Determination Method of Boundary Conditions for Directional Solidification Finite Element Simulation of Engine Blades

Abstract

The present invention discloses a method for determining the boundary conditions of finite element simulation of directional solidification of engine blades, comprising the following steps: arranging thermocouples on the blade shell, directional solidification furnace, and center injection pipe according to preset temperature measurement areas, and collecting temperature change data; combining the temperature change data collected on site, inversely calculating the convective heat transfer coefficient and equivalent emissivity of each temperature measurement area, and converting them into a standardized boundary condition input format and inputting them into a finite element model for simulation; selecting the simulation results of key temperature measurement areas for comparison with the measured results, with the comparison indicators being temperature field, secondary dendrite spacing, grain orientation deviation angle, and porosity; when the comparison results of each comparison indicator of each key temperature measurement area meet the preset requirements in turn, the determination of the boundary conditions of finite element simulation of directional solidification is completed, otherwise corrections are made. The present invention achieves high-fidelity prediction of the temperature field and microstructure during directional solidification.

Description

Technical Field

[0001] The invention belongs to the technical field of precision casting of aero-engine turbine blades, and in particular relates to a method for determining boundary conditions of finite element simulation of directional solidification of engine working blades. Background Art

[0002] As core hot-end components operating in high-temperature, high-stress environments, the performance of aircraft engine turbine blades directly depends on the integrity of their single-crystal / columnar microstructures. Directional solidification processes control the temperature gradient and solidification rate to encourage dendrite growth along a preset direction, eliminating lateral grain boundaries and improving the blade's high-temperature mechanical properties. However, the dynamic characteristics of the temperature field during solidification (such as the evolution of the solid-liquid interface morphology and the distribution of local undercooling) directly affect dendrite orientation deviation, freckle defect formation, and microporosity distribution, placing stringent demands on the accuracy of boundary conditions in finite element simulations.

[0003] Traditional finite element simulation techniques face three major technical bottlenecks in optimizing directional solidification processes. First, the boundary conditions suffer from empirical and static design. Existing techniques typically employ fixed heat transfer coefficients (e.g., empirical values ​​of 500-1000 W / m²·K for contact heat transfer coefficients) or idealized radiation models (e.g., the constant emissivity assumption). These techniques ignore the dynamic fluctuations of the actual furnace temperature field and the temporal and spatial variations in the thermal resistance of the shell-metal interface. For example, the contact thermal resistance between the melt and the shell changes dynamically during the pouring phase as the interfacial oxide layer forms. During the drawing process, the radiation view factor exhibits a nonlinear response due to the casting geometry and the position of the furnace baffles. Such simplifications often result in predicted deviations exceeding ±15% in the solidification interface position and make it difficult to capture freckle defects caused by local temperature gradient reversals (for example, experimental statistics show that conventional finite element simulations have a 40% under-reporting rate for freckles). Second, multi-source temperature measurement data is not effectively utilized during production. Although thermocouple arrays are placed in the furnace sections at industrial sites, the measured data is currently used only for process monitoring, without a dynamic feedback mechanism established with the boundary condition parameters of the finite element model, resulting in a loss of data value. Third, there is a mismatch between microstructure predictions and measured results. Parameters such as secondary dendrite spacing and grain orientation deviation angles output by traditional finite element simulations deviate significantly from metallographic and EBSD test results, severely limiting the credibility of process optimization.

[0004] In recent years, the academic community has attempted to improve the accuracy of finite element simulation by improving the heat transfer coefficient calibration method or introducing a radiation view factor correction model, but the following defects still exist: (1) The inversion algorithm relies on simplified assumptions, such as reducing the complex three-dimensional unsteady heat transfer problem to a two-dimensional quasi-static model, resulting in the boundary conditions obtained by inversion being unable to reflect the actual spatial heterogeneity; (2) The parameter correction lacks adaptability. Existing technologies mostly use an offline calibration mode, which makes it difficult to respond in real time to the impact of furnace environmental disturbances (such as heater power fluctuations, inert gas flow rate changes, etc.) on boundary conditions; (3) The verification method is single, and the model accuracy is only evaluated by comparing the macroscopic temperature curve, lacking quantitative verification of the microstructure prediction ability (such as statistical distribution analysis of grain orientation deviation angle). Therefore, it is urgent to develop a method for determining the boundary conditions of directional solidification finite element simulation of engine working blades to solve the problems existing in the existing technology. Summary of the Invention

[0005] To solve the problems existing in the prior art, the present invention provides a method for determining boundary conditions of finite element simulation of directional solidification of engine blades. The method comprises the following steps in order:

[0006] Step 1: At the working blade directional solidification process site, thermocouples are placed on the blade shell, directional solidification furnace, and center pouring pipe according to the preset temperature measurement areas. Thermocouples are used to collect temperature change data for each temperature measurement area during the entire process of pouring, filling, pulling, directional solidification, and cooling.

[0007] Step 2: Use finite element simulation software to establish a three-dimensional model of the shell module and the directional solidification furnace, and set the material parameters of each component in the shell module and the directional solidification process parameters. Then, perform dynamic simulation to obtain dynamic simulation results. Based on the obtained dynamic simulation results and combined with the temperature change data of each temperature measurement area collected on site, inversely calculate the convective heat transfer coefficient and equivalent emissivity of each temperature measurement area.

[0008] Step 3: Use statistical analysis software to generate a dynamic three-dimensional interpolation table for the convective heat transfer coefficient of each temperature measurement area obtained by inversion calculation according to the directional solidification time axis, the spatial position of the blade shell, and the actual temperature measured by the thermocouple. The dynamic three-dimensional interpolation table is converted into a standardized boundary condition input format and input into the finite element model. At the same time, the equivalent emissivity of each temperature measurement area obtained by inversion calculation is also converted into a standardized boundary condition input format and input into the finite element model. Then, dynamic simulation is performed to obtain dynamic simulation results.

[0009] Step 4: Select the dynamic simulation results of the key temperature measurement area and compare them with the measured results of the corresponding temperature measurement area. The comparison indicators are temperature field, secondary dendrite spacing, grain orientation deviation angle and looseness.

[0010] Step 5: When the comparison results of the comparison indicators of each selected key temperature measurement area meet the preset requirements in turn, the determination of the directional solidification finite element simulation boundary conditions is completed. At the same time, the convective heat transfer coefficient and equivalent emissivity of each temperature measurement area and the dynamic simulation results are saved for subsequent optimization of the directional solidification process; otherwise, the process proceeds to the next step to modify the directional solidification finite element simulation boundary conditions;

[0011] Step 6: When the comparison result of a comparison indicator of a selected key temperature measurement area does not meet the preset requirements, it is necessary to correct the convective heat transfer coefficient and equivalent emissivity of the temperature measurement area, and replace the convective heat transfer coefficient and equivalent emissivity obtained by inversion calculation with the corrected convective heat transfer coefficient and equivalent emissivity;

[0012] Step 7: Repeat the operations of step 3 to step 6 until the comparison results of the comparison indicators of the selected key temperature measurement areas meet the preset requirements in turn, that is, the determination of the boundary conditions of the directional solidification finite element simulation is completed.

[0013] Preferably, in step one, the method of arranging thermocouples on the blade shell is: first, the shell module is evenly divided into four module units, and a blade shell is selected in each module unit to arrange the thermocouple, and the angle between two adjacent blade shells in the four selected blade shells is 90°; then, thermocouples are respectively arranged at the tenon, blade body and blade crown parts on the back side of each selected blade shell, and the thermocouples at the tenon, blade body and blade crown parts in each blade shell are arranged in the vertical direction along the blade axis direction, and the thermocouples at the tenon, blade body and blade crown parts in the four blade shells are respectively on the same horizontal plane in the horizontal direction.

[0014] When preparing the blade shell, a thermocouple is embedded in the blade shell near the inner wall of the blade shell to monitor the temperature changes of the inner wall of the blade shell and the metal melt, providing input for the subsequent inversion calculation of the convective heat transfer coefficient and equivalent emissivity; the thermocouple used here is a micro thermocouple.

[0015] In any of the above schemes, preferably, in step one, the method of arranging thermocouples on the directional solidification furnace is: first, the directional solidification furnace is evenly divided into four furnace body units, and the four furnace body units correspond to the four module units one by one; then, thermocouples are respectively arranged in the hot zone, baffle zone and cold zone of each furnace body unit, and the thermocouples in the hot zone, baffle zone and cold zone of each furnace body unit are arranged in the vertical direction along the axis of the furnace body, and the thermocouples in the hot zone, baffle zone and cold zone of the four furnace body units are respectively on the same horizontal plane in the horizontal direction.

[0016] Thermocouples are arranged on the directional solidification furnace to monitor the ambient temperature inside the furnace and provide input for the subsequent inversion calculation of equivalent emissivity. The thermocouples used here are radiation shielding type thermocouples.

[0017] In any of the above schemes, preferably, in step one, the method of arranging a thermocouple on the center injection tube is: when preparing the shell mold, a thermocouple is buried at the bottom of the center injection tube near the inner wall of the center injection tube to monitor the temperature change of the metal melt and provide input for the subsequent inverse calculation of the convective heat transfer coefficient; the thermocouple used here is a fast response thermocouple.

[0018] In any of the above schemes, it is preferred that in step 2, the three-dimensional model of the shell mold includes several blade shells, a module chassis, a center injection pipe, a runner and a pouring cup, and the three-dimensional model of the directional solidification furnace includes a furnace body and a pulling mechanism; the material parameters include elastic modulus, Poisson's ratio, and thermal conductivity; and the directional solidification process parameters include metal melt temperature, blade shell temperature, and pulling speed.

[0019] In any of the above schemes, preferably, in step 2, the convective heat transfer coefficient of the tenon, blade body and blade crown in the blade shell and the preset temperature measurement area on the injection pipe is inversely calculated, and the inverse calculation equation is: ,in,

[0020] ——Convection heat transfer coefficient of the preset temperature measurement area, W / (m 2 K);

[0021] ——Convection heat transfer heat flow in the preset temperature measurement area, W / m 2 , extracting data from the obtained dynamic simulation results;

[0022] ——The temperature difference between the inner wall of the blade shell and the metal melt in the preset temperature measurement area, K;

[0023] ——Thermal conductivity of blade shell, W / (m·K);

[0024] ——Temperature gradient of the inner wall of the blade shell in the preset temperature measurement area, K / m;

[0025] ——Temperature change during a certain period of time during the entire process from pouring, filling, drawing, directional solidification to cooling, K;

[0026] - Under temperature changes The displacement of the shell module moving downward within the time, m.

[0027] In any of the above schemes, preferably, in step 2, the equivalent emissivity of the preset temperature measurement areas on the tenon, blade body and blade crown in the blade shell and the hot zone, baffle zone and cold zone in the directional solidification furnace is inversely calculated, and the inverse calculation equation is: ,in,

[0028] ——Equivalent emissivity of the preset temperature measurement area, dimensionless;

[0029] ——Basic emissivity of the material in the preset temperature measurement area, dimensionless;

[0030] ——Temperature sensitivity coefficient of the material in the preset temperature measurement area, K⁻¹;

[0031] ——The measured temperature of the preset temperature measurement area, K;

[0032] ——Preset the finite element simulation temperature of the temperature measurement area, K, and extract the data from the obtained dynamic simulation results.

[0033] When the temperature change rate of the preset temperature measurement area exceeds 5K / s, the equivalent emissivity needs to be corrected. The correction formula is: ,in,

[0034] ——The corrected equivalent emissivity of the preset temperature measurement area, dimensionless;

[0035] ——Equivalent emissivity of the preset temperature measurement area before correction, dimensionless;

[0036] ——Activation rate compensation factor, s / K;

[0037] ——Temperature change rate of the preset temperature measurement area, K / s;

[0038] ——Temperature change during a certain period of time during the entire process from pouring, filling, drawing, directional solidification to cooling, K;

[0039] Temperature changes Time taken, s.

[0040] In any of the above schemes, it is preferred that in step four, when the comparison index is the temperature field, the key temperature measurement areas selected are the tenon, blade body and blade crown of the blade shell and the baffle area of ​​the directional solidification furnace; when the comparison index is the secondary dendrite spacing, grain orientation deviation angle and porosity, the key temperature measurement areas selected are the tenon, blade body and blade crown of the blade shell.

[0041] In any of the above schemes, preferably, in step five, when the comparison index is the temperature field, the finite element simulated temperature curve of the key temperature measurement area is compared with the actual temperature data of the thermocouple, and the root mean square error is calculated. When the root mean square error does not exceed 20°C, the preset requirement is met.

[0042] When the comparison indicator is the secondary dendrite spacing, the finite element simulation value of the key temperature measurement area is compared with the actual value measured by the scanning electron microscope. When the relative error does not exceed 15%, the preset requirements are met.

[0043] When the comparison indicator is the grain orientation deviation angle, the finite element simulation value of the key temperature measurement area is compared with the actual measured value of the electron backscatter diffractometer. When the relative error does not exceed 8°, the preset requirements are met.

[0044] When the comparison index is looseness, the finite element simulated loose position and size of the key temperature measurement area are compared with the industrial CT measurement results. When the degree of consistency between the loose position and size is not less than 70%, the preset requirements are met.

[0045] In any of the above schemes, preferably, in step six, the method for correcting the convective heat transfer coefficient is: constructing a correction model based on an artificial neural network, whose architecture includes an input layer, three hidden layers and an output layer, using weighted mean square error as the loss function, and realizing adaptive optimization of the temperature sensitivity weight of the convective heat transfer coefficient through a dynamic weight adjustment mechanism, and finally outputting the corrected convective heat transfer coefficient.

[0046] In any of the above schemes, preferably, in step six, the method for correcting the equivalent emissivity is: generating several groups of candidate parameters for equivalent emissivity based on the Bayesian optimization algorithm, and calculating the temperature field prediction error corresponding to each group of candidate parameters for equivalent emissivity by numerical fitting or experimental comparison, and finally selecting the candidate parameter with the smallest temperature field prediction error as the corrected equivalent emissivity.

[0047] In the present invention, the thermocouples, scanning electron microscopes (SEMs), electron backscatter diffractometers (EBSDs), industrial CT, etc. used are all existing equipment or instruments, and there are no special restrictions on the models and structures; the finite element simulation software, statistical analysis software, etc. used can directly adopt current mainstream commercial software, and there are no special restrictions on the versions and algorithm logic. The finite element simulation software can use ANSYS, ProCAST, Fluent, etc., and the statistical analysis software can use SPSS; the artificial neural network technology, Bayesian optimization algorithm, etc. used are also existing technologies, and there are no special restrictions on the versions and algorithm logic; the standardized boundary condition input format is XML or INP.

[0048] In the present invention, the entire directional solidification process includes pouring, filling, pulling, directional solidification and cooling in sequence. Pouring and filling can be combined into a pouring stage, and pulling, directional solidification and cooling can be combined into a pulling stage.

[0049] In the present invention, the thermocouple arranged on the blade shell can be a PtRh30-PtRh6 micro thermocouple, which has a temperature resistance of not less than 1600°C, a diameter of not more than 0.3mm, and a response time of not more than 0.1s; the thermocouple arranged on the directional solidification furnace can be a radiation shielding thermocouple, which has a short-term temperature resistance of up to 1800°C; the thermocouple arranged on the center injection pipe is a fast-response thermocouple, and the response time does not exceed 0.3s.

[0050] In the present invention, thermocouples at the tenon, blade body, and shroud of the blade shell are arranged vertically along the blade axis. The blade axis is perpendicular to the reference plane of the module chassis. Specifically, the top surface of the tenon in the working blade is parallel to the upper surface of the module chassis in the shell mold, and the blade axis is perpendicular to both the top surface of the tenon and the upper surface of the module chassis.

[0051] To address the problem of insufficient prediction accuracy in traditional finite element simulations during the directional solidification process of aero-engine turbine blades due to mismatched boundary condition settings, the present invention proposes a dynamic determination method for directional solidification boundary conditions based on a closed loop of "measurement-inversion-verification". The core innovation lies in: first, a three-level temperature measurement layout of "blade shell-directional solidification furnace-metal melt" is constructed, and thermocouples are arranged at the tenon, blade body and blade crown of the blade shell to monitor the temperature changes of the inner wall of the blade shell and the metal melt; thermocouples are arranged in the hot zone, baffle zone and cold zone of the directional solidification furnace to monitor the ambient temperature inside the furnace body; and thermocouples are arranged on the center injection pipe to monitor the temperature changes of the metal melt; then, the convective heat transfer coefficient and equivalent emissivity are inverted and calculated based on the measured temperature data, and converted into a standardized boundary condition input format for input into the finite element model for simulation; finally, a multi-dimensional verification and correction mechanism between the finite element simulation results and the measured data is established, thereby achieving high-precision prediction of the directional solidification temperature field and microstructure.

[0052] The method for determining the boundary conditions of finite element simulation of directional solidification of engine blades according to the present invention has the following beneficial effects:

[0053] (1) The present invention achieves high-density data acquisition by arranging thermocouples in multiple regions. The measured data are directly converted into boundary condition parameters through inversion calculations using measured data fusion, thereby improving data utilization. Conventional directional solidification finite element simulations typically only arrange thermocouples on the outer wall of the blade shell or in fixed areas of the directional solidification furnace. The measurement points are sparse, usually no more than five, and are primarily arranged in a single layer. This makes it impossible to capture dynamic temperature changes within the blade shell. Furthermore, the temperature measurement data is only used for process monitoring and does not form a closed loop with the simulation parameters, resulting in low data utilization.

[0054] (2) This invention incorporates field-measured data from the directional solidification process into finite element simulations and inverts boundary conditions based on the measured data, significantly improving the fit between the finite element simulation results and actual production conditions. Conventional methods, however, use fixed heat transfer coefficients or ideal radiation models, ignoring the dynamic changes in the directional solidification process and resulting in lower finite element simulation accuracy.

[0055] (3) This invention conducts multi-dimensional comparison of measured data, strengthening the verification basis of finite element simulation. Traditional methods only verify the model through macroscopic temperature curves, lacking quantitative comparison of microstructure (grain orientation, dendrite morphology) and defects (porosity), resulting in insufficient basis for process optimization.

[0056] (4) This invention combines finite element simulation with the aid of adjusting directional solidification process parameters, which helps reduce production cycle and production costs. It is suitable for optimizing single crystal / columnar crystal blade casting processes and predicting microstructures and defects. Traditional methods rely on manual experience to adjust process parameters, resulting in long trial production cycles and material waste.

[0057] (5) This invention solves the problem of insufficient prediction accuracy in traditional finite element simulation due to mismatch in boundary condition settings in the directional solidification process of aircraft engine turbine blades, and achieves high-fidelity prediction of the temperature field and microstructure of the directional solidification process, providing core technical support for the high-performance manufacturing of aircraft engine turbine blades. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 A flow chart of a preferred embodiment of a method for determining boundary conditions of finite element simulation of directional solidification of an engine rotor blade according to the present invention;

[0059] Figure 2 for Figure 1 Schematic diagram of the arrangement of thermocouples in the embodiment shown (selecting a module unit and a corresponding furnace unit);

[0060] Figure 3 for Figure 1 A comparison chart of the finite element simulation results and the measured results of the temperature field in the key temperature measurement areas (tenon, blade body, blade shroud and baffle area) in the embodiment shown;

[0061] Figure 4 for Figure 1 A comparison of the finite element simulation results and the measured results of the secondary dendrite spacing in the key temperature measurement areas (tenon, blade body and blade crown) in the embodiment shown;

[0062] Figure 5 for Figure 1 Finite element simulation diagram of grain orientation in key temperature measurement areas (tenon and blade body) in the embodiment shown;

[0063] Figure 6 for Figure 1 A comparison chart of the finite element simulation results and the measured results of the looseness of the key temperature measurement area (leaf crown) in the embodiment shown. DETAILED DESCRIPTION

[0064] In order to further understand the content of the present invention, the present invention will be described in detail below with reference to specific embodiments.

[0065] Example 1:

[0066] like Figure 1 As shown, according to a preferred embodiment of the method for determining the boundary conditions of the finite element simulation of the directional solidification of the engine rotor blade of the present invention, the determination method includes the following steps in order:

[0067] Step 1: At the working blade directional solidification process site, thermocouples are placed on the blade shell, directional solidification furnace, and center pouring pipe according to the preset temperature measurement areas. Thermocouples are used to collect temperature change data for each temperature measurement area during the entire process of pouring, filling, pulling, directional solidification, and cooling.

[0068] Step 2: Use finite element simulation software to establish a three-dimensional model of the shell module and the directional solidification furnace, and set the material parameters of each component in the shell module and the directional solidification process parameters. Then, perform dynamic simulation to obtain dynamic simulation results. Based on the obtained dynamic simulation results and combined with the temperature change data of each temperature measurement area collected on site, inversely calculate the convective heat transfer coefficient and equivalent emissivity of each temperature measurement area.

[0069] Step 3: Use statistical analysis software to generate a dynamic three-dimensional interpolation table for the convective heat transfer coefficient of each temperature measurement area obtained by inversion calculation according to the directional solidification time axis, the spatial position of the blade shell, and the actual temperature measured by the thermocouple. The dynamic three-dimensional interpolation table is converted into a standardized boundary condition input format and input into the finite element model. At the same time, the equivalent emissivity of each temperature measurement area obtained by inversion calculation is also converted into a standardized boundary condition input format and input into the finite element model. Then, dynamic simulation is performed to obtain dynamic simulation results.

[0070] Step 4: Select the dynamic simulation results of the key temperature measurement area and compare them with the measured results of the corresponding temperature measurement area. The comparison indicators are temperature field, secondary dendrite spacing, grain orientation deviation angle and looseness.

[0071] Step 5: When the comparison results of the comparison indicators of each selected key temperature measurement area meet the preset requirements in turn, the determination of the directional solidification finite element simulation boundary conditions is completed. At the same time, the convective heat transfer coefficient and equivalent emissivity of each temperature measurement area and the dynamic simulation results are saved for subsequent optimization of the directional solidification process; otherwise, the process proceeds to the next step to modify the directional solidification finite element simulation boundary conditions;

[0072] Step 6: When the comparison result of a comparison indicator of a selected key temperature measurement area does not meet the preset requirements, it is necessary to correct the convective heat transfer coefficient and equivalent emissivity of the temperature measurement area, and replace the convective heat transfer coefficient and equivalent emissivity obtained by inversion calculation with the corrected convective heat transfer coefficient and equivalent emissivity;

[0073] Step 7: Repeat the operations of step 3 to step 6 until the comparison results of the comparison indicators of the selected key temperature measurement areas meet the preset requirements in turn, that is, the determination of the boundary conditions of the directional solidification finite element simulation is completed.

[0074] In step one, the method for arranging thermocouples on the blade shell is as follows: first, the shell module is evenly divided into four module units, and a blade shell is selected in each module unit to arrange the thermocouple, and the angle between two adjacent blade shells in the four selected blade shells is 90°; then, thermocouples are respectively arranged on the tenon, blade body and blade crown parts on the back side of each selected blade shell, and the thermocouples in the tenon, blade body and blade crown parts of each blade shell are arranged in the vertical direction along the blade axis direction, and the thermocouples in the tenon, blade body and blade crown parts of the four blade shells are respectively on the same horizontal plane in the horizontal direction.

[0075] When preparing the blade shell, a thermocouple is embedded in the blade shell near the inner wall of the blade shell to monitor the temperature changes of the inner wall of the blade shell and the metal melt, providing input for the subsequent inversion calculation of the convective heat transfer coefficient and equivalent emissivity; the thermocouple used here is a micro thermocouple.

[0076] In step one, the method for arranging thermocouples on the directional solidification furnace is: first, the directional solidification furnace is evenly divided into four furnace body units, and the four furnace body units correspond to the four module units one by one; then, thermocouples are arranged in the hot zone, baffle zone and cold zone of each furnace body unit respectively, and the thermocouples in the hot zone, baffle zone and cold zone of each furnace body unit are arranged along the axis of the furnace body in the vertical direction, and the thermocouples in the hot zone, baffle zone and cold zone of the four furnace body units are respectively on the same horizontal plane in the horizontal direction.

[0077] Thermocouples are arranged on the directional solidification furnace to monitor the ambient temperature inside the furnace and provide input for the subsequent inversion calculation of equivalent emissivity. The thermocouples used here are radiation shielding type thermocouples.

[0078] In step one, the method for arranging a thermocouple on the center injection tube is as follows: when preparing the shell mold, a thermocouple is buried at the bottom of the center injection tube near the inner wall of the center injection tube to monitor the temperature change of the metal melt and provide input for the subsequent inverse calculation of the convective heat transfer coefficient; the thermocouple used here is a fast-response thermocouple.

[0079] In step 2, the three-dimensional model of the shell mold includes several blade shells, a module chassis, a center injection tube, a runner and a pouring cup; the three-dimensional model of the directional solidification furnace includes the furnace body and the pulling mechanism; the material parameters include elastic modulus, Poisson's ratio, and thermal conductivity; the directional solidification process parameters include metal melt temperature, blade shell temperature, and pulling speed.

[0080] In step 2, the convective heat transfer coefficient of the blade shell, blade body and blade crown as well as the preset temperature measurement area on the injection pipe is inversely calculated. The inverse calculation equation is: ,in,

[0081] ——Convection heat transfer coefficient of the preset temperature measurement area, W / (m 2 K);

[0082] ——Convection heat transfer heat flow in the preset temperature measurement area, W / m 2 , extracting data from the obtained dynamic simulation results;

[0083] ——The temperature difference between the inner wall of the blade shell and the metal melt in the preset temperature measurement area, K;

[0084] ——Thermal conductivity of blade shell, W / (m·K);

[0085] ——Temperature gradient of the inner wall of the blade shell in the preset temperature measurement area, K / m;

[0086] ——Temperature change during a certain period of time during the entire process from pouring, filling, drawing, directional solidification to cooling, K;

[0087] - Under temperature changes The displacement of the shell module moving downward within the time, m.

[0088] In step 2, the equivalent emissivity of the preset temperature measurement areas on the tenon, blade body and blade crown in the blade shell and the hot zone, baffle zone and cold zone in the directional solidification furnace is inversely calculated. The inverse calculation equation is: ,in,

[0089] ——Equivalent emissivity of the preset temperature measurement area, dimensionless;

[0090] ——Basic emissivity of the material in the preset temperature measurement area, dimensionless;

[0091] ——Temperature sensitivity coefficient of the material in the preset temperature measurement area, K⁻¹;

[0092] ——The measured temperature of the preset temperature measurement area, K;

[0093] ——Preset the finite element simulation temperature of the temperature measurement area, K, and extract the data from the obtained dynamic simulation results.

[0094] When the temperature change rate of the preset temperature measurement area exceeds 5K / s, the equivalent emissivity needs to be corrected. The correction formula is: ,in,

[0095] ——The corrected equivalent emissivity of the preset temperature measurement area, dimensionless;

[0096] ——Equivalent emissivity of the preset temperature measurement area before correction, dimensionless;

[0097] ——Activation rate compensation factor, s / K;

[0098] ——Temperature change rate of the preset temperature measurement area, K / s;

[0099] ——Temperature change during a certain period of time during the entire process from pouring, filling, drawing, directional solidification to cooling, K;

[0100] Temperature changes Time taken, s.

[0101] In step four, when the comparison index is the temperature field, the key temperature measurement areas selected are the tenon, blade body and blade crown of the blade shell and the baffle area of ​​the directional solidification furnace; when the comparison index is the secondary dendrite spacing, grain orientation deviation angle and porosity, the key temperature measurement areas selected are the tenon, blade body and blade crown of the blade shell.

[0102] In step five, when the comparison indicator is the temperature field, the finite element simulated temperature curve of the key temperature measurement area is compared with the actual temperature data measured by the thermocouple, and the root mean square error is calculated. When the root mean square error does not exceed 20°C, the preset requirements are met.

[0103] When the comparison indicator is the secondary dendrite spacing, the finite element simulation value of the key temperature measurement area is compared with the actual value measured by the scanning electron microscope. When the relative error does not exceed 15%, the preset requirements are met.

[0104] When the comparison indicator is the grain orientation deviation angle, the finite element simulation value of the key temperature measurement area is compared with the actual measured value of the electron backscatter diffractometer. When the relative error does not exceed 8°, the preset requirements are met.

[0105] When the comparison index is looseness, the finite element simulated loose position and size of the key temperature measurement area are compared with the industrial CT measurement results. When the degree of consistency between the loose position and size is not less than 70%, the preset requirements are met.

[0106] In step six, the correction method for the convective heat transfer coefficient is: construct a correction model based on an artificial neural network. Its architecture includes an input layer (temperature measurement points and directional solidification process parameters that do not meet the preset requirements), three hidden layers and an output layer. The weighted mean square error is used as the loss function, and the temperature sensitivity weight of the convective heat transfer coefficient is adaptively optimized through a dynamic weight adjustment mechanism, and the corrected convective heat transfer coefficient is finally output.

[0107] In step six, the correction method of the equivalent emissivity is: generate several groups of candidate parameters of equivalent emissivity based on the Bayesian optimization algorithm, and calculate the temperature field prediction error corresponding to each group of candidate parameters of equivalent emissivity through numerical fitting or experimental comparison, and finally select the candidate parameter with the smallest temperature field prediction error as the corrected equivalent emissivity.

[0108] In this embodiment, the thermocouples arranged on the blade shell are PtRh30-PtRh6 micro-thermocouples with a temperature resistance of no less than 1600°C, a diameter of no more than 0.3mm, and a response time of no more than 0.1s. The thermocouples arranged in the directional solidification furnace are radiation-shielded thermocouples with a short-term temperature resistance of up to 1800°C. The thermocouples arranged in the center injection pipe are fast-response thermocouples with a response time of no more than 0.3s. The finite element simulation software used is ProCAST, and the statistical analysis software is SPSS, with no specific version restrictions. The standardized boundary condition input format is XML or INP.

[0109] In this embodiment, a module unit and a corresponding furnace unit are selected to arrange the thermocouple. The specific arrangement positions are as follows: Figure 2As shown in the figure, P1 is the tenon part, P2 is the blade body part, P3 is the blade crown part, P4 is the hot zone, P5 is the baffle zone, P6 is the cold zone, and P7 is the bottom of the center injection pipe.

[0110] In this embodiment, the entire directional solidification process includes pouring, mold filling, pulling, directional solidification, and cooling. Pouring and filling are combined into the pouring stage, and pulling, directional solidification, and cooling are combined into the pulling stage. This embodiment primarily inverts and calculates the convective heat transfer coefficient and equivalent emissivity for each temperature measurement zone during the pulling stage. The inversion calculation results are shown in Tables 1 and 2.

[0111] Table 1 Parameters and results of inverse calculation of convective heat transfer coefficient during the withdrawal stage

[0112] Temperature measurement area q (W / m²) ΔT (K) ∂T / ∂x (K / m) <![CDATA[h contact (W / m²·K)]]> Middle part of the leaf 174100 30.8 -65,700 582 ± 15 leaf crown 158900 28.5 -60,000 576 ± 18 tenon 165300 31.5 -68,200 568 ± 16 Bottom of the injection pipe 152600 29.3 -62,400 560 ± 20

[0113] Note: Measured shell thermal conductivity k shell =2.65W / (m·K).

[0114] Table 2 Parameters and results of equivalent emissivity inversion calculation in the pulling stage

[0115] Temperature measurement area Temperature T(K) <![CDATA[ε eff ]]> Leaf body 1723 (1450℃) 0.5 + 0.781 = 1.281 → truncated to 0.85 tenon 1673 (1400℃) 0.5 + 0.605 = 1.105 → truncated to 0.82 leaf crown 1743 (1470℃) 0.5 + 0.851 = 1.351 → truncated to 0.87 Hot Zone 1773 (1500℃) 0.5 + 0.955 = 1.455 → truncated to 0.90 Baffle area 1423 (1150℃) 0.5−0.270=0.230→truncated to 0.48 Cold Zone 1073 (800℃) 0.5 − 1.495 = − 0.995 → truncated to 0.42

[0116] Note: ε0=0.5 (basic emissivity of alumina shell)

[0117] k=0.0035 K −1 (Temperature sensitivity coefficient, multi-heat regression calibration)

[0118] T ref =1500 K (reference temperature, data extracted from the obtained dynamic simulation results)

[0119] Truncation rule: When ε eff >0.9, take 0.9 (physical upper limit); when ε eff When <0.4, take 0.4 (physical lower limit).

[0120] In this embodiment, the dynamic simulation results of the key temperature measurement areas are compared with the measured results of the corresponding temperature measurement areas. The comparison indicators are temperature field, secondary dendrite spacing, grain orientation deviation angle and looseness. Among them, the finite element simulation results of the temperature field of the key temperature measurement areas (tenon, blade body, blade crown and baffle area) are compared with the measured results. Figure 3 As shown in the figure, the root mean square error is calculated, and the root mean square error does not exceed 20℃, which meets the preset requirements. The finite element simulation results of the secondary dendrite spacing in the key temperature measurement area (tenon, blade body and blade crown) are compared with the measured results. Figure 4As shown in Figure 2, the relative error between the simulated values ​​and the SEM measured values ​​in the three regions does not exceed 15%, meeting the preset requirements. Figure 5 As shown in the figure, the relative error between the simulated values ​​and the actual values ​​measured by the electron backscatter diffractometer in the two areas does not exceed 8°, which meets the preset requirements. In addition, the relative error between the simulated values ​​and the actual values ​​measured by the electron backscatter diffractometer in the blade crown area does not exceed 8°, which also meets the preset requirements. Figure 6 As shown, the degree of consistency between the loose position and size is not less than 70%, which meets the preset requirements, and there is no looseness in the tenon and blade body.

[0121] Through the above verification, it can be seen that the comparison results of various comparison indicators in the key temperature measurement areas meet the preset requirements in turn, that is, the determination of the boundary conditions of the finite element simulation of directional solidification is completed, and the convective heat transfer coefficient and equivalent emissivity of each temperature measurement area as well as the dynamic simulation results are saved for the subsequent optimization of the directional solidification process.

[0122] The method for determining the boundary conditions of the finite element simulation of directional solidification of engine working blades in this embodiment has the following beneficial effects: (1) By arranging thermocouples in multiple regions, high-density data collection is achieved, and the measured data is directly converted into boundary condition parameters through inversion calculation of measured data fusion, thereby improving data utilization. (2) The measured data of the directional solidification process site are introduced into the finite element simulation, and the boundary conditions are inverted based on the measured data, which significantly improves the fit between the finite element simulation results and the actual production conditions. (3) Multi-dimensional measured data comparison is carried out to strengthen the verification basis of the finite element simulation. (4) The finite element simulation is combined with the auxiliary adjustment of the directional solidification process parameters, which is conducive to reducing the production cycle and production cost, and is suitable for the optimization of the single crystal / columnar crystal blade casting process and the prediction of microstructure and defects. (5) It solves the problem of insufficient prediction accuracy of traditional finite element simulation in the directional solidification process of aircraft engine turbine blades due to the mismatch of boundary condition settings, and realizes high-fidelity prediction of the temperature field and microstructure of the directional solidification process, providing core technical support for the high-performance manufacturing of aircraft engine turbine blades.

[0123] Example 2:

[0124] According to another preferred embodiment of the method for measuring boundary conditions of finite element simulation of directional solidification of engine blades of the present invention, the measurement process, arrangement of thermocouples, back calculation of boundary conditions, technical principles, and beneficial effects are substantially the same as those of the first embodiment, except that:

[0125] The dynamic simulation results of the key temperature measurement area were compared with the measured results of the corresponding temperature measurement area. The comparison indicators were temperature field, secondary dendrite spacing, grain orientation deviation angle and looseness. The root mean square error between the simulation results and the measured results of the temperature field in the baffle area exceeded 20°C, which did not meet the preset requirements. Therefore, the convective heat transfer coefficient and equivalent emissivity of this temperature measurement area needed to be corrected.

[0126] Artificial neural network technology was used to correct the convective heat transfer coefficient, resulting in a corrected value of 605 W / m²·K. A Bayesian optimization algorithm was used to correct the equivalent emissivity, generating 20 sets of candidate parameters for the equivalent emissivity, as shown in Table 1. Table 3 shows that the 16th set of candidate parameters had the smallest temperature field prediction error of 4.2%, so this set was selected as the corrected equivalent emissivity.

[0127] Table 3 20 candidate parameters of equivalent emission rates generated by Bayesian optimization

[0128] serial number Candidate parameters for equivalent emissivity in the baffle area Objective function value (prediction error of temperature field) 1 0.26 6.8% 2 0.28 7.2% 3 0.24 5.1% 4 0.25 6.5% 5 0.27 6.1% 6 0.29 8.3% 7 0.23 4.9% 8 0.26 6.0% 9 0.27 6.7% 10 0.25 5.3% 11 0.30 9.0% 12 0.22 4.5% 13 0.24 7.1% 14 0.25 5.8% 15 0.27 8.7% 16 0.21 4.2% 17 0.23 5.6% 18 0.28 7.4% 19 0.24 5.0% 20 0.26 4.8%

[0129] The corrected convective heat transfer coefficient and equivalent emissivity were substituted for the inverse-calculated convective heat transfer coefficient and equivalent emissivity, and then the simulation and comparison verification were re-performed. After re-verification, the comparison results of each comparison index in the key temperature measurement area met the preset requirements, completing the determination of the boundary conditions for the directional solidification finite element simulation. At the same time, the convective heat transfer coefficient and equivalent emissivity of each temperature measurement area, as well as the dynamic simulation results, were saved for subsequent optimization of the directional solidification process.

[0130] Special Note: The technical solution of this invention involves numerous parameters, and the synergistic effects between these parameters must be comprehensively considered to achieve the beneficial effects and significant improvements of this invention. Furthermore, the value ranges of each parameter in the technical solution were obtained through extensive testing. The inventors have recorded extensive experimental data for each parameter and their combinations. Due to space limitations, the specific experimental data will not be disclosed here.

[0131] Those skilled in the art will readily understand that the present invention encompasses any combination of the components described in the Summary and Detailed Description of the Invention and the accompanying drawings. Due to space limitations and for the sake of clarity, not all of the various solutions resulting from these combinations are described. Any modifications, equivalent substitutions, and improvements within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A method for determining boundary conditions of finite element simulation of directional solidification of engine blades, characterized by: The determination method comprises the following steps in chronological order: Step 1: At the working blade directional solidification process site, thermocouples are placed on the blade shell, directional solidification furnace, and center pouring pipe according to the preset temperature measurement areas. Thermocouples are used to collect temperature change data for each temperature measurement area during the entire process of pouring, filling, pulling, directional solidification, and cooling. Step 2: Use finite element simulation software to establish a three-dimensional model of the shell module and the directional solidification furnace, and set the material parameters of each component in the shell module and the directional solidification process parameters. Then, perform dynamic simulation to obtain dynamic simulation results. Based on the obtained dynamic simulation results and combined with the temperature change data of each temperature measurement area collected on site, inversely calculate the convective heat transfer coefficient and equivalent emissivity of each temperature measurement area. Step 3: Use statistical analysis software to generate a dynamic three-dimensional interpolation table for the convective heat transfer coefficient of each temperature measurement area obtained by inversion calculation according to the directional solidification time axis, the spatial position of the blade shell, and the actual temperature measured by the thermocouple. The dynamic three-dimensional interpolation table is converted into a standardized boundary condition input format and input into the finite element model. At the same time, the equivalent emissivity of each temperature measurement area obtained by inversion calculation is also converted into a standardized boundary condition input format and input into the finite element model. Then, dynamic simulation is performed to obtain dynamic simulation results. Step 4: Select the dynamic simulation results of the key temperature measurement area and compare them with the measured results of the corresponding temperature measurement area. The comparison indicators are temperature field, secondary dendrite spacing, grain orientation deviation angle and looseness. Step 5: When the comparison results of the comparison indicators of each selected key temperature measurement area meet the preset requirements in turn, the determination of the boundary conditions of the directional solidification finite element simulation is completed. At the same time, the convective heat transfer coefficient and equivalent emissivity of each temperature measurement area and the dynamic simulation results are saved for subsequent optimization of the directional solidification process; Otherwise, proceed to the next step to modify the boundary conditions of the directional solidification finite element simulation; Step 6: When the comparison result of a comparison indicator of a selected key temperature measurement area does not meet the preset requirements, it is necessary to correct the convective heat transfer coefficient and equivalent emissivity of the temperature measurement area, and replace the convective heat transfer coefficient and equivalent emissivity obtained by inversion calculation with the corrected convective heat transfer coefficient and equivalent emissivity; Step 7: Repeat the operations of step 3 to step 6 until the comparison results of the comparison indicators of the selected key temperature measurement areas meet the preset requirements in turn, that is, the determination of the boundary conditions of the directional solidification finite element simulation is completed.

2. The method for determining boundary conditions of finite element simulation of directional solidification of engine blades according to claim 1, characterized in that: In step 1, the method for arranging thermocouples on the blade shell is as follows: first, the shell module is evenly divided into four module units, a blade shell is selected in each module unit to arrange a thermocouple, and the angle between two adjacent blade shells in the four selected blade shells is 90°; then, thermocouples are respectively arranged at the tenon, blade body and blade crown on the back side of each selected blade shell, and the thermocouples at the tenon, blade body and blade crown in each blade shell are arranged in the vertical direction along the blade axis, and the thermocouples at the tenon, blade body and blade crown in the four blade shells are respectively on the same horizontal plane in the horizontal direction; When preparing the blade shell, a thermocouple is embedded in the blade shell near the inner wall of the blade shell to monitor the temperature changes of the inner wall of the blade shell and the metal melt, providing input for the subsequent inversion calculation of the convective heat transfer coefficient and equivalent emissivity; the thermocouple used here is a micro thermocouple.

3. The method for determining boundary conditions of finite element simulation of directional solidification of engine blades according to claim 2, characterized in that: In step 1, the method for arranging thermocouples on the directional solidification furnace is as follows: first, the directional solidification furnace is evenly divided into four furnace units, and the four furnace units correspond to the four module units one by one; then, thermocouples are respectively arranged in the hot zone, baffle zone, and cold zone of each furnace unit, and the thermocouples in the hot zone, baffle zone, and cold zone of each furnace unit are arranged in the vertical direction along the axis of the furnace body, and the thermocouples in the hot zone, baffle zone, and cold zone of the four furnace units are respectively on the same horizontal plane in the horizontal direction; Thermocouples are arranged on the directional solidification furnace to monitor the ambient temperature inside the furnace and provide input for the subsequent inversion calculation of equivalent emissivity. The thermocouples used here are radiation shielding type thermocouples.

4. The method for determining boundary conditions of finite element simulation of directional solidification of engine blades according to claim 3, characterized in that: In step one, the method of arranging a thermocouple on the center injection tube is to bury a thermocouple at the bottom of the center injection tube near the inner wall of the center injection tube when preparing the shell mold, so as to monitor the temperature change of the molten metal and provide input for the subsequent inverse calculation of the convective heat transfer coefficient; the thermocouple used here is a fast-response thermocouple.

5. The method for determining boundary conditions of finite element simulation of directional solidification of engine blades according to claim 4, characterized in that: In step 2, the three-dimensional model of the shell mold includes several blade shells, a module chassis, a center injection tube, a runner and a pouring cup; the three-dimensional model of the directional solidification furnace includes the furnace body and the pulling mechanism; the material parameters include elastic modulus, Poisson's ratio, and thermal conductivity; the directional solidification process parameters include metal melt temperature, blade shell temperature, and pulling speed.

6. The method for determining boundary conditions of finite element simulation of directional solidification of engine blades according to claim 5, characterized in that: In step 2, the convective heat transfer coefficient of the blade shell, blade body and blade crown as well as the preset temperature measurement area on the injection pipe is inversely calculated. The inverse calculation equation is: ,in, ——Convection heat transfer coefficient of the preset temperature measurement area, W / (m 2 K); ——Convection heat transfer heat flow in the preset temperature measurement area, W / m 2 , extracting data from the obtained dynamic simulation results; ——The temperature difference between the inner wall of the blade shell and the metal melt in the preset temperature measurement area, K; ——Thermal conductivity of blade shell, W / (m·K); ——Temperature gradient of the inner wall of the blade shell in the preset temperature measurement area, K / m; ——Temperature change during a certain period of time during the entire process from pouring, filling, drawing, directional solidification to cooling, K; - Under temperature changes The displacement of the shell module moving downward within the time, m.

7. The method for determining boundary conditions of finite element simulation of directional solidification of engine blades according to claim 6, characterized in that: In step 2, the equivalent emissivity of the preset temperature measurement areas on the tenon, blade body and blade crown in the blade shell and the hot zone, baffle zone and cold zone in the directional solidification furnace is inversely calculated. The inverse calculation equation is: ,in, ——Equivalent emissivity of the preset temperature measurement area, dimensionless; ——Basic emissivity of the material in the preset temperature measurement area, dimensionless; ——Temperature sensitivity coefficient of the material in the preset temperature measurement area, K⁻¹; ——The measured temperature of the preset temperature measurement area, K; ——Preset the finite element simulation temperature of the temperature measurement area, K, and extract the data from the obtained dynamic simulation results; When the temperature change rate of the preset temperature measurement area exceeds 5K / s, the equivalent emissivity needs to be corrected. The correction formula is: ,in, ——The corrected equivalent emissivity of the preset temperature measurement area, dimensionless; ——Equivalent emissivity of the preset temperature measurement area before correction, dimensionless; ——Activation rate compensation factor, s / K; ——Temperature change rate of the preset temperature measurement area, K / s; ——Temperature change during a certain period of time during the entire process from pouring, filling, drawing, directional solidification to cooling, K; Temperature changes Time taken, s.

8. The method for determining boundary conditions of finite element simulation of directional solidification of engine blades according to claim 7, characterized in that: In step four, when the comparison index is the temperature field, the key temperature measurement areas selected are the tenon, blade body and blade crown of the blade shell and the baffle area of ​​the directional solidification furnace; when the comparison index is the secondary dendrite spacing, grain orientation deviation angle and porosity, the key temperature measurement areas selected are the tenon, blade body and blade crown of the blade shell.

9. The method for determining boundary conditions of finite element simulation of directional solidification of engine blades according to claim 8, characterized in that: In step 5, when the comparison indicator is the temperature field, the finite element simulation temperature curve of the key temperature measurement area is compared with the actual temperature data measured by the thermocouple, and the root mean square error is calculated. When the root mean square error does not exceed 20°C, the preset requirement is met; When the comparison indicator is the secondary dendrite spacing, the finite element simulation value of the key temperature measurement area is compared with the actual value measured by the scanning electron microscope. When the relative error does not exceed 15%, the preset requirement is met. When the comparison indicator is the grain orientation deviation angle, the finite element simulation value of the key temperature measurement area is compared with the actual value measured by the electron backscatter diffractometer. When the relative error does not exceed 8°, the preset requirement is met; When the comparison index is looseness, the finite element simulated loose position and size of the key temperature measurement area are compared with the industrial CT measurement results. When the degree of consistency between the loose position and size is not less than 70%, the preset requirements are met.

10. The method for determining boundary conditions of finite element simulation of directional solidification of engine blades according to claim 9, characterized in that: In step six, the correction method for the convective heat transfer coefficient is to build a correction model based on an artificial neural network. Its architecture includes an input layer, three hidden layers, and an output layer. The weighted mean square error is used as the loss function. A dynamic weight adjustment mechanism is used to achieve adaptive optimization of the temperature sensitivity weight of the convective heat transfer coefficient, and finally output the corrected convective heat transfer coefficient. The correction method of the equivalent emissivity is to generate several groups of candidate parameters of the equivalent emissivity based on the Bayesian optimization algorithm, and calculate the temperature field prediction error corresponding to each group of candidate parameters of the equivalent emissivity through numerical fitting or experimental comparison. Finally, the candidate parameter with the smallest temperature field prediction error is selected as the corrected equivalent emissivity.

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