A multi-scale simulation method for carburized gear inner oxidation heat treatment

Abstract

The application discloses a carburizing gear inner oxidation heat treatment multi-scale simulation method, which is characterized in that being applied to the technical field of mechanical manufacturing and gear engineering, and comprises the following steps: constructing a carburizing gear inner oxidation heat treatment molecular dynamics model based on LAMMPS, analyzing metal element diffusion, atomic migration, crystal lattice change and driving force of microstructure evolution; discussing the essence of microstructure change from the electronic structure level by DFT, analyzing the electronic structure and energy change of grain boundaries and the like, and making clear the correlation between microstructure and macroscopic performance; establishing an inner oxidation dynamics model based on COMSOL in combination with heat transfer, diffusion and phase change theory, and exploring the correlation between heat conduction and phase change; and establishing a three-dimensional geometric model and analyzing the influence of various factors on performance. The carburizing inner oxidation process is deeply analyzed in the application, the micro-migration mechanism of metal elements, the evolution law of crystal grains and the formation and growth mechanism of the oxidation layer are analyzed, and the application provides a solid theoretical basis and technical support for heat treatment process optimization of the carburizing gear.

Description

Technical Field

[0001] This invention relates to the fields of mechanical manufacturing and gear engineering technology, and more specifically to a multi-scale simulation method for internal oxidation heat treatment of carburized gears. Background Technology

[0002] In modern mechanical transmission systems, carburized gears, as core components, are widely used in automobiles, aerospace, energy, and other fields. Their service performance directly affects the reliability and stability of the entire system. Internal oxidation heat treatment, a key process for improving the surface properties of carburized gears, involves infiltrating carbon atoms into the gear surface in a specific atmosphere, accompanied by the oxidation of internal alloying elements, aiming to improve the gear's hardness, wear resistance, and fatigue strength. However, the complex physicochemical changes during internal oxidation, such as the migration and diffusion of metal elements at the microscale, the abnormal evolution of grain boundaries, the dynamic evolution of phase interfaces, and the resulting uneven stress distribution, severely restrict the fatigue strength and wear resistance of carburized gears, becoming a bottleneck limiting further performance improvements.

[0003] While traditional experimental research methods can directly obtain material performance data, they have limitations in revealing the microscopic mechanisms of internal oxidation processes and cannot deeply analyze the complex physicochemical processes under the coupling of multiple factors. The rise of multi-scale simulation technology provides a new approach to solving this problem. This technology integrates multiple theories and methods such as molecular dynamics (MD), density functional theory (DFT), and continuum models, enabling comprehensive and in-depth simulation of the internal oxidation process of carburizing across multiple levels, from the microscopic atomic scale to the macroscopic component scale. Through multi-scale simulation, not only can the migration trajectories of metal atoms in the crystal lattice be accurately captured, revealing the influence mechanism of microstructure evolution on macroscopic performance, but it can also provide precise theoretical guidance for optimizing process parameters, thereby effectively improving the overall performance of carburized gears, reducing production costs, and shortening the research and development cycle.

[0004] Therefore, a multi-scale simulation method for the internal oxidation heat treatment of carburized gears is urgently needed to be solved by those skilled in the art. This method can reveal the microscopic mechanism of the internal oxidation heat treatment process of carburized gears, deeply analyze the complex physicochemical process under the coupling effect of multiple factors, span multiple levels from the microscopic atomic scale to the macroscopic component scale, realize a comprehensive and in-depth simulation of the internal oxidation process of carburized gears, accurately capture the migration trajectory of metal atoms in the crystal lattice, reveal the influence mechanism of microstructure evolution on macroscopic performance, and provide accurate theoretical guidance for the optimization of process parameters. Summary of the Invention

[0005] In view of this, the present invention provides a multi-scale simulation method for the internal oxidation heat treatment of carburized gears. By comprehensively utilizing advanced computational simulation tools such as LAMMPS, DFT, and COMSOL Multiphysics, a complete cross-scale simulation system of "microscopic atomic scale - mesoscopic crystal scale - macroscopic component scale" is constructed. This system deeply analyzes the microscopic migration mechanism of metal elements, the evolution law of grains, and the formation and growth mechanism of oxide layer during the internal oxidation process of carburizing, providing a solid theoretical foundation and technical support for the optimization of the heat treatment process of carburized gears.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A multi-scale simulation method for internal oxidation heat treatment of carburized gears includes: Step 1: Based on LAMMPS software, a molecular dynamics model of internal oxidation heat treatment of carburized gears was constructed to analyze the diffusion behavior of metal elements at the microscale, atomic migration paths and dynamic changes of crystal structure during the internal oxidation process of carburizing, revealing the intrinsic driving force of microstructure evolution. Step 2: Using density functional theory (DFT), we explore the essential reasons for microstructure changes from the electronic structure level, analyze the electronic structure characteristics and energy change laws of grain boundaries, mixed crystal structure, phase interface and new phase formation during carburizing and internal oxidation, and clarify the intrinsic relationship between microstructure and macroscopic properties. Step 3: Based on COMSOL Multiphysics and combined with heat transfer, diffusion theory and phase transition theory, establish an internal oxidation kinetic model to explore the correlation mechanism between heat conduction and phase transition behavior during heating, carburizing and cooling processes; Step 4: Establish a three-dimensional geometric model of the carburized gear, comprehensively consider temperature changes, atmosphere control, carburizing process parameters and cooling rate factors, simulate the dynamic changes of the internal temperature field and stress field of the gear during the heat treatment process, and analyze the influence of each factor on the gear performance.

[0007] Optionally, in step 1, a molecular dynamics model of the internal oxidation heat treatment of the carburized gear is constructed based on LAMMPS software, specifically as follows: The EMA potential function is used to describe the interactions between atoms in a metallic system; Based on the chemical composition of carburized gears, the atomic types are clearly defined, and each atomic type is assigned attribute parameters including mass and charge. A simulation box is created using periodic boundary conditions; When initializing the atomic positions, Fe atoms are arranged according to a face-centered cubic lattice structure to construct a nanocrystalline model with initial grain boundary defects; The Nose-Hoover hot bath method was used to relax the simulation system to achieve thermal equilibrium.

[0008] Optionally, in step 2, density functional theory is used to explore the essential reasons for microstructure changes at the electronic structure level, analyzing the electronic structure characteristics and energy change laws of grain boundaries, mixed-grain structures, phase interfaces, and new phase formation during carburizing and internal oxidation processes. Specifically: The electronic structure of grain boundaries and phase interfaces was calculated using VASP software based on the plane wave pseudopotential method and the PBE functional under the generalized gradient approximation. Dynamic simulations of the interaction between grain boundaries and oxidation products during oxidation were performed, and the activation energies of grain boundary migration at different oxidation stages were calculated to understand the mechanism of oxidation-induced grain boundary migration. Using Thermo-Calc software and the TCFE7 thermodynamic database, the activity, chemical potential, and phase equilibrium relationship of alloying elements during carburizing were calculated. By adjusting the carbon potential, the precipitation sequence and thermodynamic driving force of cementite and oxide phase under different carbon potential conditions were simulated.

[0009] Optionally, in step 2, the plane wave pseudopotential is selected as the projected augmented wave pseudopotential.

[0010] Optionally, in step 2, the VASP software based on the plane wave pseudopotential method is used to calculate the electronic structure of the grain boundary and phase interface using the PBE functional under the generalized gradient approximation, specifically as follows: Grain boundary structures with different orientation differences are created by rotating and displacing an ideal crystal structure, and the grain boundary energy is calculated using the following formula:

[0011] in, Grain boundary energy; The total energy of the system including grain boundaries; The energy of an ideal crystal with the same number of atoms; The area of ​​the grain boundary; Carbon and oxygen atoms are introduced into the grain boundary model, and the segregation energy is calculated using the following formula:

[0012] in, This refers to the segregation energy of carbon and oxygen atoms at the grain boundary; The total energy of the system after carbon and oxygen atoms have segregated at the grain boundaries; This refers to the grain boundary energy when there is no segregation. The number of segregating atoms; This represents the chemical potential of the segregating atoms in the bulk phase. The electronic density of states at grain boundaries was further calculated, and austenite / cementite and oxide / matrix phase interface models were established when constructing the phase interface models. For the austenite / cementite phase interface, different crystallographic orientation relationships were considered, including the Kurdjumov-Sachs orientation relationship and the Nishiyama-Wassermann orientation relationship. For the oxide / matrix phase interface, Al2O3 / Fe and Cr2O3 / Fe phase interfaces were studied.

[0013] Optionally, in step 2, after simulating the precipitation sequence and thermodynamic driving force of cementite and oxide phases under different carbon potential conditions by adjusting the carbon potential, the method further includes: performing first-principles calculations using VASP software, calculating the formation energy and electronic structure by constructing a model containing cementite and oxide phases, and verifying the accuracy of the thermodynamic calculation results.

[0014] Optionally, in step 3, an internal oxidation kinetic model is established based on COMSOL Multiphysics and combined with heat transfer, diffusion theory, and phase transition theory, specifically as follows: Based on COMSOL Multiphysics, a three-dimensional heat transfer-diffusion-phase transformation coupled model of carburized gears is constructed, and boundary conditions are defined for key components, heating rate and cooling medium selection in the carburizing atmosphere. At the same time, a grain size-dependent oxygen diffusion coefficient is introduced. The key components in the carburizing atmosphere include: CO partial pressure and CH4 partial pressure; the selection of cooling media includes oil quenching and gas quenching; and the corresponding cooling boundary conditions defined according to the actual situation include: temperature and heat transfer coefficient. An unstructured mesh is used to refine the tooth root and tooth surface regions, and an adaptive time step algorithm is used to solve the transient heat conduction and mass diffusion equations.

[0015] Optionally, in step 3, a grain size-dependent oxygen diffusion coefficient is introduced, specifically: The relationship between the oxygen diffusion coefficient and the grain diameter is established as follows:

[0016] in, To introduce a grain size-dependent oxygen diffusion coefficient; The initial diffusion coefficient; The grain diameter; The characteristic length is denoted as .

[0017] Optionally, in step 4, a three-dimensional geometric model of the carburized gear is established, specifically as follows: A three-dimensional geometric model of the carburized gear was constructed using CAD software. The constructed three-dimensional model was then imported into COMSOL Multiphysics software for mesh generation, and unstructured meshes were used to refine the tooth root and tooth surface regions. The thermophysical parameters of carburized gear steel, including thermal conductivity and coefficient of linear expansion, are obtained at different temperatures and input into the COMSOL model; In the simulated carburizing process, the target temperature and heating rate of the heating stage are set to simulate the heating process in actual production; the carburizing time is set by controlling the carbon potential in the carburizing atmosphere to keep it within a preset range to ensure that carbon atoms can fully penetrate into the gear surface; in the quenching stage, the quenching temperature is set and the quenching time is adjusted according to the size of the gear and the material properties. Simultaneously considering the impact of the release of latent heat of phase transformation on the temperature field, the effect of martensitic transformation on the temperature gradient is simulated by setting the release amount and conditions of latent heat of phase transformation.

[0018] As can be seen from the above technical solution, compared with the prior art, this invention discloses a multi-scale simulation method for the internal oxidation heat treatment of carburized gears. This invention constructs a cross-scale simulation system encompassing "microscopic atomic scale - mesoscopic crystal scale - macroscopic component scale," and comprehensively utilizes tools such as LAMMPS, DFT, and COMSOL Multiphysics to successfully reveal the microscopic migration mechanism of metal elements, grain evolution laws, and oxide layer formation and growth mechanism during the internal oxidation heat treatment of carburized gears, clarifying the intrinsic relationship between microstructure and macroscopic performance. Simultaneously, it effectively analyzes the complex physicochemical processes under the coupled effects of multiple factors, accurately captures the migration trajectory of metal atoms, and can simulate the dynamic changes of temperature and stress fields and the influence of various factors on gear performance. This provides precise theoretical guidance for optimizing the heat treatment process parameters of carburized gears, helping to improve the overall performance of gears, reduce production costs, and shorten the R&D cycle. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0020] Figure 1 This is a schematic diagram of the method flow of the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] Example 1: Embodiment 1 of this invention discloses a multi-scale simulation method for internal oxidation heat treatment of carburized gears, such as... Figure 1 As shown, it includes: Step 1: Based on LAMMPS software, a molecular dynamics model of internal oxidation heat treatment of carburized gears is constructed to analyze the diffusion behavior of metal elements at the microscale, atomic migration paths and dynamic changes of crystal structure during the internal oxidation process of carburizing, revealing the intrinsic driving force of microstructure evolution.

[0023] A molecular dynamics model for the internal oxidation heat treatment of carburized gears was constructed using LAMMPS software, specifically as follows: This invention selects SAE5120H carburized gear steel, which is widely used in automotive gear manufacturing, as the simulation object and uses LAMMPS software to construct its molecular dynamics model.

[0024] The EMA potential function is used to describe the interactions between atoms in a metallic system. Accurate description of these interactions is crucial in model construction; therefore, the EAM (Embedded Atom Method) potential function, which effectively describes atomic interactions in metallic systems, was chosen. The EAM potential function considers the total energy of the system as the sum of the atomic embedding energy and the interatomic pair potential, fully taking into account the diffusion and overlap effects of electron clouds in metals. It accurately reflects the complex many-body interactions between metal atoms and has significant advantages for simulating atomic diffusion and microstructural evolution in metallic materials at high temperatures.

[0025] Based on the chemical composition of carburized gears, the atomic types are clearly defined, and each atomic type is assigned attribute parameters including mass and charge. When defining atomic types, based on the chemical composition of SAE 5120H steel, the atomic types of Fe, C, Mn, Cr, Al, and N are identified, and each atomic type is assigned accurate mass and charge attribute parameters. For example, the Fe atom, as the matrix atom, has a mass of 55.85 amu and a charge of 0; the C atom has a mass of 12.01 amu and plays a crucial role in the carburizing process, and its charge is also set to 0. By reasonably setting these parameters, it is ensured that the model can accurately reflect the atomic structure and properties of the material.

[0026] A periodic boundary condition is used to create the simulation box. This boundary condition effectively avoids errors caused by boundary effects in the simulated system, making the simulation results closer to the properties of real materials. The size of the simulation box is optimized and determined based on actual research needs and computational resources, set to 5nm×5nm×5nm in the x, y, and z directions respectively. This ensures that the system contains a sufficient number of atoms to meet the requirements of statistical analysis, while avoiding excessive computational costs due to an overly large system.

[0027] When initializing atomic positions, based on the crystal structure of SAE5120H steel, Fe atoms are arranged according to a face-centered cubic lattice structure to construct a nanocrystalline model with initial grain boundary defects. This model can more realistically reflect the existence of grain boundaries in actual materials and their influence on atomic diffusion and microstructure evolution. The introduction of grain boundary defects is achieved by randomly perturbing the positions of some atoms to simulate the irregularity of atomic arrangement at grain boundaries.

[0028] The Nose-Hoover hot bath method was used to relax the simulated system to achieve thermal equilibrium. During relaxation, the simulation temperature was set to the typical range of 850-950℃ for carburizing processes. The atomic velocity was gradually adjusted to allow the system's temperature and energy to reach a stable state. The relaxation steps were set to 10,000 steps, with each step having a time step of 1 fs, ensuring that the system was fully relaxed within a sufficiently long time to provide a stable initial state for subsequent atomic diffusion simulations.

[0029] To ensure that the selected EAM potential function accurately describes the interatomic interactions, it underwent rigorous verification. The accuracy of the simulation results was evaluated by comparing them with experimentally measured grain boundary diffusion coefficients. The experimental data came from diffusion experiments conducted on SAE5120H steel at different temperatures. Techniques such as radioactive tracer atom analysis or electron probe microanalysis (EPMA) were used to accurately measure the diffusion coefficient of carbon atoms at grain boundaries.

[0030] Potential function verification and simulation accuracy: Comparative analysis of the simulated diffusion coefficient of carbon atoms at grain boundaries with experimental data revealed a good trend consistency between the simulation results and experimental data, but some numerical deviations existed. To further improve simulation accuracy, the parameters of the EAM potential function were optimized. By minimizing the mean square error between the simulated and experimental diffusion coefficients, fine adjustments were made to the embedding energy and potential parameters in the potential function. After multiple iterative optimizations, the deviation between the simulated diffusion coefficient and the experimental data was significantly reduced.

[0031] In addition, sensitivity analyses were conducted on other parameters of the simulation system, investigating the effects of factors such as time step, simulation box size, and number of atoms on the simulation results. The results show that the choice of time step has a significant impact on the accuracy and computational efficiency of the simulation results. When the time step is too large, unreasonable jumps in atomic trajectories occur, leading to increased deviations in the simulation results; while a time step that is too small, although improving simulation accuracy, significantly increases computational costs. Considering both computational accuracy and efficiency, the optimal time step was determined to be 1 fs.

[0032] Increasing the size of the simulation box and the number of atoms can improve the statistical reliability of the simulation results, but it also leads to a significant increase in computational resources. By comparing the simulation results with different sizes of simulation boxes and the number of atoms, it was found that when the size of the simulation box reaches 5nm×5nm×5nm and the number of atoms reaches the order of 10^5, the statistical fluctuations of the simulation results are small and can meet the research requirements.

[0033] Microscopic evolution of metal elements during internal oxidation process: In the initial, intense carburizing stage, high concentrations of carbon atoms are rapidly injected into the gear steel surface driven by the concentration gradient. Molecular dynamics simulations clearly show that the rapid diffusion of carbon atoms leads to significant changes in the grain boundary structure. The atomic arrangement at the grain boundaries was originally relatively disordered, and the infiltration of carbon atoms further exacerbated this disorder, increasing the energy of the grain boundaries. Simultaneously, the interatomic spacing at the grain boundaries changes, and the coordination environment of some atoms also alters. These changes in microstructure provide favorable conditions for subsequent oxygen atom infiltration and oxidation reactions.

[0034] As the carburizing process proceeds, oxygen atoms begin to penetrate into the material along grain boundary channels. When oxygen atoms encounter alloying elements such as Al and Cr at the grain boundaries, a strong chemical reaction occurs, combining to form nanoscale oxides, such as Al₂O₃ and Cr₂O₃. Detailed analysis of the simulated trajectories revealed the kinetic pathway of this oxidation reaction: oxygen atoms are first adsorbed by Al and Cr atoms at the grain boundaries, forming adsorbed oxygen atoms; subsequently, the adsorbed oxygen atoms undergo electron transfer with Al and Cr atoms, forming chemical bonds and gradually agglomerating into nanoscale oxide particles.

[0035] During the growth of oxide products, their size and distribution were found to be closely related to carburizing time and temperature. With prolonged carburizing time, the size and quantity of oxide products gradually increased. This is because, during longer carburizing times, more oxygen atoms have the opportunity to diffuse to the grain boundaries and participate in the oxidation reaction, leading to continuous growth and aggregation of oxide particles. The effect of temperature on oxide products is more complex. Within a certain temperature range, as the temperature increases, the atomic diffusion rate accelerates, and the oxidation reaction rate also increases, resulting in a rapid increase in the size and quantity of oxide products. However, when the temperature exceeds a certain critical value, due to intensified grain boundary migration and reorganization, the defect structure at the grain boundaries changes, which in turn inhibits the growth of oxide products.

[0036] The local lattice distortion caused by grain boundary oxidation significantly modulates the diffusion barrier of carbon atoms. Calculations of the diffusion barrier near grain boundaries in different oxidation states revealed that the presence of oxidation products significantly increases the diffusion barrier. This is because the formation of oxidation products alters the atomic arrangement and electron cloud distribution at the grain boundaries, requiring carbon atoms to overcome a higher energy barrier for diffusion. This increased diffusion barrier has a dual impact on the carburizing process: on the one hand, it inhibits rapid carbon diffusion at grain boundaries, resulting in a more uniform carburizing process and improved carburized layer quality; on the other hand, an excessively high diffusion barrier can also lead to a slow carburizing rate, affecting production efficiency.

[0037] Step 2: Using density functional theory (DFT), we explore the essential reasons for microstructure changes from the electronic structure level, analyze the electronic structure characteristics and energy change laws of grain boundaries, mixed crystal structure, phase interface and new phase formation during carburizing and internal oxidation, and clarify the intrinsic relationship between microstructure and macroscopic properties.

[0038] Density functional theory is used to explore the essential reasons for microstructure changes at the electronic structure level. The electronic structure characteristics and energy change patterns of grain boundaries, mixed-grain structures, phase interfaces, and new phase formation during carburizing and internal oxidation are analyzed. Specifically: The VASP software based on the plane wave pseudopotential method was used to calculate the electronic structure of grain boundaries and phase interfaces using the PBE (Perdew-Burke-Ernzerhof) functional under the generalized gradient approximation (GGA). In order to accurately describe the interaction between electrons and ion cores, the projected fused wave (PAW) pseudopotential was selected for the plane wave pseudopotential.

[0039] The electronic structure of grain boundaries and phase interfaces was calculated using VASP software based on the plane-wave pseudopotential method and the PBE functional under the generalized gradient approximation, specifically: Grain boundary structures with different orientation differences were created by rotating and displacing ideal crystal structures. Two typical grain boundary types, Σ3 and Σ5, were studied in detail. For Σ3 grain boundaries, a coherent twin boundary model was adopted, in which the atomic arrangement at the interface exhibits high periodicity and symmetry; while Σ5 grain boundaries were constructed as incoherent grain boundary models, with relatively disordered atomic arrangement at the interface, exhibiting more defects and distortions.

[0040] The grain boundary energy is calculated using the following formula:

[0041] in, Grain boundary energy; The total energy of the system including grain boundaries; The energy of an ideal crystal with the same number of atoms; Let be the area of ​​the grain boundary. Calculations show that Σ3 grain boundaries, due to the high orderliness of their atomic arrangement, have a low grain boundary energy of approximately 0.5 J / m. 2 The Σ5 grain boundary, due to the presence of numerous defects and distortions, has a relatively high grain boundary energy, reaching 0.8 J / m. 2 .

[0042] To further analyze the impact of grain boundary segregation on interface stability, carbon and oxygen atoms were introduced into the grain boundary model, and the segregation energy was calculated using the following formula:

[0043] in, This refers to the segregation energy of carbon and oxygen atoms at the grain boundary; The total energy of the system after carbon and oxygen atoms have segregated at the grain boundaries; This refers to the grain boundary energy when there is no segregation. The number of segregating atoms; The chemical potential of the segregating atoms in the bulk phase is given. The results show that the segregation energies of carbon and oxygen atoms at the grain boundaries are both negative, indicating that they tend to segregate at the grain boundaries. The segregation of carbon and oxygen atoms significantly reduces the grain boundary energy and enhances the stability of the grain boundaries. This is because the segregating atoms form strong chemical bonds with the atoms at the grain boundaries, compensating for the energy loss at the grain boundaries.

[0044] Further calculations of the density of electronic states (DOS) at the grain boundaries revealed a significant change in the DOS near the Fermi level after the segregation of carbon and oxygen atoms. The 2p orbitals of carbon and oxygen atoms strongly hybridized with the 3d orbitals of iron atoms at the grain boundaries, forming new bonding and antibonding states. This not only altered the electronic structure at the grain boundaries but also affected their mechanical and chemical properties.

[0045] In constructing the phase interface model, phase interface models for austenite / cementite and oxide / matrix were established respectively. For the austenite / cementite phase interface, different crystallographic orientation relationships were considered, including the Kurdjumov-Sachs (KS) orientation relationship and the Nishiyama-Wassermann (NW) orientation relationship. Under the KS orientation relationship, the atomic arrangement of the austenite and cementite interface exhibits a certain regularity, and the interface energy is relatively low. Under the NW orientation relationship, the disorder of the atomic arrangement of the interface increases, and the interface energy is relatively high.

[0046] For oxide / matrix interfaces, the Al₂O₃ / Fe and Cr₂O₃ / Fe interfaces were studied in detail. Calculations show that chemical bonds are formed between the oxide and the matrix, and the interfacial energy is closely related to the type of oxide, its crystal structure, and the arrangement of interfacial atoms. The Al₂O₃ / Fe interface has a relatively low interfacial energy due to the stronger chemical bond between Al and Fe; while the Cr₂O₃ / Fe interface has a relatively high interfacial energy due to the weaker chemical bond between Cr and Fe.

[0047] Oxidation-induced grain boundary migration mechanism: Dynamic simulations of the interaction between grain boundaries and oxidation products during oxidation revealed that the nucleation and growth of oxidation products at grain boundaries significantly influence grain boundary migration behavior. In the initial stages of oxidation, oxygen atoms are adsorbed by alloying elements such as Al and Cr at grain boundaries, forming initial oxidation product nuclei. These oxidation product nuclei interact strongly with the grain boundaries, leading to distortion of the local grain boundary structure and an increase in grain boundary energy.

[0048] As the oxidation reaction proceeds, the oxidation product nuclei gradually grow, forming a continuous oxide layer. The growth of this oxide layer generates stress, which acts on the grain boundaries, becoming the driving force for grain boundary migration. During grain boundary migration, the relative position of the oxide product layer and the grain boundary changes, further influencing the migration rate and direction of the grain boundaries.

[0049] To gain a deeper understanding of the mechanism of oxidation-induced grain boundary migration, the activation energies of grain boundary migration at different oxidation stages were calculated. The results show that in the early stage of oxidation, due to the small size of the oxidation product nuclei, the hindrance to grain boundary migration is small, and the activation energy of grain boundary migration is relatively low; as the oxidation product layer grows, its hindrance to grain boundary migration increases, and the activation energy of grain boundary migration increases significantly.

[0050] During oxidation, grain boundary migration exhibits significant inhomogeneity. Due to variations in oxidation levels and stress distribution at different locations along the grain boundaries, bending and twisting occur during migration. This inhomogeneous grain boundary migration further promotes anomalous grain growth and the formation of mixed-grain structures. Anomalous grain growth refers to the phenomenon where a few grains grow at a much higher rate than others, resulting in uneven grain size distribution. In oxidation-induced grain boundary migration, the inhomogeneity of the migration allows some grains to receive more material during growth, leading to rapid growth and the formation of anomalous grains.

[0051] The formation of mixed-grain structures is due to the engulfing and fusion of grains with different orientations and sizes during grain boundary migration. In an oxidizing environment, the migration activity of grain boundaries increases, leading to more frequent interactions between grains. Some small grains are engulfed by larger grains during grain boundary migration, while some large grains split and recombine through interactions with other grains, ultimately forming a mixed-grain structure.

[0052] New phase formation and tissue evolution dynamics: Using Thermo-Calc software and the TCFE7 thermodynamic database, the activity, chemical potential, and phase equilibrium relationship of alloying elements during carburizing were calculated. By adjusting the carbon potential (0.8-1.2%), the precipitation sequence and thermodynamic driving force of cementite (Fe3C) and oxide phase under different carbon potential conditions were simulated.

[0053] Calculations show that in the initial stage of carburizing, a high carbon concentration gradient is formed in the austenitic matrix due to the rapid diffusion of carbon atoms. When the carbon concentration exceeds a certain threshold, cementite begins to nucleate at defects such as grain boundaries and dislocations. As the carburizing process proceeds, the cementite particles gradually grow, and their growth rate is controlled by the diffusion rate of carbon atoms and the interfacial energy.

[0054] Regarding the precipitation of oxide phases, simulation results show that during carburizing, oxygen atoms have a strong affinity for alloying elements such as Al and Cr, and preferentially combine with them to form oxides. Oxides such as Al2O3 and Cr2O3 have a greater nucleation driving force at grain boundaries, and therefore precipitate more easily at grain boundaries.

[0055] To verify the accuracy of the thermodynamic calculations, after simulating the precipitation sequence and thermodynamic driving force of cementite and oxide phases under different carbon potentials by adjusting the carbon potential, the calculations also included: first-principles calculations using VASP software. By constructing a model including cementite and oxide phases, the formation energy and electronic structure were calculated to verify the accuracy of the thermodynamic calculations. The results show that the formation energy of cementite is negative, indicating its thermodynamic stability; the formation energy of the oxide phase is also negative, consistent with the thermodynamic calculation results, further verifying the reliability of the thermodynamic calculations.

[0056] Under different carbon potentials, the size distribution of the new phases exhibits significant differences. When the carbon potential is low (0.8%), the precipitation of cementite and oxide phases is relatively uniform, and their sizes are small. As the carbon potential increases (1.2%), the growth rate of cementite accelerates, and its size increases, while the precipitation of oxide phases is suppressed, and their size decreases. This is because under high carbon potential conditions, the diffusion rate of carbon atoms accelerates, providing more material supply for the growth of cementite, while simultaneously inhibiting the diffusion of oxygen atoms, thereby reducing the formation of oxide phases.

[0057] The inhibitory effect of high carbon potential on grain boundary oxidation is mainly reflected in the following two aspects: On the one hand, the diffusion rate of carbon atoms is accelerated under high carbon potential, which increases the carbon concentration at the grain boundary and reduces the solubility of oxygen atoms at the grain boundary, thereby inhibiting grain boundary oxidation; on the other hand, the rapid growth of cementite under high carbon potential occupies the position of the grain boundary, hinders the contact between oxygen atoms and alloying elements, and further inhibits grain boundary oxidation.

[0058] Under low carbon potential conditions, oxides precipitate continuously along grain boundaries, leading to a decrease in grain boundary strength. This is because oxides have high hardness and brittleness, and continuous precipitation at grain boundaries creates weak points, reducing the bonding strength of the grain boundaries. When the material is subjected to external forces, cracks easily initiate and propagate at these weak points, resulting in a decrease in the material's mechanical properties.

[0059] Step 3: Based on COMSOL Multiphysics and combined with heat transfer, diffusion theory and phase transition theory, establish an internal oxidation kinetic model to explore the correlation mechanism between heat conduction and phase transition behavior during heating, carburizing and cooling processes.

[0060] Based on COMSOL Multiphysics, and combined with heat transfer, diffusion theory, and phase transition theory, an internal oxidation kinetic model is established, specifically as follows: Based on the powerful multiphysics modeling capabilities of COMSOL Multiphysics, a three-dimensional heat transfer-diffusion-phase transformation coupled model of carburized gears is constructed. Boundary conditions are defined for key components in the carburizing atmosphere, heating rate, and selection of cooling medium. At the same time, a grain size-dependent oxygen diffusion coefficient is introduced.

[0061] The key components of the carburizing atmosphere include CO partial pressure and CH4 partial pressure. Appropriate boundary conditions are set to simulate the interaction between the atmosphere and the gear surface during the actual carburizing process. For example, the CO partial pressure in the carburizing atmosphere is set to 0.1-0.3 atm, and the CH4 partial pressure is set to 0.05-0.1 atm to simulate a typical carburizing atmosphere environment.

[0062] The heating rate, as one of the important factors affecting the internal oxidation process, was set to a range of 5-15℃ / min in the model to study the internal oxidation behavior under different heating rates.

[0063] The choice of cooling medium has a crucial impact on the final performance of gears. This invention considers both oil quenching and gas quenching, and defines corresponding cooling boundary conditions based on actual conditions. For oil quenching, the temperature of the quenching oil is set to 80-100℃, and the heat transfer coefficient is set to 500-1000W / (m²). For gas quenching, the temperature of the cooling gas is set to 20-40℃, and the heat transfer coefficient is set to 100-300W / (m²). K).

[0064] To further investigate the influence of grain size on the internal oxidation process, a grain size-dependent oxygen diffusion coefficient is introduced, specifically: The relationship between the oxygen diffusion coefficient and the grain diameter is established as follows:

[0065] in, To introduce a grain size-dependent oxygen diffusion coefficient; The initial diffusion coefficient is 1 × 10⁻⁶. -9 m² / s; The grain diameter; The characteristic length is 0.1 μm. This relationship allows us to quantify the diffusion behavior of oxygen within the material at different grain sizes (1-10 levels), thereby analyzing the influence of grain size on the oxide layer growth rate.

[0066] When constructing the model, considering the complex physical phenomena in areas such as the tooth root and tooth surface during carburizing and internal oxidation, an unstructured mesh was used to refine the tooth root and tooth surface areas. By refining the local mesh, the changes in physical quantities such as temperature gradient, concentration gradient and stress distribution in these areas can be captured more accurately, thereby improving the accuracy of the simulation results.

[0067] An adaptive time-step algorithm is employed when solving the transient heat conduction and mass diffusion equations. This algorithm automatically adjusts the time step based on the rate of change of physical quantities. A smaller time step is used in regions of rapid change to ensure computational stability and accuracy, while a larger time step is used in regions of relatively stable change to improve computational efficiency. For example, in the initial stage of carburizing, due to the rapid diffusion of carbon and oxygen atoms, temperature and concentration changes drastically. In this case, the adaptive time-step algorithm automatically sets the time step to a small value, such as 0.01 s. In the later stage of carburizing, as the changes in physical quantities gradually stabilize, the time step gradually increases, such as to 0.1 s.

[0068] To verify the accuracy of the model, the simulation results were compared with experimental data. Experiments were conducted under the same process conditions to measure parameters such as the thickness of the internal oxide layer, hardness distribution, and microstructure of the carburized gears, and the results were compared and analyzed in detail with the simulation results. The results show that the simulation results and experimental data exhibit good consistency in trends. The deviation between the simulated and experimental values ​​for the internal oxide layer thickness is within 10%, and the simulated results for the hardness distribution also reflect the changing trend of the experimental measurements well. This fully verifies the accuracy and reliability of the constructed multiphysics coupling model, providing a solid foundation for further research on the influence of grain size on the internal oxidation process.

[0069] The regulatory mechanism of grain size on the internal oxidation process: Simulation analysis of the internal oxidation process under different grain sizes revealed that grain size has a significant regulatory effect on oxygen diffusion behavior and oxide layer growth. Under fine grain (level 10) conditions, the oxygen diffusion flux along the grain boundaries increases significantly due to the larger total grain boundary area. Simulation results show that the oxygen diffusion flux along the grain boundaries in fine-grained structures is 30% higher than that in coarse-grained structures (level 1), allowing oxygen atoms to penetrate into the material interior more quickly, thereby promoting oxide layer growth. Specifically, the internal oxide layer thickness in fine-grained structures increases by 25% compared to coarse-grained structures, indicating that grain refinement can significantly accelerate the internal oxidation process.

[0070] Further investigation into the competitive relationship between grain boundary oxidation and internal carbon diffusion revealed that while fine-grained structures promote oxygen penetration, they also accelerate carbide precipitation. During carburizing, carbon atoms diffuse into the grain interior driven by a concentration gradient. However, in fine-grained structures, due to the abundance of grain boundaries, carbon atoms more readily aggregate at these boundaries and combine with alloying elements to form carbides. This carbide precipitation consumes a significant amount of carbon atoms, thus affecting the carburizing process and creating an "oxidation-carburizing" interaction layer.

[0071] This interaction layer significantly impacts the final microstructure hardness and residual stress distribution of the gear. In fine-grained microstructures, the abundant precipitation of carbides significantly increases the hardness of the interaction layer, but also enhances the brittleness of the microstructure. Regarding residual stress, the volume changes accompanying the formation of the oxide layer and carbides result in substantial residual stress within the interaction layer. This residual stress may reduce the fatigue strength and service life of the gear.

[0072] Conversely, in coarse-grained microstructures, oxygen diffusion is slower, the growth of the inner oxide layer is relatively slow, but carbide precipitation is also relatively less, thus the influence of the "oxidation-carburization" interaction layer is relatively weaker. This indicates that grain size control can effectively alter the physicochemical behavior during the internal oxidation process, thereby optimizing the performance of carburized gears. By rationally controlling the grain size, it is possible to reduce the thickness of the inner oxide layer and the adverse effects of the "oxidation-carburization" interaction layer while ensuring a certain carburizing effect, thereby improving the overall performance of carburized gears.

[0073] Step 4: Establish a three-dimensional geometric model of the carburized gear, comprehensively consider temperature changes, atmosphere control, carburizing process parameters and cooling rate factors, simulate the dynamic changes of the internal temperature field and stress field of the gear during the heat treatment process, and analyze the influence of each factor on the gear performance.

[0074] A three-dimensional geometric model of the carburized gear is established, specifically as follows: Using CAD software such as SolidWorks or CATIA, a 3D geometric model of the carburized gear is constructed. During the modeling process, the design parameters of the gear are strictly followed to ensure the geometric accuracy of the model, including the accuracy of key parameters such as tooth profile, module, number of teeth, and tooth width. Taking a typical involute spur gear as an example, with a module of 5, 30 teeth, and a tooth width of 20mm, a high-quality 3D gear model is generated through precise parametric modeling.

[0075] The constructed 3D model was imported into COMSOL Multiphysics software for mesh generation. Considering the complex physical phenomena in the tooth root and tooth surface regions during carburizing and internal oxidation of the gear, unstructured meshes were used to refine the meshes in these regions to improve the accuracy of the simulation results. Through multiple experiments and optimizations, a suitable mesh size was determined. In the tooth root and tooth surface regions, the mesh size was refined to 0.1-0.2 mm, while in other regions of the gear, the mesh size was appropriately increased to 0.5-1 mm to balance computational accuracy and computational cost.

[0076] Accurately setting the thermophysical parameters of the material is crucial during the simulation. Based on material handbooks and relevant experimental data, thermophysical parameters of carburized gear steel, including thermal conductivity and coefficient of linear expansion, are obtained at different temperatures and input into the COMSOL model; for example, the thermal conductivity of carburized gear steel at room temperature is 45 W / (m²). As temperature increases, the thermal conductivity gradually decreases, reaching 30 W / (m²) at 900℃. The coefficient of linear expansion also varies with temperature; in the range of 20-100℃, the coefficient of linear expansion is 12×10⁻⁶. -6 / ℃, while in the range of 800-900℃, the coefficient of linear expansion increases to 15×10 -6 / ℃.

[0077] During the simulated carburizing process, the target temperature (900℃) and heating rate (10℃ / min) of the heating stage are set to simulate the heating process in actual production; the carburizing time (4-8h) is set by controlling the carbon potential in the carburizing atmosphere to keep it within a preset range (1.0-1.2%) to ensure that carbon atoms can fully penetrate into the gear surface; in the quenching stage, the quenching temperature is set (oil bath quenching is used in the quenching stage, and the oil bath temperature is set to 20-100℃), and the quenching time is adjusted according to the size and material properties of the gear. Simultaneously, the influence of the release of latent heat of phase transformation on the temperature field is considered during the simulation. Martensitic transformation is an exothermic process; the simulation simulates the effect of the martensitic transformation on the temperature gradient by setting the release amount and conditions of the latent heat. The latent heat of martensitic transformation is approximately 300-400 J / g. In the simulation, the release amount of latent heat is set to 350 J / g, and the release time and rate of the latent heat are determined based on the kinetic model of martensitic transformation.

[0078] The influence of process parameters on gear performance: Simulations of different temperature change rates, such as 10℃ / min and 20℃ / min, revealed a significant impact of temperature change rate on residual stress distribution. At a temperature change rate of 10℃ / min, the temperature gradient inside the gear is relatively small, resulting in a more uniform residual stress distribution. However, when the temperature change rate increases to 20℃ / min, the temperature gradient inside the gear increases significantly, leading to residual stress concentration in areas such as the tooth root and tooth surface. In the tooth root transition zone, due to changes in geometry, stress concentration is even more severe, with peak residual stress reaching 500-600 MPa. This indicates that rapid temperature changes exacerbate residual stress concentration, increasing the risk of gear fatigue failure.

[0079] The duration of carburizing time also significantly impacts gear performance. Comparing simulation results for carburizing times of 6 hours and 8 hours, it was found that the thickness of the carburized layer gradually increases with increasing carburizing time, but the rate of increase gradually slows down. At a carburizing time of 6 hours, the carburized layer thickness reaches 0.8-1.0 mm, while at 8 hours, the thickness increases to 1.2-1.4 mm. Simultaneously, extending the carburizing time also alters the distribution of residual stress; the peak residual stress decreases slightly, but the distribution range widens. This is because the longer carburizing process allows carbon atoms to diffuse more deeply into the gear's interior, thus changing the distribution of residual stress.

[0080] The flow rate of the cooling medium also significantly affects the cooling uniformity and residual stress distribution of gears. Simulations of different cooling medium flow rates revealed that at lower flow rates, the cooling rate on the gear surface is uneven, leading to uneven residual stress distribution and making the gear surface prone to distortion. Conversely, while excessively high flow rates accelerate cooling, they also generate greater thermal stress, which is detrimental to gear performance. Optimizing the cooling medium flow rate showed that controlling the flow rate within a certain range, such as 0.5-1.0 m / s, can effectively reduce the gear surface distortion rate, keeping it within ≤0.05 mm, while also reducing the concentration of residual stress.

[0081] In the tooth root transition zone, oxidation-induced microcracks are prone to form due to geometric stress concentration. Simulations of stress distribution and oxide layer growth in the tooth root transition zone under different process parameters revealed that the presence of the oxide layer further exacerbates stress concentration and reduces the fatigue strength of the tooth root. To mitigate the risk of stress concentration and microcrack formation in the tooth root transition zone, a process optimization strategy focusing on controlling grain size and cooling uniformity is proposed. Refining the grain size to level 8-9 effectively improves the material's strength and toughness, reducing the impact of stress concentration. Simultaneously, optimizing the cooling process ensures cooling uniformity, reducing thermal stress and thus lowering the tooth surface distortion rate, thereby improving the overall performance of the gear.

[0082] To verify the accuracy of the multi-scale simulation results, a series of experimental studies were conducted. The morphology of the oxides at the grain boundaries of the carburized gears was meticulously observed using scanning electron microscopy (SEM), clearly revealing the distribution characteristics of the oxides at the grain boundaries. The results show that the oxides exhibit a continuous or discontinuous network distribution at the grain boundaries, which is highly consistent with the nucleation and growth patterns of oxides at grain boundaries predicted by molecular dynamics simulations.

[0083] The distribution of alloying elements such as Al and Cr near grain boundaries was quantitatively analyzed using electron probe microanalysis (EPMA), and the concentration changes of alloying elements at grain boundaries and within grains were accurately measured. Experimental data showed that Al and Cr elements were significantly enriched at grain boundaries, which is consistent with the segregation behavior of alloying elements at grain boundaries predicted in molecular dynamics and DFT simulations, further verifying the predictions regarding the size and location of oxidation products in the simulation results.

[0084] The surface hardness of the carburized gears was tested using a Rockwell hardness tester. The results showed that the surface hardness values ​​were between 58 and 62 HRC, exhibiting good consistency with the COMSOL simulation results. The residual stress on the gear surface was measured using an X-ray residual stress analyzer. The measured stress values ​​were within the range of -400 to -600 MPa, with a consistency of over 90% with the simulation results. This demonstrates that the multi-scale simulation model can accurately predict the hardness and residual stress distribution of carburized gears during heat treatment, providing a reliable basis for process optimization.

[0085] Although the multi-scale simulation model has achieved good results in predicting the microstructure evolution and macroscopic performance of carburized gears, certain errors still exist. In-depth analysis revealed that the simulation process did not fully consider the influence of inclusions on grain boundary migration and oxidation processes, as well as the dynamic coarsening process of grain boundary precipitates. These factors led to discrepancies between the simulation results and experimental data.

[0086] To address these issues, a model parameter correction method based on experimental data is proposed. By comparing experimentally measured microstructure parameters and performance data with simulation results, optimization algorithms are used to adjust key parameters in the model, such as diffusion coefficient and grain boundary energy, to reduce simulation errors. After parameter correction, the multi-scale simulation model significantly improves the prediction accuracy of the microstructure evolution and macroscopic performance of carburized gears, more accurately reflecting the actual internal oxidation process in carburizing, and providing more reliable support for process optimization and product quality control.

[0087] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0088] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-scale simulation method for internal oxidation heat treatment of carburized gears, characterized in that, include: Step 1: Based on LAMMPS software, a molecular dynamics model of internal oxidation heat treatment of carburized gears was constructed to analyze the diffusion behavior of metal elements at the microscale, atomic migration paths and dynamic changes of crystal structure during the internal oxidation process of carburizing, revealing the intrinsic driving force of microstructure evolution. In step 1, a molecular dynamics model for the internal oxidation heat treatment of carburized gears is constructed based on LAMMPS software, specifically as follows: The EAM potential function is used to describe the interactions between atoms in a metallic system; Based on the chemical composition of carburized gears, the atomic types are clearly defined, and each atomic type is assigned attribute parameters including mass and charge. A simulation box is created using periodic boundary conditions; When initializing the atomic positions, Fe atoms are arranged according to a face-centered cubic lattice structure to construct a nanocrystalline model with initial grain boundary defects; The Nose-Hoover hot bath method was used to relax the simulation system to achieve thermal equilibrium. Step 2: Based on the evolution law of microstructure in carburizing and internal oxidation obtained in Step 1, density functional theory (DFT) is used to explore the essential reasons for the changes in microstructure from the electronic structure level. The electronic structure characteristics and energy change law of grain boundaries, mixed crystal structure, phase interface and new phase formation during carburizing and internal oxidation are analyzed to clarify the intrinsic relationship between microstructure and macroscopic performance. Density functional theory is used to explore the essential reasons for microstructure changes at the electronic structure level. The electronic structure characteristics and energy change patterns of grain boundaries, mixed-grain structures, phase interfaces, and new phase formation during carburizing and internal oxidation are analyzed. Specifically: The electronic structure of grain boundaries and phase interfaces was calculated using VASP software based on the plane wave pseudopotential method and the PBE functional under the generalized gradient approximation. Dynamic simulations of the interaction between grain boundaries and oxidation products during oxidation were performed, and the activation energies of grain boundary migration at different oxidation stages were calculated to understand the mechanism of oxidation-induced grain boundary migration. Using Thermo-Calc software and the TCFE7 thermodynamic database, the activity, chemical potential and phase equilibrium relationship of alloying elements during carburizing were calculated. By adjusting the carbon potential, the precipitation sequence and thermodynamic driving force of cementite and oxide phase under different carbon potential conditions were simulated. Step 3: Based on the evolution law of microstructure in carburizing internal oxidation obtained in Step 1 and the electronic structure characteristics and energy change law at the mesoscopic crystal scale obtained in Step 2, an internal oxidation kinetic model is established based on COMSOL Multiphysics and combined with heat transfer, diffusion theory and phase transition theory to explore the correlation mechanism between heat conduction and phase transition behavior during heating, carburizing and cooling processes. Based on COMSOL Multiphysics, and combined with heat transfer, diffusion theory, and phase transition theory, an internal oxidation kinetic model is established, specifically as follows: Based on COMSOL Multiphysics, a three-dimensional heat transfer-diffusion-phase transformation coupled model of carburized gears is constructed, and boundary conditions are defined for key components, heating rate and cooling medium selection in the carburizing atmosphere. At the same time, a grain size-dependent oxygen diffusion coefficient is introduced. The key components in the carburizing atmosphere include: CO partial pressure and CH4 partial pressure; the selection of the cooling medium includes oil quenching and gas quenching, and the corresponding cooling boundary conditions defined according to the actual situation include: temperature and heat transfer coefficient. Unstructured meshes are used to refine the tooth root and tooth surface regions, and an adaptive time step algorithm is used when solving the transient heat conduction and mass diffusion equations. Step 4: Based on the evolution law of the microstructure of carburizing internal oxidation obtained in Step 1 and the electronic structure characteristics and energy change law at the mesoscopic crystal scale obtained in Step 2, and the internal oxidation kinetic model established in Step 3 as the model basis, a three-dimensional geometric model of the carburized gear is established. Taking into account the factors of temperature change, atmosphere control, carburizing process parameters and cooling rate, the dynamic changes of the internal temperature field and stress field of the gear during the heat treatment process are simulated, and the influence of each factor on the gear performance is analyzed. A three-dimensional geometric model of the carburized gear is established, specifically as follows: A three-dimensional geometric model of the carburized gear was constructed using CAD software. The constructed three-dimensional model was then imported into COMSOL Multiphysics software for mesh generation, and unstructured meshes were used to refine the tooth root and tooth surface regions. The thermophysical parameters of carburized gear steel, including thermal conductivity and coefficient of linear expansion, are obtained at different temperatures and input into the COMSOL model; In the simulated carburizing process, the target temperature and heating rate of the heating stage are set to simulate the heating process in actual production; the carburizing time is set by controlling the carbon potential in the carburizing atmosphere to keep it within a preset range to ensure that carbon atoms can fully penetrate into the gear surface; in the quenching stage, the quenching temperature is set and the quenching time is adjusted according to the size of the gear and the material properties. Simultaneously considering the impact of the release of latent heat of phase transformation on the temperature field, the effect of martensitic transformation on the temperature gradient is simulated by setting the release amount and conditions of latent heat of phase transformation.

2. The multi-scale simulation method for internal oxidation heat treatment of carburized gears according to claim 1, characterized in that, In step 2, the plane wave pseudopotential is selected as the projected augmented wave pseudopotential.

3. The multi-scale simulation method for internal oxidation heat treatment of carburized gears according to claim 1, characterized in that, In step 2, the VASP software based on the plane wave pseudopotential method is used to calculate the electronic structure of the grain boundary and phase interface using the PBE functional under the generalized gradient approximation. Specifically: Grain boundary structures with different orientation differences are created by rotating and displacing an ideal crystal structure, and the grain boundary energy is calculated using the following formula: in, Grain boundary energy; The total energy of the system including grain boundaries; The energy of an ideal crystal with the same number of atoms; The area of ​​the grain boundary; Carbon and oxygen atoms are introduced into the grain boundary model, and the segregation energy is calculated using the following formula: in, This represents the segregation energy of carbon and oxygen atoms at the grain boundary; The total energy of the system after carbon and oxygen atoms have segregated at the grain boundaries; This refers to the grain boundary energy when there is no segregation. The number of segregating atoms; This represents the chemical potential of segregated atoms in the bulk phase. The electronic density of states at grain boundaries was further calculated, and austenite / cementite and oxide / matrix phase interface models were established when constructing the phase interface models. For the austenite / cementite phase interface, different crystallographic orientation relationships were considered, including the Kurdjumov-Sachs orientation relationship and the Nishiyama-Wassermann orientation relationship. For the oxide / matrix phase interface, Al2O3 / Fe and Cr2O3 / Fe phase interfaces were studied.

4. The multi-scale simulation method for internal oxidation heat treatment of carburized gears according to claim 1, characterized in that, Step 2, after simulating the precipitation sequence and thermodynamic driving force of cementite and oxide phases under different carbon potential conditions by adjusting the carbon potential, also includes: performing first-principles calculations using VASP software, calculating the formation energy and electronic structure by constructing a model containing cementite and oxide phases, and verifying the accuracy of the thermodynamic calculation results.

5. The multi-scale simulation method for internal oxidation heat treatment of carburized gears according to claim 1, characterized in that, In step 3, a grain size-dependent oxygen diffusion coefficient is introduced, specifically: The relationship between the oxygen diffusion coefficient and the grain diameter is established as follows: in, To introduce a grain size-dependent oxygen diffusion coefficient; The initial diffusion coefficient; The grain diameter; The characteristic length is denoted as .

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