeling. Subsequently, the processing unit generates a polynomial approximation of the process behavior by fitting a multivariable function that includes linear terms, pairwise interaction terms, and second-order terms for each process parameter.The adjustment is made using the least squares method, whereby the coefficients are calculated in such a way as to minimize the cumulative deviation between predicted and measured grain size values.

[0051] The processing unit then performs statistical validation of the generated model by calculating residuals for each data point. Each residual represents the difference between the predicted and experimentally measured grain size. The processing unit also assesses the statistical significance of each term in the polynomial representation using analysis of variance. Terms that contribute only marginally to the predictive power are identified based on significance thresholds and selectively removed to obtain a reduced model with improved generalizability. The processing unit also verifies that the residuals are randomly distributed and within acceptable limits. This ensures that the model is free of systematic biases and adequately represents the underlying physical process.

[0052] Once the predictive model is created, the optimization unit uses this model as the basis for determining optimal process parameters. First, the optimization unit generates an initial set of candidate parameter sets. Each candidate set represents a possible combination of nitrogen pressure, argon pressure, and rotational speed within predefined limits. Each parameter set is encoded in a structured representation that allows for systematic manipulation during the optimization process. The optimization unit then evaluates each candidate set by inserting the parameter values ​​into the predictive model to obtain a corresponding particle size value, which serves as a quality indicator.

[0053] The optimization process is iterative. Candidate parameter sets are selected for further processing based on their fitness values, with preference given to those with smaller grain sizes. The selected parameter sets are recombined by combining segments of parameter values ​​from different sets to generate new candidate sets and thus explore the solution space. Additionally, controlled perturbations are introduced into the selected parameter sets to maintain diversity and prevent premature convergence. The optimization unit continuously evaluates the newly generated parameter sets, compares their fitness values, and retains the best candidates for subsequent iterations.

[0054] Throughout the iterative process, constraints are enforced to ensure that all candidate parameter sets remain within the permissible operating limits of the deposition system. Parameter sets exceeding predefined limits are either corrected or excluded from further evaluation. The optimization process continues until a convergence condition is met. This could be, for example, achieving a minimum particle size, stabilizing fitness values ​​over several iterations, or reaching a predefined number of iterations.

[0055] After determining the optimal parameter set, the control unit receives the optimized values ​​and converts them into control signals for the gas supply and the rotary drive. The control unit adjusts the gas flow regulators to achieve the desired nitrogen and argon pressures and regulates the motor speed to achieve the specified rotational speed. These adjustments are made in a controlled and gradual manner to ensure process stability and prevent abrupt fluctuations in the vacuum chamber.

[0056] The system operates in a closed-loop control system. The sensor unit continuously monitors the process parameters and transmits updated data to the processing unit. This unit periodically calibrates the predictive model based on the newly acquired data, adapting it to process changes such as equipment deviations or environmental fluctuations. The optimization unit then updates the optimal parameter set based on the refined model, and the control unit implements the updated control measures in real time. This continuous feedback mechanism enables the system to maintain optimal coating conditions throughout the entire coating process.

[0057] Furthermore, the data acquisition unit manages an archive of process parameters and associated particle size measurements, which is used by the processing unit to improve the robustness of the model over time. By incorporating historical and real-time data, the system increases predictive accuracy and reduces the uncertainty of the optimization results. The integration of predictive modeling, iterative optimization, and control in a single system enables the efficient investigation of the process parameter space while minimizing the need for extensive experimental trials.

[0058] The described system thus achieves a coordinated interplay between physical coating components and artificial intelligence, enabling precise control of the coating microstructure. Through the dynamic adjustment of process parameters based on predictive and optimization methods, the system ensures the consistent production of coatings with minimized grain size, improved hardness, and optimized performance characteristics.

[0059] The invention relates to a machine-integrated device for the intelligent control of a PVD coating system. The device comprises a vacuum coating chamber, a target material holder for receiving a titanium source, a substrate holder with a rotary drive, and gas inlet assemblies for regulating the nitrogen and argon gas pressure. The substrate holder is mechanically coupled to a variable-speed motor, which enables controlled rotation of the rotary table.

[0060] The device also includes a multi-sensor measuring system with pressure sensors for measuring nitrogen and argon gas pressures in the range of 0.16 × 10 -3 mbar up to 4.34 × 10 -3mbar, rotation sensors for measuring the turntable speed in the range of 3.98 to 9.02 rpm, and an interface for surface characterization that enables grain size measurements using atomic force microscopy (AFM). As described in the experimental setup, the AFM-based measurement allows for the non-destructive determination of grain size within a defined scan area.

[0061] The core of the invention is a computational modeling system integrated into the device, which implements a response surface methodology for creating a quadratic polynomial model that describes the relationship between process variables and coating particle size. The model is dynamically generated using experimental and real-time data and is defined by a multivariable polynomial expression containing linear, interaction, and quadratic terms for nitrogen pressure, argon pressure, and rotary table speed.

[0062] The modeling engine also performs statistical validation using ANOVA-based significance tests and residual error analysis to ensure that the generated model maintains a predictive accuracy within a predefined threshold, which is typically above 96% in validation experiments. The system eliminates insignificant terms through a model reduction routine to improve predictive robustness.

[0063] In addition to modeling, the device includes a genetic optimization unit. This unit is configured to encode process parameters in chromosome structures, perform selection, crossover, and mutation operations, and iteratively evaluate fitness functions from the RSM model. The optimization unit operates under predefined constraints corresponding to the process parameter ranges and uses stochastic selection procedures to achieve a global optimum.

[0064] The fitness function is defined as a transformation of the quadratic model and allows the direct calculation of grain size based on candidate parameter sets. The optimization unit performs several iterations until the convergence criteria are met. This leads to optimal parameter values, such as a nitrogen pressure of approximately 1.5 × 10⁻⁶. -3 mbar, an argon pressure of approximately 3.8 × 10 -3 mbar and a rotary table speed of approximately 5 rpm, resulting in minimum particle sizes of about 7.35 µm.

[0065] The device also includes a closed-loop control system in which the optimized parameters are transmitted to actuators that control the gas flow regulators and motor speed controllers within the PVD chamber. The system continuously monitors the particle size of the feedstock and recalibrates the model and the optimization cycle, thus enabling adaptive control of the coating process.

[0066] The machine integrates the computing unit with the coating chamber via a control interface, thus ensuring synchronized operation between physical coating processes and computer-aided optimization routines. This architecture enables a reduction in the number of test series, improved coating uniformity, and increased tool performance.

[0067] The invention represents a significant technological advancement by integrating modeling and optimization directly into the PVD coating system. It eliminates reliance on empirical trial-and-error methods and enables adaptive, real-time control of coating parameters. The hybrid RSM-GA approach ensures high predictive accuracy and efficient convergence to optimal solutions, resulting in reduced grain size, improved coating hardness, and extended tool life. Furthermore, the system minimizes material consumption, reduces processing time, and improves the reproducibility of coating quality.

[0068] The drawing and the preceding description illustrate embodiments. Those skilled in the art will recognize that one or more of the described elements can be combined to form a single functional element. Alternatively, certain elements can be divided into several functional elements. Elements of one embodiment can be added to another. For example, the process flows described here can be modified and are not limited to the manner described herein. Furthermore, the actions of a flowchart need not be performed in the sequence shown; nor do all actions necessarily need to be carried out. Actions that do not depend on other actions can be performed in parallel with the other actions. The scope of protection of the embodiments is in no way limited by these specific examples. Numerous variations, whether explicitly stated in the description or not, such as...Differences in structure, dimensions, and materials are possible. The scope of protection of the embodiments is at least as comprehensive as described by the following claims.

[0069] The advantages, other benefits, and problem solutions have been described above with reference to specific embodiments. However, the advantages, benefits, problem solutions, and any components that can effect or enhance an advantage, benefit, or solution are not to be construed as critical, necessary, or essential features or components of the claims. REFERENCES 100 A system for modeling and optimizing the process parameters in physical vapor deposition with regard to the grain size of titanium nitride. 102 Vacuum coating chamber 104 Gas supply unit 106 Substrate mounting unit 108 Sensor unit 110 data acquisition units 112 processing units 114 Optimization Unit 116 Control unit

Claims

A system for modeling and optimizing the process parameters of physical vapor deposition for determining the grain size of titanium nitride, comprising: a vacuum coating chamber designed to hold a substrate and a titanium starting material for coating formation; a gas supply unit operationally connected to the vacuum coating chamber and configured to regulate a nitrogen and an argon gas supply within predefined pressure ranges; a substrate holding unit located within the vacuum coating chamber and mechanically coupled to a rotary drive unit configured to control the rotational movement of the substrate at variable speeds; a sensor unit with pressure sensors for measuring the nitrogen and argon gas pressure and a rotary sensor element for measuring the rotational speed of the substrate holding unit;a data acquisition unit operationally linked to the sensor unit and configured to receive process parameter data in real time; a processing unit operationally coupled to the data acquisition unit, wherein the processing unit is configured to generate a predictive mathematical model representing a relationship between the nitrogen gas pressure, the argon gas pressure, the rotational speed and a coating particle size parameter, wherein the predictive mathematical model includes a multivariate polynomial representation including interaction and higher-order terms;an optimization unit that is operationally coupled to the processing unit and configured to iteratively determine an optimal set of process parameters by evaluating candidate parameter sets against the predictive mathematical model using an evolutionary search procedure that includes selection, recombination, and perturbation operations; and a control unit that is operationally coupled to the gas supply unit and the rotary drive unit and configured to adjust the nitrogen gas pressure, the argon gas pressure, and the rotational speed according to the optimal set of process parameters, the system being configured to minimize the coating grain size by continuously updating the predictive mathematical model and applying optimized process parameters during operation. System according to claim 1, wherein the processing unit is further configured to perform statistical validation of the predictive mathematical model by calculating residual values ​​between predicted grain size and measured grain size and evaluating the statistical significance of individual model terms by analysis of variance, and wherein the processing unit selectively removes non-significant terms to improve model accuracy. System according to claim 1, wherein the optimization unit is configured to encode each process parameter as a numerical sequence, combine multiple sequences into candidate solutions, and iteratively generate new candidate solutions by exchanging segments between sequences and introducing controlled variations to explore a global search space. System according to claim 1, wherein the optimization unit is further configured to apply constraints corresponding to predefined lower and upper limits of nitrogen gas pressure, argon gas pressure and rotational speed, such that candidate solutions outside the predefined limits are excluded from evaluation. System according to claim 1, wherein the sensor unit further comprises a temperature sensor element configured to monitor the substrate temperature within the vacuum coating chamber, and wherein the processing unit incorporates temperature data into the predictive mathematical model to improve the prediction accuracy. The system according to claim 1 further comprises a surface characterization interface configured to receive grain size measurement data from an external microscopy device, wherein the received grain size measurement data are used by the processing unit to update and recalibrate the predictive mathematical model. System according to claim 1, wherein the processing unit is configured to generate a reduced polynomial model by eliminating interaction terms and higher-order terms that do not meet a predefined statistical significance threshold, thereby improving computational efficiency during optimization. System according to claim 1, wherein the optimization unit is configured to determine a fitness value for each candidate parameter set based on the predicted grain size and iteratively refines the candidate parameter sets until a convergence condition is met which corresponds to a minimum grain size threshold or a maximum number of iterations. System according to claim 1, wherein the control unit is configured to implement a closed control loop by continuously receiving updated parameter values ​​from the optimization unit and dynamically adjusting the gas supply unit and the rotary drive unit during an ongoing coating process. System according to claim 1, wherein the data acquisition unit is configured to store historical process data and corresponding particle size measurements, and wherein the processing unit uses the stored data to improve the predictive capability by iterative refinement of the mathematical model.

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