Determination method of engine working blade directional solidification finite element simulation boundary condition

Abstract

The invention discloses an engine working blade directional solidification finite element simulation boundary condition determination method, which comprises the following steps: arranging thermocouples on a blade shell, a directional solidification furnace and a central casting pipe according to a preset temperature measurement area, and collecting temperature change data; in combination with temperature change data collected on site, the convective heat transfer coefficient and the equivalent emissivity of each temperature measurement area are inversely calculated, and the convective heat transfer coefficient and the equivalent emissivity are converted into a standardized boundary condition input format to be input into a finite element model for simulation; the simulation result of the key temperature measurement area is selected to be compared with the actual measurement result, and the comparison indexes are the temperature field, the secondary dendritic crystal spacing, the grain orientation deviation angle and the looseness in sequence; and when the comparison results of the comparison indexes of the key temperature measurement areas meet the preset requirements in sequence, determining that the directional solidification finite element simulation boundary conditions are measured, or else, correcting the directional solidification finite element simulation boundary conditions. According to the method, high-fidelity prediction of the temperature field and the microstructure in the directional solidification process is realized.

Description

Technical Field

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

[0002] As a core hot-end component in a high-temperature and high-stress environment, the performance of aero-engine turbine blades directly depends on the integrity of single-crystal / columnar crystal structures. The directional solidification process controls the temperature gradient and solidification rate to promote the growth of dendrites along a preset direction, thereby eliminating transverse grain boundaries and improving the high-temperature mechanical properties of the blades. 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 the dendrite orientation deviation, the formation of freckle defects, and the distribution of micro-porosity, which pose strict requirements on the accuracy of the finite element simulation boundary conditions.

[0003] Traditional finite element simulation technology faces three major technical bottlenecks in the optimization of the directional solidification process: First, there are empirical and static defects in the setting of boundary conditions. Existing technologies usually adopt a fixed heat transfer coefficient (such as an empirical value of the contact heat transfer coefficient of 500 - 1000 W / m²·K) or an idealized radiation model (such as a constant emissivity assumption), ignoring the dynamic fluctuation characteristics of the actual furnace temperature field and the spatio-temporal differences in the thermal resistance at the mold-metal interface. For example, the contact thermal resistance between the melt and the mold during the pouring stage changes dynamically with the formation of the interface oxide layer, and the radiation view factor during the pulling process shows a non-linear response due to changes in the casting geometry and the position of the furnace baffle. Such simplified treatments lead to a prediction deviation of the solidification interface position generally exceeding ±15%, and it is difficult to capture freckle defects caused by local temperature gradient inversion (such as experimental statistics showing that the false negative rate of traditional finite element simulation for freckles is as high as 40%). Second, multi-source temperature measurement data during production is not effectively utilized. Although thermocouple arrays are arranged in the furnace body in the industrial field, the measured data is currently only used for process monitoring and no dynamic feedback mechanism is established with the boundary condition parameters of the finite element model, resulting in the loss of data value. Third, there is a mismatch between the predicted and measured results of the microstructure. The deviation between parameters such as the secondary dendrite arm spacing and the grain orientation deviation angle output by traditional finite element simulation and the results of metallographic and EBSD detection is relatively significant, seriously restricting the credibility of process optimization.

[0004] In recent years, the academic community has attempted to improve the accuracy of finite element simulations by improving the heat transfer coefficient calibration method or introducing a radiation view factor correction model. However, there are still the following defects: (1) The inversion algorithm relies on simplified assumptions. For example, a complex three-dimensional unsteady heat transfer problem is reduced 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 self-adaptability. Existing technologies mostly adopt an offline calibration mode and it is difficult to respond in real time to the influence of furnace environment disturbances (such as heater power fluctuations, inert gas flow rate changes, etc.) on the boundary conditions; (3) The verification method is single. Only the model accuracy is evaluated by comparing the macroscopic temperature curves, lacking quantitative verification of the microstructural prediction ability (such as the statistical distribution analysis of grain orientation deviation angles). Therefore, there is an urgent need to develop a method for determining the boundary conditions of the finite element simulation of the directional solidification of engine working blades to solve the problems existing in the existing technologies. Summary of the Invention

[0005] To solve the problems existing in the existing technologies, the present invention provides a method for determining the boundary conditions of the finite element simulation of the directional solidification of engine working blades. The determination method includes the following steps in sequence:

[0006] Step 1: At the site of the directional solidification process of the working blade, thermocouples are arranged on the blade shell mold, the directional solidification furnace and the middle runner according to the preset temperature measurement areas, and the temperature change data of each temperature measurement area during the whole process of pouring, filling, drawing, directional solidification to cooling are collected through the thermocouples respectively;

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

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

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

[0010] Step Five: When the comparison results of the comparison indicators for each key temperature measurement area selected all meet the preset requirements in sequence, the determination of the boundary conditions for the directional solidification finite element simulation is completed. Meanwhile, 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; otherwise, proceed to the next step to correct the boundary conditions for the directional solidification finite element simulation.

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

[0012] Step Seven: Repeat the operations in Step Three to Step Six until the comparison results of the comparison indicators for each key temperature measurement area selected all meet the preset requirements in sequence, that is, the determination of the boundary conditions for the directional solidification finite element simulation is completed.

[0013] Preferably, in Step One, the method of arranging thermocouples on the blade shell is as follows: First, evenly divide the shell module into four module units, select a blade shell in each module unit to arrange thermocouples, and the angle between two adjacent blade shells among the four selected blade shells is 90°; then, arrange thermocouples at the tenon, blade body, and blade crown parts on the back side of the blade in each selected blade shell respectively. The thermocouples at the tenon, blade body, and blade crown parts in each blade shell are arranged along the blade axis direction in the vertical direction, and the thermocouples at the tenon, blade body, and blade crown parts in the four blade shells are on the same horizontal plane in the horizontal direction.

[0014] When preparing the blade shell, bury the thermocouples at positions close to the inner wall of the blade shell to monitor the temperature changes of the inner wall of the blade shell and the molten metal, providing input for the subsequent inverse calculation of the convective heat transfer coefficient and equivalent emissivity; the thermocouples used here are micro-thermocouples.

[0015] Preferably, in any of the above solutions, in Step One, the method of arranging thermocouples on the directional solidification furnace is as follows: First, evenly divide the directional solidification furnace into four furnace body units, and the four furnace body units correspond to the four module units one by one; then, arrange thermocouples at the hot zone, baffle zone, and cold zone parts in each furnace body unit respectively. The thermocouples at the hot zone, baffle zone, and cold zone parts in each furnace body unit are arranged along the furnace axis direction in the vertical direction, and the thermocouples at the hot zone, baffle zone, and cold zone parts in the four furnace body units are on the same horizontal plane in the horizontal direction.

[0016] A thermocouple is arranged on the directional solidification furnace to monitor the ambient temperature inside the furnace body and provide input for the subsequent inversion calculation of the equivalent emissivity. The thermocouple used here is a radiation-shielded thermocouple.

[0017] In any of the above solutions, preferably, in step one, the method of arranging the thermocouple on the ingate pipe is as follows: when preparing the mold shell module, a thermocouple is buried at a position close to the inner wall of the bottom of the ingate pipe to monitor the temperature change of the molten metal and provide input for the subsequent inversion calculation of the convective heat transfer coefficient. The thermocouple used here is a fast-response thermocouple.

[0018] In any of the above solutions, preferably, in step two, the three-dimensional model of the mold shell module includes several blade mold shells, a module chassis, an ingate pipe, a runner, and a sprue 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; the directional solidification process parameters include molten metal temperature, blade mold shell temperature, and pulling speed.

[0019] In any of the above solutions, preferably, in step two, the convective heat transfer coefficients of the tenons, blade bodies, and blade crowns in the blade mold shell and the preset temperature measurement areas on the ingate pipe are inversely calculated, and the inverse calculation equation is , where

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

[0021] ——The convective heat transfer flux of the preset temperature measurement area, W / m 2 , and data is extracted from the obtained dynamic simulation results;

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

[0023] ——The thermal conductivity of the blade mold shell, W / (m·K);

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

[0025] ——The temperature change during a certain period from pouring, filling, pulling, directional solidification to cooling, K;

[0026] ——During the time of temperature change , the displacement of the mold shell module moving downward, m.

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

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

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

[0030] —— The 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] —— The finite element simulation temperature of the preset temperature measurement area, K, and data are extracted from the obtained dynamic simulation results.

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

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

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

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

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

[0038] —— The temperature change during a certain period from pouring, filling, drawing, directional solidification to cooling, K;

[0039] —— The temperature change The time used, s.

[0040] Preferably, in any of the above solutions, 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 zone of the directional solidification furnace; when the comparison indices are the secondary dendrite arm spacing, grain orientation deviation angle and porosity, the key temperature measurement areas selected are all the tenon, blade body and blade crown of the blade shell.

[0041] Preferably, in any of the above solutions, in step five, when the comparison index is the temperature field, the finite element simulation temperature curve of the key temperature measurement area is compared with the thermocouple measured temperature data, and the root mean square error is calculated. When the root mean square error does not exceed 20 °C, the preset requirements are met.

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

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

[0044] When the comparison index is porosity, the finite element simulated porosity position and size of the key temperature measurement area are compared with the industrial CT measured result. When the coincidence degree of the porosity position and size is not less than 70%, the preset requirements are met.

[0045] Preferably, in any of the above solutions, in step six, the correction method for the convective heat transfer coefficient is as follows: a correction model is constructed based on an artificial neural network, and its architecture includes an input layer, three hidden layers and an output layer. The weighted mean square error is used as the loss function, and the adaptive optimization of the temperature sensitivity weight of the convective heat transfer coefficient is realized through a dynamic weight adjustment mechanism, and finally the corrected convective heat transfer coefficient is output.

[0046] Preferably, in any of the above solutions, in step six, the correction method for the equivalent emissivity is as follows: several groups of candidate parameters of the equivalent emissivity are generated based on the Bayesian optimization algorithm, and the temperature field prediction errors corresponding to each group of candidate parameters of the equivalent emissivity are calculated respectively by means of numerical fitting or experimental comparison. Finally, the candidate parameter with the smallest temperature field prediction error is selected as the corrected equivalent emissivity.

[0047] In the present invention, the thermocouple, scanning electron microscope (SEM), electron backscatter diffraction instrument (EBSD), 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 the current mainstream commercial software, and there are no special restrictions on the versions and algorithm logics. The finite element simulation software can adopt ANSYS, ProCAST, Fluent, etc., and the statistical analysis software can adopt SPSS; the artificial neural network technology, Bayesian optimization algorithm, etc. used are also all existing technologies, and there are no special restrictions on the versions and algorithm logics; the standardized boundary condition input format is XML or INP.

[0048] In the present invention, the whole process of the directional solidification process successively includes processes such as pouring, filling, pulling, directional solidification, and cooling. The pouring and filling can be combined into a pouring stage, and the pulling, directional solidification, and cooling can be combined into a pulling stage.

[0049] In the present invention, the thermocouples arranged on the blade shell can adopt PtRh30-PtRh6 micro thermocouples, with a temperature resistance of not less than 1600 °C, a diameter of not more than 0.3 mm, and a response time of not more than 0.1 s; the thermocouples arranged on the directional solidification furnace can adopt radiation shielded thermocouples, with a short-term temperature resistance reaching 1800 °C; the thermocouples arranged on the tundish are fast response thermocouples, with a response time of not more than 0.3 s.

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

[0051] Aiming at the problem of insufficient prediction accuracy caused by the mismatch of boundary condition settings in the traditional finite element simulation of the directional solidification process of aeroengine turbine blades, the present invention proposes a dynamic measurement method for the directional solidification boundary conditions based on the "measurement-inversion-verification" closed loop. Its core innovation lies in: First, construct a three-level temperature measurement layout of "blade shell-directional solidification furnace-metal melt". Thermocouples are respectively arranged at the tenon, blade body, and blade crown parts of the blade shell to monitor the temperature changes of the inner wall of the blade shell and the metal melt. Thermocouples are respectively arranged at the hot zone, baffle zone, and cold zone parts of the directional solidification furnace to monitor the ambient temperature inside the furnace body. Thermocouples are arranged on the tundish to monitor the temperature changes of the metal melt. Then, based on the measured temperature data, inversely calculate the convective heat transfer coefficient and the equivalent emissivity, and convert them into a standardized boundary condition input format and input it into the finite element model for simulation. Finally, establish a multi-dimensional verification and correction mechanism for the finite element simulation results and the measured data, so as to achieve high-precision prediction of the directional solidification temperature field and microstructure.

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

[0053] (1) By arranging thermocouples in multiple regions, the present invention realizes high-density data acquisition, and directly converts the measured data into boundary condition parameters through inversion calculation of the measured data fusion, improving the data utilization rate. In traditional directional solidification finite element simulations, thermocouples are usually arranged only on the outer wall of the blade shell or in fixed regions of the directional solidification furnace. The measurement points are sparse, usually no more than 5, and mainly arranged in a single layer, unable to capture the dynamic temperature changes inside the blade shell. Moreover, the temperature measurement data is only used for process monitoring and does not form a closed loop with the simulation parameters, resulting in a low data utilization rate.

[0054] (2) The present invention introduces the measured data from the directional solidification process site into the finite element simulation, and inverts the boundary conditions based on the measured data, significantly improving the fit between the finite element simulation results and the actual production conditions. Traditional methods use fixed heat transfer coefficients or ideal radiation models, ignoring the dynamic changes in the directional solidification process, resulting in low accuracy of the finite element simulation.

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

[0056] (4) The present invention combines finite element simulation to assist in adjusting the directional solidification process parameters, which is beneficial to reducing the production cycle and production cost, and is applicable to the optimization of single crystal / columnar crystal blade casting processes and the prediction of microstructures and defects. Traditional methods rely on manual experience to adjust process parameters, resulting in problems such as long trial production cycles and material waste.

[0057] (5) The present invention solves the problem of insufficient prediction accuracy caused by mismatched boundary condition settings in the traditional finite element simulation of the directional solidification process of aeroengine turbine blades, realizing high-fidelity prediction of the temperature field and microstructure during the directional solidification process, and providing core technical support for the high-performance manufacturing of aeroengine turbine blades. Description of the Drawings

[0058] Figure 1 It is a flowchart of a preferred embodiment of the method for determining the boundary conditions of the finite element simulation of the directional solidification of the working blade of the engine according to the present invention;

[0059] Figure 2 It is Figure 1 A schematic diagram of the arrangement of thermocouples in the illustrated embodiment (selecting a module unit and a corresponding furnace body unit);

[0060] Figure 3 It is Figure 1 A comparison diagram of the finite element simulation results and the measured results of the temperature field in the key temperature measurement regions (tenon, blade body, blade crown, and baffle region) in the illustrated embodiment;

[0061] Figure 4 For Figure 1 Comparison diagram of the finite element simulation results and the measured results of the secondary dendrite arm spacing in the key temperature measurement regions (tenon, blade body, and blade crown) in the shown embodiment;

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

[0063] Figure 6 For Figure 1 Comparison diagram of the finite element simulation results and the measured results of the porosity in the key temperature measurement region (blade crown) in the shown embodiment. Detailed implementation manners

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

[0065] Embodiment 1:

[0066] As Figure 1 shown, according to a preferred embodiment of the method for determining the boundary conditions of the finite element simulation of the directionally solidified working blade of the present invention, the determination method includes the following steps in sequence:

[0067] Step 1: At the site of the directionally solidified process of the working blade, thermocouples are arranged on the blade shell mold, the directional solidification furnace, and the middle runner according to the preset temperature measurement regions, and the temperature change data of each temperature measurement region during the whole process of pouring, filling, drawing, directional solidification to cooling are collected respectively through the thermocouples;

[0068] Step 2: Use the finite element simulation software to establish a three-dimensional model of the shell mold module and the directional solidification furnace, set the material parameters and directional solidification process parameters of each component in the shell mold module, and then perform dynamic simulation to obtain the dynamic simulation results; according to the obtained dynamic simulation results, and in combination with the temperature change data of each temperature measurement region collected on site, the convective heat transfer coefficient and the equivalent emissivity of each temperature measurement region are inversely calculated respectively;

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

[0070] Step 4: Compare the dynamic simulation results of the selected key temperature measurement regions with the measured results of the corresponding temperature measurement regions. The comparison indicators are, in sequence, the temperature field, secondary dendrite arm spacing, grain orientation deviation angle, and porosity;

[0071] Step 5: When the comparison results of each comparison indicator for each selected key temperature measurement region all meet the preset requirements in sequence, the determination of the boundary conditions for the directional solidification finite element simulation is completed. At the same time, save the convective heat transfer coefficient, equivalent emissivity, and dynamic simulation results of each temperature measurement region for the subsequent optimization of the directional solidification process; otherwise, proceed to the next step to correct the boundary conditions for the directional solidification finite element simulation;

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

[0073] Step 7: Repeat the operations in Steps 3 to 6 until the comparison results of each comparison indicator for each selected key temperature measurement region all meet the preset requirements in sequence, that is, the determination of the boundary conditions for the directional solidification finite element simulation is completed.

[0074] In Step 1, the method of arranging thermocouples on the blade shell is as follows: First, evenly divide the shell module into four module units, select a blade shell in each module unit to arrange thermocouples, and the angle between two adjacent blade shells among the four selected blade shells is 90°; then, arrange thermocouples at the tenon, blade body, and blade crown parts on the back side of the blade in each selected blade shell respectively. The thermocouples at the tenon, blade body, and blade crown parts in each blade shell are arranged along the blade axis direction in the vertical direction, and the thermocouples at the tenon, blade body, and blade crown parts in the four blade shells are on the same horizontal plane in the horizontal direction.

[0075] When preparing the blade shell, bury the thermocouples at positions close to the inner wall of the blade shell to monitor the temperature changes of the inner wall of the blade shell and the molten metal, providing input for the subsequent inverse calculation of the convective heat transfer coefficient and equivalent emissivity; the thermocouples used here are micro-thermocouples.

[0076] In Step 1, the method of arranging thermocouples on the directional solidification furnace is as follows: First, evenly divide the directional solidification furnace into four furnace body units, and the four furnace body units correspond to the four module units one by one; then, arrange thermocouples at the hot zone, baffle zone, and cold zone parts in each furnace body unit respectively. The thermocouples at the hot zone, baffle zone, and cold zone parts in each furnace body unit are arranged along the furnace axis direction in the vertical direction, and the thermocouples at the hot zone, baffle zone, and cold zone parts in the four furnace body units are on the same horizontal plane in the horizontal direction.

[0077] A thermocouple is arranged on the directional solidification furnace to monitor the ambient temperature inside the furnace body and provide input for the subsequent inversion calculation of the equivalent emissivity. The thermocouple used here is a radiation shielded thermocouple.

[0078] In step one, the method of arranging the thermocouple on the middle runner is as follows: When preparing the shell mold module, a thermocouple is buried at a position near the inner wall of the bottom of the middle runner to monitor the temperature change of the molten metal and provide input for the subsequent inversion calculation of the convective heat transfer coefficient. The thermocouple used here is a fast response thermocouple.

[0079] In step two, the three-dimensional model of the shell mold module includes several blade shells, a module chassis, a middle runner, a runner, and a pouring cup. 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. The directional solidification process parameters include the molten metal temperature, the blade shell temperature, and the pulling speed.

[0080] In step two, the convective heat transfer coefficients of the tenons, blade bodies, and blade crowns in the blade shell and the preset temperature measurement area on the middle runner are inversely calculated. The inverse calculation equation is , where

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

[0082] ——The convective heat transfer flux of the preset temperature measurement area, W / m 2 , and data is extracted from the obtained dynamic simulation results;

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

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

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

[0086] ——The temperature change during a certain period from pouring, filling, pulling, directional solidification to cooling, K;

[0087] ——During the time of temperature change , the displacement of the shell mold module moving downward, m.

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

[0089] —— the equivalent emissivity of the preset temperature measurement region, dimensionless;

[0090] —— the basic emissivity of the material in the preset temperature measurement region, dimensionless;

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

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

[0093] —— the finite element simulation temperature of the preset temperature measurement region, K, and data is extracted from the obtained dynamic simulation results.

[0094] When the temperature change rate of the preset temperature measurement region exceeds 5 K / s, the equivalent emissivity needs to be corrected, and the correction formula is , where

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

[0096] —— the equivalent emissivity of the preset temperature measurement region before correction, dimensionless;

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

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

[0099] —— the temperature change during a certain period from pouring, filling, drawing, directional solidification to cooling, K;

[0100] —— the temperature change the time used, s.

[0101] In Step 4, when the comparison index is the temperature field, the key temperature measurement regions selected are the tenon, blade body, and blade crown of the blade shell and the baffle zone of the directional solidification furnace; when the comparison indices are the secondary dendrite arm spacing, grain orientation deviation angle, and porosity, the key temperature measurement regions selected are all the tenon, blade body, and blade crown of the blade shell.

[0102] In Step 5, when the comparison index is the temperature field, the finite element simulation temperature curve of the key temperature measurement area is compared with the 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 index is the secondary dendrite arm spacing, the finite element simulation value of the key temperature measurement area is compared with the value measured by the scanning electron microscope. When the relative error does not exceed 15%, the preset requirements are met.

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

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

[0106] In Step 6, the correction method for the convective heat transfer coefficient is as follows: a correction model is constructed based on an artificial neural network, and its architecture includes an input layer (temperature measurement points that do not meet the preset requirements, directional solidification process parameters), three hidden layers, and an output layer. The weighted mean square error is used as the loss function, and the adaptive optimization of the temperature sensitivity weight of the convective heat transfer coefficient is realized through a dynamic weight adjustment mechanism. Finally, the corrected convective heat transfer coefficient is output.

[0107] In Step 6, the correction method for the equivalent emissivity is as follows: several groups of candidate parameters for the equivalent emissivity are generated based on the Bayesian optimization algorithm, and the temperature field prediction errors corresponding to each group of candidate parameters for the equivalent emissivity are calculated respectively through numerical fitting or experimental comparison. Finally, the candidate parameter with the smallest temperature field prediction error is selected 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 not less than 1600 °C, a diameter of not more than 0.3 mm, and a response time of not more than 0.1 s; the thermocouples arranged on the directional solidification furnace are radiation shielded thermocouples, with a short-term temperature resistance of up to 1800 °C; the thermocouples arranged on the middle runner are fast response thermocouples, with a response time of not more than 0.3 s. The finite element simulation software used is ProCAST, and the statistical analysis software is SPSS. There is no special limitation on the version; the standardized boundary condition input format is XML or INP.

[0109] In this embodiment, one module unit and a corresponding furnace unit are selected to arrange thermocouples, and the specific arrangement positions are as Figure 2As shown in the figure, P1 in the figure 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 downsprue.

[0110] In this embodiment, the whole process of the directional solidification process successively includes processes such as pouring, filling, pulling, directional solidification, and cooling. The pouring and filling are combined into a pouring stage, and the pulling, directional solidification, and cooling are combined into a pulling stage. This embodiment mainly performs inverse calculation of the convective heat transfer coefficient and the equivalent emissivity for each temperature measurement area in the pulling stage, and the inverse calculation results are shown in Tables 1 and 2.

[0111] Table 1 Inverse calculation parameters and results of the convective heat transfer coefficient in the pulling stage

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

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

[0114] Table 2 Inverse calculation parameters and results of the equivalent emissivity in the pulling stage

[0115] Temperature measurement area Temperature T (K) <![CDATA[ε eff > Blade 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 Blade shroud 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 zone 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, calibrated by multi-furnace regression)

[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 < 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 successively the temperature field, secondary dendrite arm spacing, grain orientation deviation angle, and porosity. Among them, the finite element simulation results of the temperature field in the key temperature measurement areas (tenon, blade body, blade crown, and baffle zone) are compared with the measured results as Figure 3 shown. The root mean square error is calculated, and the root mean square error does not exceed 20 °C, meeting the preset requirements. The finite element simulation results of the secondary dendrite arm spacing in the key temperature measurement areas (tenon, blade body, and blade crown) are compared with the measured results as Figure 4As shown, the relative errors between the simulated values and the measured values by SEM in the three regions do not exceed 15%, meeting the preset requirements. The finite element simulation of the grain orientation in the key temperature measurement regions (dovetail and blade body) is as Figure 5 shown. The relative errors between the simulated values and the measured values by electron backscatter diffraction in the two regions do not exceed 8°, meeting the preset requirements. In addition, the relative error between the simulated value and the measured value by electron backscatter diffraction of the grain orientation in the shroud region also does not exceed 8°, meeting the preset requirements. The comparison between the finite element simulation results and the measured results of the porosity in the key temperature measurement region (shroud) is as Figure 6 shown. The coincidence degree of the porosity position and size is not less than 70%, meeting the preset requirements, and no porosity is generated in the dovetail and blade body regions.

[0121] It can be seen from the above verification that the comparison results of each comparison index in the key temperature measurement region all meet the preset requirements in turn, that is, the determination of the boundary conditions for the directional solidification finite element simulation is completed, and the convective heat transfer coefficient, equivalent emissivity and dynamic simulation results of each temperature measurement region are saved for the subsequent optimization of the directional solidification process.

[0122] The method for determining the boundary conditions of the directional solidification finite element simulation of the engine working blade in this embodiment has the following beneficial effects: (1) By arranging thermocouples in multiple regions, high-density data acquisition is realized, and the measured data is directly converted into boundary condition parameters through the inversion calculation of the measured data fusion, improving the data utilization rate. (2) Introducing the measured data on the directional solidification process site into the finite element simulation and inversely calculating the boundary conditions based on the measured data significantly improves the fitting degree between the finite element simulation results and the actual production conditions. (3) Conducting multi-dimensional comparison of measured data strengthens the verification basis of the finite element simulation. (4) Combining the finite element simulation to assist in adjusting the directional solidification process parameters is beneficial to reducing the production cycle and production cost, and is applicable to the optimization of the single crystal / columnar crystal blade casting process and the prediction of microstructure and defects. (5) Solving the problem of insufficient prediction accuracy caused by the mismatch of boundary condition setting in the directional solidification process of aero-engine turbine blades by traditional finite element simulation, realizing the high-fidelity prediction of the temperature field and microstructure during the directional solidification process, and providing core technical support for the high-performance manufacturing of aero-engine turbine blades.

[0123] Embodiment 2:

[0124] According to another preferred embodiment of the method for determining the boundary conditions of the directional solidification finite element simulation of the engine working blade of the present invention, its determination process, thermocouple arrangement, back-calculation of boundary conditions, technical principle, beneficial effects, etc. are basically the same as those in Embodiment 1, except that:

[0125] The dynamic simulation results of the selected key temperature measurement regions are compared with the measured results of the corresponding temperature measurement regions. The comparison indicators are, in sequence, the temperature field, secondary dendrite arm spacing, grain orientation deviation angle, and porosity. Among them, the root mean square error between the simulated result and the measured result of the temperature field in the baffle region exceeds 20 °C, not meeting the preset requirements. Therefore, it is necessary to correct the convective heat transfer coefficient and equivalent emissivity of this temperature measurement region.

[0126] The convective heat transfer coefficient is corrected using artificial neural network technology, and the corrected convective heat transfer coefficient is 605 W / m²·K. The equivalent emissivity is corrected using the Bayesian optimization algorithm, generating 20 groups of candidate parameters for the equivalent emissivity, as shown in Table 1. As can be seen from Table 3, the temperature field prediction error of the 16th group of candidate parameters is the smallest, at 4.2%. Therefore, this group of candidate parameters is selected as the corrected equivalent emissivity.

[0127] Table 3 Candidate parameters of 20 groups of equivalent emissivity generated by Bayesian optimization

[0128] Number Candidate parameters for the equivalent emissivity of the baffle zone Objective function value (prediction error of the 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 are correspondingly substituted for the convective heat transfer coefficient and equivalent emissivity obtained by inverse calculation, and then the simulation and comparison verification are carried out again. After re-verification, the comparison results of each comparison indicator in the key temperature measurement region all meet the preset requirements in sequence, that is, the determination of the boundary conditions for the directional solidification finite element simulation is completed. At the same time, the convective heat transfer coefficient, equivalent emissivity, and dynamic simulation results of each temperature measurement region are saved for the subsequent optimization of the directional solidification process.

[0130] Special note: Many parameters are involved in the technical solution of the present invention. The synergistic effects between various parameters need to be comprehensively considered to obtain the beneficial effects and significant progress of the present invention. Moreover, the value ranges of each parameter in the technical solution are obtained through a large number of experiments. For each parameter and the mutual combination of various parameters, the inventor has recorded a large amount of experimental data. Due to space limitations, the specific experimental data are not disclosed here.

[0131] It is not difficult for those skilled in the art to understand that the present invention includes any combination of the invention content and specific implementation parts of the present invention specification and the parts shown in the drawings. Due to space limitations and to make the specification concise, the various solutions formed by these combinations are not described one by one. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for determining boundary conditions of a finite element simulation of directionally solidified engine working blades, characterized in that: The measurement method includes the following steps in sequence: Step 1: At the site of the single crystal solidification process of the working blade, thermocouples are arranged on the blade shell mold, the single crystal solidification furnace, and the downsprue according to the preset temperature measurement areas, and the temperature change data of each temperature measurement area during the whole process of pouring, filling, drawing, single crystal solidification, and cooling are collected through the thermocouples respectively; Step 2: Use finite element simulation software to establish a three-dimensional model of the shell mold module and the single crystal solidification furnace, set the material parameters of each component in the shell mold module and the single crystal solidification process parameters, and then perform dynamic simulation to obtain the dynamic simulation results; according to the obtained dynamic simulation results, and combining with the temperature change data of each temperature measurement area collected on site, the convective heat transfer coefficient and equivalent emissivity of each temperature measurement area are inversely calculated respectively; Step 3: Use statistical analysis software to generate a dynamic three-dimensional interpolation table of the convective heat transfer coefficients of each temperature measurement area obtained by inverse calculation according to the single crystal solidification time axis, the spatial position of the blade shell mold, and the temperature measured by the thermocouple, and convert the dynamic three-dimensional interpolation table into a standardized boundary condition input format and input it into the finite element model. At the same time, the equivalent emissivities of each temperature measurement area obtained by inverse calculation are also converted into a standardized boundary condition input format and input into the finite element model, and then dynamic simulation is performed to obtain the dynamic simulation results; Step 4: Select the dynamic simulation results of the key temperature measurement areas and compare them with the measured results of the corresponding temperature measurement areas. The comparison indexes are the temperature field, secondary dendrite arm spacing, grain orientation deviation angle, and porosity in sequence; Step 5: When the comparison results of each comparison index of each selected key temperature measurement area all meet the preset requirements in sequence, the determination of the finite element simulation boundary conditions for single crystal solidification is completed, and the convective heat transfer coefficient, equivalent emissivity, and dynamic simulation results of each temperature measurement area are saved for the subsequent optimization of the single crystal solidification process; Otherwise, go to the next step to correct the finite element simulation boundary conditions for single crystal solidification; Step 6: When the comparison result of a certain comparison index of a certain selected key temperature measurement area does not meet the preset requirements, the convective heat transfer coefficient and equivalent emissivity of this temperature measurement area need to be corrected, and the corrected convective heat transfer coefficient and equivalent emissivity are correspondingly replaced with the convective heat transfer coefficient and equivalent emissivity obtained by inverse calculation; Step 7: Repeat the operations in Step 3 to Step 6 until the comparison results of each comparison index of each selected key temperature measurement area all meet the preset requirements in sequence, that is, the determination of the finite element simulation boundary conditions for single crystal solidification is completed.

2. The method for determining the boundary conditions of the directional solidification finite element simulation of the engine working blade according to claim 1, wherein: In Step 1, the method of arranging thermocouples on the blade shell mold is as follows: First, evenly divide the shell mold module into four module units. Select one blade shell mold in each module unit to arrange thermocouples. The included angle between two adjacent blade shell molds among the four selected blade shell molds is 90°. Then, arrange thermocouples at the tenon, blade body, and blade crown parts on the back side of the blade in each selected blade shell mold. The thermocouples at the tenon, blade body, and blade crown parts in each blade shell mold are arranged along the blade axis direction in the vertical direction. The thermocouples at the tenon, blade body, and blade crown parts in the four blade shell molds are on the same horizontal plane in the horizontal direction. When preparing the blade shell mold, bury the thermocouples at positions close to the inner wall of the blade shell mold to monitor the temperature changes of the inner wall of the blade shell mold and the molten metal, providing input for the subsequent inversion calculation of the convective heat transfer coefficient and the equivalent emissivity. The thermocouples used here are micro-thermocouples.

3. The method for determining the boundary conditions of the directional solidification finite element simulation of the engine working blade according to claim 2, wherein: In Step 1, the method of arranging thermocouples on the directional solidification furnace is as follows: First, evenly divide the directional solidification furnace into four furnace body units, and the four furnace body units correspond one-to-one with the four module units. Then, arrange thermocouples at the hot zone, baffle zone, and cold zone parts in each furnace body unit. The thermocouples at the hot zone, baffle zone, and cold zone parts in each furnace body unit are arranged along the furnace body axis direction in the vertical direction. The thermocouples at the hot zone, baffle zone, and cold zone parts in the four furnace body units are on the same horizontal plane in the horizontal direction. Arrange thermocouples on the directional solidification furnace to monitor the ambient temperature inside the furnace body, providing input for the subsequent inversion calculation of the equivalent emissivity. The thermocouples used here are radiation-shielded thermocouples.

4. The method for determining the boundary conditions of the directional solidification finite element simulation of the engine working blade according to claim 3, characterized in that: In Step 1, the method of arranging thermocouples on the downsprue is as follows: When preparing the shell mold module, bury a thermocouple at a position close to the inner wall of the bottom of the downsprue to monitor the temperature change of the molten metal, providing input for the subsequent inversion calculation of the convective heat transfer coefficient. The thermocouples used here are fast-response thermocouples.

5. The method for determining the boundary conditions of the finite element simulation of the directionally solidified engine working blade according to claim 4, characterized in that: In Step 2, the three-dimensional model of the shell mold module includes several blade shell molds, a module chassis, a downsprue, a runner, and a pouring cup. 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. The directional solidification process parameters include molten metal temperature, blade shell mold temperature, and pulling speed.

6. The method for determining the boundary conditions of the directional solidification finite element simulation of the engine working blade according to claim 5, characterized in that: In step 2, inversely calculate the convective heat transfer coefficients of the tenons, blade bodies, blade crowns in the blade shell and the preset temperature measurement areas on the downsprue. The inverse calculation equation is , where ——Convective heat transfer coefficient of the preset temperature measurement area, W / (m 2 ·K); —— Convective heat transfer heat flux in the preset temperature measurement area, W / m 2 , extract data from the obtained dynamic simulation results; ——Temperature difference between the inner wall of the blade shell in the preset temperature measurement area and the molten metal, K; ——Thermal conductivity of the blade shell, W / (m·K); —— Temperature gradient on the inner wall of the blade shell in the preset temperature measurement area, K / m; —— Temperature change during a certain period in the whole process from pouring, filling, drawing, directional solidification to cooling, K; —— the displacement of the shell mold module moving downward during the time of temperature change, m. ​ 7. The method for determining the boundary conditions of the directional solidification finite element simulation of the engine working blade according to claim 6, wherein: 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 on the hot zone, baffle zone and cold zone in the directional solidification furnace is inversely calculated, and the inverse calculation equation is , where —— Equivalent emissivity of the preset temperature measurement area, dimensionless; ——Base emissivity of the preset temperature measurement area material, dimensionless; ——Temperature sensitivity coefficient of the material in the preset temperature measurement area, K⁻¹; ——Measured temperature of the preset temperature measurement area, K; ——The finite element simulated temperature of the preset temperature measurement area, K, extracting data from the obtained dynamic simulation results; When the temperature change rate of the preset temperature measurement area exceeds 5K / s, it is necessary to correct the equivalent emissivity. The correction formula is , where —— Equivalent emissivity after correction of the preset temperature measurement area, dimensionless; ——Equivalent emissivity before correction of the preset temperature measurement area, dimensionless; —— Activation rate compensation factor, s / K; —— Rate of temperature change in the preset temperature measurement area, K / s; —— Temperature change during a certain period in the whole process from pouring, filling, drawing, directional solidification to cooling, K; —— Time taken for temperature change Unit: s 8. The method for determining the boundary conditions of the directional solidification finite element simulation of the engine working blade according to claim 7, characterized in that: In Step 4, when the comparison index is the temperature field, the key temperature measurement regions selected are the tenon, blade body, and blade crown of the blade shell mold and the baffle zone of the directional solidification furnace. When the comparison indices are secondary dendrite arm spacing, grain orientation deviation angle, and porosity, the key temperature measurement regions selected are all the tenon, blade body, and blade crown of the blade shell mold.

9. The method for determining the boundary conditions of the directional solidification finite element simulation of the engine working blade according to claim 8, wherein: In Step 5, when the comparison index is the temperature field, compare the finite element simulation temperature curve of the key temperature measurement region with the thermocouple measured temperature data, and calculate the root mean square error. When the root mean square error does not exceed 20°C, it meets the preset requirements. When the comparison index is secondary dendrite arm spacing, compare the finite element simulation value of the key temperature measurement region with the scanning electron microscope measured value. When the relative error does not exceed 15%, it meets the preset requirements. When the comparison index is the grain orientation deviation angle, the finite element simulation values in the key temperature measurement area are compared with the measured values by the electron backscatter diffraction instrument. When the relative error does not exceed 8°, the preset requirements are met. When the comparison index is porosity, the finite element simulated porosity position and size in the key temperature measurement area are compared with the measured results by industrial CT. When the coincidence degree of the porosity position and size is not less than 70%, the preset requirements are met.

10. The method for determining the boundary conditions of the finite element simulation of the directionally solidified engine working blade according to claim 9, characterized in that: In step six, the correction method of the convective heat transfer coefficient is to construct 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, and the adaptive optimization of the temperature sensitivity weight of the convective heat transfer coefficient is realized through a dynamic weight adjustment mechanism, and finally the corrected convective heat transfer coefficient is output. 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 by numerical fitting or experimental comparison, and finally select the candidate parameter with the smallest temperature field prediction error as the corrected equivalent emissivity.

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